×

Historical review of internal state variable theory for inelasticity. (English) Zbl 1431.74031

Summary: A review of the development and the usages of internal state variable (ISV) theory are presented in this paper. The history of different developments leading up the formulation of the watershed paper by Coleman and Gurtin is discussed. Following the Coleman and Gurtin thermodynamics, different researchers have employed the ISV theory for dislocations, creep, continuum damage mechanics (CDM), unified-creep-plasticity (UCP), polymers, composites, biomaterials, particulate materials, multiphase and multiphysics materials, materials processing, multiscale modeling, integrating materials science (structure – property relations) into applied mechanics formulations, and design optimization under uncertainty for use in practical engineering applications.

MSC:

74C99 Plastic materials, materials of stress-rate and internal-variable type
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abe, N., 1997. Consolidation analysis of natural clay by flow surface history variable model. In: Proceedings of the International Offshore and Polar Engineering Conference, vol. 1. pp. 827 – 831.
[2] Abriata, J. P.; Laughlin, D. E.: The third law of thermodynamics and low temperature phase stability, Progress in materials science 49, 367-387 (2004)
[3] Al-Rub, Rashid K. Abu; Voyiadjis, George Z.; Bammann, Douglas J.: Athermodynamic based higher-order gradient theory for size dependent plasticity, International journal of solids and structures 44, No. 9, 2888-2923 (2007) · Zbl 1121.74011 · doi:10.1016/j.ijsolstr.2006.08.034
[4] Al-Rub, Rashid K. Abu: Interfacial gradient plasticity governs scale-dependent yield strength and strain hardening rates in micro/nano structured metals, International journal of plasticity 24, No. 8, 1277-1306 (2008) · Zbl 1388.74077
[5] Argon, A. S.: Materials science and engineering, Materials science and engineering 3, 24 (1968)
[6] Ahmed, H.; Wells, M. A.; Maijer, D. M.; Howes, B. J.; Van Der Winden, M. R.: Modelling of microstructure evolution during hot rolling of AA5083 using an internal state variable approach integrated into an FE model, Materials science and engineering A 390, No. 1 – 2, 278-290 (2005)
[7] Aktaa, J.; Schinke, B.: Influence of the hardening state on time dependent damage and its consideration in a unified damage model, Fatigue and fracture of engineering materials & structures 19, No. 9, 1143-1151 (1996)
[8] Allen, D.H., Beek, J.M., 1985. On the use of internal state variables in thermoviscoplastic constitutive equations. In: NASA Conference Publication. pp. 83 – 101.
[9] Allen, D. H.; Harris, C. E.; Groves, S. E.: Thermomechanical constitutive theory for elastic composites with distributed damage-I. Theoretical development, International journal of solids and structures 23, No. 9, 1301-1318 (1987) · Zbl 0634.73108 · doi:10.1016/0020-7683(87)90107-7
[10] Arruda, E. M.; Boyce, M. C.; Quintus-Bosz, H.: Effects of initial anisotropy on the finite strain deformation behavior of glassy polymers, International journal of plasticity 9, No. 7, 783-811 (1993)
[11] Arruda, E. M.; Boyce, M. C.: Evolution of plastic anisotropy in amorphous polymers during finite straining, International journal of plasticity 9, No. 6, 697-720 (1993)
[12] Anand, L.; Gurtin, M. E.: A theory of amorphous solids undergoing large deformations, with applications to polymeric glasses, International journal of solids and structures 40, 1465-1487 (2003) · Zbl 1045.74016 · doi:10.1016/S0020-7683(02)00651-0
[13] Anand, L.; Ames, N. M.: On modeling the micro-indentation response of an amorphous polymer, International journal of plasticity 22, No. 6, 1123-1170 (2006) · Zbl 1176.74038 · doi:10.1016/j.ijplas.2005.07.006
[14] Anand, L.; Ames, N. M.; Srivastava, V.; Chester, S.: A thermo-mechanically coupled theory for large deformations of amorphous polymers, part 1: formulation, International journal of plasticity 25, No. 8, 1474-1494 (2009) · Zbl 1165.74011 · doi:10.1016/j.ijplas.2008.11.004
[15] Argon, A. S.: A theory for the low temperature plastic deformation of glassy polymers, Philosophical magazine 28, 839-865 (1973)
[16] Ashby, M. F.: The deformation of plastically non-homogeneous alloys, Strengthening methods in crystals, 137-192 (1971)
[17] Ashby, M. F.: Physical modelling of materials problems, Materials science and technology 8, No. 2, 102-111 (1992)
[18] Astaf’ev, V. I.: Description of creep hardening by means of internal tensor variable, Mechanics of solids (English translation of izvestiya akademii nauk SSSR, mekhanika tverdogo tela) 22, No. 2, 128-135 (1987)
[19] Aubertin, M.; Gill, D. E.; Ladanyi, B.: Internal variable model for the creep of rocksalt, Rock mechanics and rock engineering 24, No. 2, 81-97 (1991)
[20] Aubertin, M.; Julien, M. R.; Servant, S.; Gill, D. E.: Rate-dependent model for the ductile behavior of salt rocks, Canadian geotechnical journal 36, No. 4, 660-674 (1999)
[21] Aubertin, M.; Yahya, O. M. L.; Julien, M.: Modeling mixed hardening of alkali halides with a modified version of an internal state variables, International journal of plasticity 15, No. 10, 1067-1088 (1999) · Zbl 0977.74504 · doi:10.1016/S0749-6419(99)00025-X
[22] Austin, R. A.; Mcdowell, D. L.; Benson, D. J.: Numerical simulation of shock wave propagation in spatially-resolved particle systems, Modelling and simulation in materials science and engineering 14, 537-561 (2006)
[23] Bammann, D.J., 1984. An internal variable model of viscoplasticity. In: Aifantis, E.C., Davison, L., (Eds.), Media with Microstructures and Wage Propagation. Pergamon Press. International Journal of Engineering Science, 8 – 10, 1041.
[24] Bammann, D. J.: Modeling temperature and strain rate dependent large of metals, Applied mechanics reviews 43, No. 5 (1990)
[25] Bammann, D. J.: A model of crystal plasticity containing a natural length scale, Materials science and engineering A, 406-410 (2001)
[26] Bammann, D. J.; Aifantis, E.: On the perfect lattice-dislocated state interaction, Mechanics of structured media (1981)
[27] Bammann, D. J.; Aifantis, E. C.: On a proposal for a continuum with microstructure, Acta mechanica 45, No. 1 – 2, 91-121 (1982) · Zbl 0523.73088 · doi:10.1007/BF01295573
[28] Bammann, D. J.; Aifantis, E. C.: A model for finite-deformation plasticity, Acta mechanica 69, 97-117 (1987) · Zbl 0627.73046 · doi:10.1007/BF01175716
[29] Bammann, D. J.; Aifantis, E. C.: A damage model for ductile metals, Nuclear engineering and design 116, 355-362 (1989)
[30] Bammann, D. J.; Dawson, P. R.: Modeling the initial state of a material and its effect on further deformation, Material parameter estimation for modern constitutive equations 43, 13-20 (1993)
[31] Bammann, D. J.; Johnson, G. C.: On the kinematics of finite-deformation plasticity, Acta mechanica 70, 1-13 (1987) · Zbl 0624.73047 · doi:10.1007/BF01174643
[32] Bammann, D. J.; Chiesa, M. L.; Mcdonald, A.; Kawahara, W. A.; Dike, J. J.; Revelli, V. D.: Prediction of ductile failure in metal structures, Failure criteria and analysis in dynamic response 107, 7-12 (1990)
[33] Bammann, D. J.; Chiesa, M. L.; Horstemeyer, M. F.; Weingarten, L. I.: Failure in ductile materials using finite element methods, Structural crashworthiness and failure (1993)
[34] Bammann, D. J.; Prantil, V. C.; Lathrop, J. F.: A plasticity model for materials undergoing phase transformations, Simulation of materials processing: theory, methods and applications. NUMIFORM 95, 219-224 (1995)
[35] Bauschinger, J., 1886. On the change of the elastic limit and strength of iron and steel, by drawing out, by heating and cooling, and by repetition of loading. In: Proceedings of Institution of Civil Engineers, vol. 463.
[36] Besson, J.: Damage of ductile materials deforming under multiple plastic or viscoplastic mechanisms, International journal of plasticity 25, 2204-2221 (2009)
[37] Besson, J.: Continuum models of ductile fracture: a review, International journal of damage mechanics 19, 2-52 (2010)
[38] Bhanderi, D. R.; Oden, J. J.: International journal of non-linear mechanics, International journal of non-linear mechanics 8, 261 (1973)
[39] Bilby, B. A.: Report of the conference on defects in crystalline solids, Physical society, 124 (1954) · Zbl 0056.23502
[40] Bilby, B. A.; Bullough, R.; Smith, E.: Proceedings of the royal society of London series A – mathematical and physical sciences, Proceedings of the royal society of London series A – mathematical and physical sciences 231, 263 (1955)
[41] Bilby, B. A.; Smith, E.: Proceedings of the royal society of London series A – mathematical and physical sciences, Proceedings of the royal society of London series A – mathematical and physical sciences 236 (1956)
[42] Bilby, B. A.; Bullough, R.; Gardener, L. R. T.; Smith, E.: Proceedings of the royal society of London series A – mathematical and physical sciences, Proceedings of the royal society of London series A – mathematical and physical sciences 244, 538 (1958)
[43] Bilby, B. A.: Continuous distribution of dislocations, Progress in solid mechanics 1, 331-398 (1960)
[44] Bishop, J. F. W.; Hill, R.: A theoretical derivation of the plastic properties of a polycrystalline face-centered metal, Philosophical magazine series 7, No. 42, 1298-1307 (1951) · Zbl 0044.45002
[45] Bo, Z.; Lagoudas, D. C.: Thermomechanical modeling of polycrystalline smas under cyclic loading, part I: Theoretical derivations, International journal of engineering science 37, No. 9, 1089 (1999) · Zbl 1210.74049 · doi:10.1016/S0020-7225(98)00113-X
[46] Bodner, S. R.; Partom, Y.: Constitutive equations for elastic – viscoplastic strain hardening materials, Journal of applied mechanics – transactions of the ASME, 11-12 (1975)
[47] Boyce, M.; Parks, D.; Argon, A. S.: Large inelastic deformation of glassy polymers, part 1: rate dependent constitutive model, Mechanics of materials 7, 15-33 (1988)
[48] Bridgman, P. W.: Proceedings of the American Academy of arts and sciences, Proceedings of the American Academy of arts and sciences 58, 163 (1923)
[49] Brown, S. B.; Kim, K. H.; Anand, L.: An internal variable constitutive model for hot working of metals, International journal of plasticity 5, 95 (1989) · Zbl 0695.73002 · doi:10.1016/0749-6419(89)90025-9
[50] Buckley, S. N.; Entwistle, K. M.: The bauschinger effect in super-pure aluminum single crystals and polycrystals, Acta metallurgica 4, 352-361 (1956)
[51] Burgers, J. M.: Some considerations on the fields of stress connected with dislocations in a regular crystal lattice I., Proceedings of konshat nederlands akdemie. Wetensch 42, 293 (1939) · Zbl 0026.03501
[52] Busso, E. P.: A continuum theory for dynamic recrystallization with microstructure-related length scales, International journal of plasticity 14, No. 4 – 5, 355-372 (1998) · Zbl 0942.74009 · doi:10.1016/S0749-6419(98)00008-4
[53] Cai, Z. Y.; Li, X. S.: Development of dilatancy theory and constitutive model of sand, Yantu gongcheng xuebao/chinese journal of geotechnical engineering 29, No. 8, 1122-1128 (2007)
[54] Cantournet, S.; Desmorat, R.; Besson, J.: Mullins effect and cyclic stress softening of filled elastomers by internal sliding and friction thermodynamics model, International journal of solids and structures 46, No. 11 – 12, 2255-2264 (2009) · Zbl 1217.74018 · doi:10.1016/j.ijsolstr.2008.12.025
[55] Carnot, S., 1824. Reflections on the motive power of fire and on machines fitted to develop that powder. Paris: Chez Bachelier, Libraire, Quai Des Augustins, No. 55.
[56] Chaboche, J. L.: Viscoplastic constitutive equations for the description of cyclic and anisotropic behaviour of metals, Bulletin de l’ academie polonaise des sciences, serie des science technique 25, No. 1, 33-42 (1977)
[57] Chaboche, J. L.: Continuous damage mechanics – a tool to describe phenomena before crack initiation, Nuclear engineering and design 64, 233-247 (1981)
[58] Chaboche, J. L.: On the constitutive equations of materials under monotonic or cyclic loadings, Recherche aérospatiale 5, 31-43 (1983)
[59] Chaboche, J. L.; Rousselier, G.: On the plastic and viscoplastic constitutive equations – part I: Rules developed with internal variable concept, Journal of pressure vessel technology – transactions of the ASME 105, 153-158 (1983)
[60] Chaboche, J. L.: Continuum damage mechanics: present state and future trends, International seminar on local approach of fracture (1986)
[61] Chaboche, J. L.: Continuum damage mechanics: part I – general concepts, Journal of applied mechanics 55, 59-64 (1988)
[62] Chaboche, J. L.: Continuum damage mechanics: part II – damage growth, crack initiation, and crack growth, Journal of applied mechanics 55, 65-72 (1988)
[63] Chaboche, J. L.: Constitutive equations for cyclic plasticity and cyclic viscoplasticity, International journal of plasticity 5, No. 3, 247 (1989) · Zbl 0695.73001 · doi:10.1016/0749-6419(89)90015-6
[64] Chaboche, J. L.; Freed, A. D.; Walker, K. P.: Viscoplastic theory with thermodynamic considerations, Acta mechanica 90, No. 1 – 4, 155-174 (1991) · Zbl 0749.73032 · doi:10.1007/BF01177406
[65] Chaboche, J. L.: Cyclic viscoplastic constitutive equations, part I: a thermodynamically consistent formulation, Journal of applied mechanics – transactions of the ASME 60, No. 4, 813-821 (1993) · Zbl 0816.73014
[66] Chen, X.: Coupled hygro-thermo-viscoelastic fracture theory, International journal of fracture 148, No. 1, 47-55 (2007) · Zbl 1264.74241
[67] Chuzhoy, L.; Devor, R. E.; Kapoor, S. F.; Bammann, D. J.: Microstructure level modeling of ductile iron machining, Journal of manufacturing science and engineering – transactions of the ASME 124, 162-169 (2002)
[68] Chuzhoy, L.; Devor, R. E.; Kapoor, S. G.; Beaudoin, A. J.; Bammann, D. J.: Machining simulation of ductile iron and its constituents. Part I: Estimation of material model parameters and their validation, ASME journal of manufacturing science and engineering 125, 181-191 (2003)
[69] Cimmelli, V. A.; Rogolino, P.: On the mathematical structure of thermodynamics with internal variables, Journal of non-equilibrium thermodynamics 26, No. 3, 231-242 (2001) · Zbl 0994.80002 · doi:10.1515/JNETDY.2001.016
[70] Cheng, H.H., Dusseault, M.B., 2002. Continuum damage theories and petroleum geomechanics. In: Proceedings of the SPE/ISRM Rock Mechanics in Petroleum Engineering Conference. pp. 362 – 367.
[71] Clausius, R., 1850. Über die bewegende Kraft der Wärme, Part I, Part II, Annalen der Physik 79, 368 – 397, 500 – 524. See English Translation: On the Moving Force of Heat, and the Laws regarding the Nature of Heat Itself Which are Deducible Therefrom. Philosophical Magazine. 2 (1851) 1 – 21, 102 – 119.
[72] Cocks, A. C. F.; Ashby, M. G.: Intergranular fracture during power-law creep under multiaxial stresses, Metal science, 395-402 (1980)
[73] Cocks, A. C. F.; Ponter, A. R. S.: Constitutive equations for plastic deformation of solids: part II. A composite model, European journal of mechanics – A/solids 10, No. 4, 351-369 (1991) · Zbl 0755.73041
[74] Coleman, B. D.; Noll, W.: Archive for rational mechanics and analysis, Archive for rational mechanics and analysis 4, 97-128 (1959)
[75] Coleman, B. D.; Gurtin, M. E.: Thermodynamics with internal state variables, Journal of chemical physics 47, 597 (1967)
[76] Collins, I. F.; Kelly, P. A.: A thermomechanical analysis of a family of soil models, Geotechnique 52, No. 7, 507-518 (2002)
[77] Cosserat, E., Cosserat, F., 1909. Théorie des corps déformables. Hermann et Fils, Paris. · JFM 40.0862.02
[78] Cosserat, E.; Cosserat, F.: Theorie des corps deformables, herman, pari, Bulletin of the American mathematical society 19, 242-246 (1913)
[79] De Pablo, J. J.; Curtin, W. A.: Multiscale modeling in advanced materials research: challenges, novel methods, and emerging applications, MRS bulletin 32, 905-909 (2007)
[80] Dillon, O. W.; Kratochvil, J.: Strain gradient theory of plasticity, International journal of solids and structures 6, No. 12, 1513-1533 (1970) · Zbl 0262.73036 · doi:10.1016/0020-7683(70)90061-2
[81] Dimaggio, F. L.; Sandler, I. S.: Material model for granular soils, Journal of the engineering mechanics division – ASCE 97, No. EM3, 935-950 (1971)
[82] Dorgan, R. J.; Voyiadjis, G. Z.: Nonlocal dislocation based plasticity incorporating gradients of hardening, Mechanics of materials 35, No. 8, 721-732 (2003)
[83] Dorris, J. F.; Nemat-Nasser, S.: A plasticity model for flow of granular materials under triaxial stress states, International journal of solids structures 18, No. 6, 497-531 (1980) · Zbl 0482.73027 · doi:10.1016/0020-7683(82)90066-X
[84] Drucker, D.C., 1949. In: Proceedings of Symposia in Applied Mathematics, vol. 1. p. 181. · Zbl 0036.39903
[85] Drucker, D. C.; Gibson, R. E.; Henkel, D. J.: Soil mechanics and work hardening theories of plasticity, Transactions of the American society of civil engineers 122, 338-346 (1957)
[86] Eckart, C.: Thermodynamics of irreversible processes, I. The simple fluid, Physical review A 58, 267 (1940) · Zbl 0026.28002
[87] Eckart, C.: Theory of elasticity and anelasticity, Physical review 73, 373 (1948) · Zbl 0032.22201
[88] Eggert, G. M.; Dawson, P. R.: On the use of internal variable constitutive equations in transient forming processes, International journal of mechanical sciences 29, No. 2, 95-113 (1987) · Zbl 0601.73042 · doi:10.1016/0020-7403(87)90045-2
[89] Emeriault, F.; Cambou, B.: Micromechanical modelling of anisotropic non-linear elasticity of granular medium, International journal of solids and structures 33, No. 18, 2591-2607 (1996) · Zbl 0924.73203 · doi:10.1016/0020-7683(95)00170-0
[90] Engelbrecht, J.; Vendelin, M.; Maugin, G. A.: Hierarchical internal variables reflecting microstructural properties: application to cardiac muscle contraction, Journal of non-equilibrium thermodynamics 25, No. 2, 119-130 (2000) · Zbl 0970.74046 · doi:10.1515/JNETDY.2000.008
[91] Eringen, A. C.: Mechanics of continua, (1967) · Zbl 0222.73001
[92] Eringen, A. E.: Theory of micropolar elasticity, Fracture – an advanced treatise 2, 621-693 (1968) · Zbl 0266.73004
[93] Fish, J.: Bridging the scales in nanoengineering and science, Journal of nanoparticle research 8, 577-594 (2006)
[94] Fleck, N. A.; Muller, G. M.; Ashby, M. F.; Hutchinson, J. W.: Strain gradient plasticity: theory and experiment, Acta materialia 42, 475-487 (1994)
[95] Fleck, N. A.: On the cold compaction of powders, Journal of the mechanics and physics of solids 43, No. 9, 1409-1431 (1995) · Zbl 0921.73125 · doi:10.1016/0022-5096(95)00039-L
[96] Foerch, R.; Besson, J.; Cailletaud, G.; Pilvin, P.: Polymorphic constitutive equations in finite element codes, Computer methods in applied mechanics and engineering 141, No. 3 – 4, 355-372 (1997) · Zbl 0893.73061 · doi:10.1016/S0045-7825(96)01111-5
[97] Follansbee, P.S., Kocks, U.F., Regazzoni, G., 1985. Mechanical Threshold of dynamically deformed copper and nitronic 40. In: International Conference on Mechanical and Physical Behaviour of Materials under Dynamic Loading, Paris, France, 2 September 1985.
[98] Follansbee, P. S.: Metallurgical applications of shock-wave and high-strain rate phenomena, , 451 (1986)
[99] Follansbee, P. S.; Kocks, U. F.: Acta metallurgica, Acta metallurgica 36, 81 (1988)
[100] Follansbee, P. S.; Huang, J. C.; Gray, G. T.: Low-temperature and high-strain-rate deformation of nickel and nickel – carbon alloys and analysis of the constitutive behavior according to an internal state variable model, Acta metallurgica 38, No. 7, 1241-1254 (1990)
[101] Follansbee, P. S.; Gray, G. T.: Dynamic deformation of shock prestrained copper, Materials science & engineering A: structural materials: properties, microstructure and processing 138, No. 1, 23-31 (1991)
[102] Fondrk, M. T.; Bahniuk, E. H.; Davy, D. T.: Damage model for nonlinear tensile behavior of cortical bone, Journal of biomechanical engineering, transactions of the ASME 121, No. 5, 533-541 (1999)
[103] Forest, S.: Micromorphic approach for gradient elasticity, viscoplasticity, and damage, Journal of engineering mechanics 135, No. 3, 117-131 (2009)
[104] Francaviglia, M.; Restuccia, L.; Rogolino, P.: Entropy production in polarizable bodies with internal variables, Journal of non-equilibrium thermodynamics 29, No. 3, 221-235 (2004) · Zbl 1111.80003 · doi:10.1515/JNETDY.2004.052
[105] Frank, F. C.: The influence of dislocations on crystal growth, Discussions of the Faraday society 5, 48 (1949) · Zbl 0033.24002
[106] Frank, F. C.: Crystal dislocations, elementary concepts and definitions, Philosophical magazine 42, 809 (1951) · Zbl 0043.23501
[107] Fu, Y. M.; Wang, Y.: Nonlinear dynamic responses of composite plates based on the damage model with internal state variables, Hunan daxue xuebao/journal of hunan university natural sciences 31, No. 6, 70-74 (2004)
[108] Fuschi, P.; Polizzotto, C.: Internal-variable constitutive model for rate-independent plasticity with hardening saturation surface, Acta mechanica 129, No. 1-2, 73-95 (1998) · Zbl 0926.74018 · doi:10.1007/BF01379651
[109] Garmestani, H.; Vaghar, M.; Hart, E. W.: A unified model for inelastic deformation of polycrystalline materials – application to transient behavior in cyclic loading and relaxation, International journal of plasticity 17, No. 10, 1367-1391 (2001) · Zbl 1055.74013 · doi:10.1016/S0749-6419(00)00089-9
[110] Gangalee, A.; Gurland, J.: On the fracture of silicon particles inaluminum – silicon alloys, Transactions of the metallurgical society of AIME 239, 269-272 (1967)
[111] Garofalo, F.: Transactions of the metallurgical society of AIME, Transactions of the metallurgical society of AIME 227, 351-356 (1963)
[112] Gearing, B. P.; Anand, L.: On modeling the deformation and fracture response of glassy polymers due to shear-yielding and crazing, International journal of solids and structures 41, No. 11-12, 3125-3150 (2004) · Zbl 1119.74574 · doi:10.1016/j.ijsolstr.2004.01.017
[113] Germain, P.; Nguyen, Q. S.; Suquet, P.: Continuum thermodynamics, Journal of applied mechanics – transactions of the ASME 50, 1010 (1983) · Zbl 0536.73004 · doi:10.1115/1.3167184
[114] Gibbs, J. W.: Graphical method in thermodynamics of fluids, Transactions of the connecticut Academy 1, 309-342 (1873) · JFM 05.0585.01
[115] Gibbs, J. W.: A method of geometrical representation of the thermodynamic properties of substances by means of surfaces, Transactoions of the connecticut Academy 2, 382-404 (1873) · JFM 05.0585.02
[116] Gilat, A.; Goldberg, R. K.; Roberts, G. D.: Strain rate sensitivity of epoxy resin in tensile and shear loading, Journal of aerospace engineering 20, No. 2, 75-89 (2007)
[117] Gillis, P. P.; Gilman, J. J.: Journal of applied physics, Journal of applied physics 36, 3370 (1965)
[118] Gilman, J.J., 1966. In: Proceedings of the 5th US – National Congress Applied Mechanics. ASME, New York. p. 385
[119] Gilman, J.J., 1968. In: Lindholm (Ed.), Symposium on the Mechanical Behavior of Materials under Dynamics Loads, San Antonio, TX, San Antonio, TX. Springer-Verlag, New York. · Zbl 0153.37701
[120] Gilman, J. J.: Micromechanics of flow in solids, (1969)
[121] Ghorbel, E.: A viscoplastic constitutive model for polymeric materials, International journal of plasticity 24, No. 11, 2032-2058 (2008) · Zbl 1148.74010 · doi:10.1016/j.ijplas.2008.01.003
[122] Green, A. E.; Rivlin, R. S.: The mechanics of nonlinear materials with memory, Archive for rational mechanics and analysis 1, 1-34 (1957) · Zbl 0079.17602 · doi:10.1007/BF00297992
[123] Green, A. E.; Naghdi, P. M.: A general theory of an elastic – plastic continuum, Archive for rational mechanics and analysis 18, 251 (1965) · Zbl 0133.17701 · doi:10.1007/BF00251666
[124] Griffith, .A.: Philosophical transactions of the royal society of London series A – mathematical and physical sciences, Philosophical transactions of the royal society of London series A – mathematical and physical sciences 221, 163-198 (1921)
[125] Guo, Y. B.; Wen, Q.; Horstemeyer, M. F.: An internal state variable plasticity-based approach to determine dynamic loading history effects on material property in manufacturing processes, International journal of mechanical sciences 47, 1423-1441 (2005) · Zbl 1192.74053 · doi:10.1016/j.ijmecsci.2005.04.015
[126] Guo, Y. B.; Wen, Q.; Woodbury, K. A.: Dynamic material behavior modeling using internal state variable plasticity and its application in hard machining simulations, Journal of manufacturing science and engineering, transactions of the ASME 128, No. 3, 749-759 (2006)
[127] Guo, Y.B., Anurag, S., 2008. Finite element modeling and simulation of micromachining random multiphase materials. Paper Presented at NAMRC. In: Tansactions of the North American Manufacturing Research Institution of SME, vol. 36. pp. 373 – 380.
[128] Gurson, A. L.: Continuum theory of ductile rupture by void nucleation and growth: part I – yield criteria and flow rules for porous ductile media, Journal of engineering materials and technology – transactions of the ASME 99, 1-15 (1977)
[129] Hahn, H. T.; Jaunzemis, W.: Dislocation theory of plasticity, International journal of mechanical sciences 11, No. 10, 1065 (1973) · Zbl 0272.73052 · doi:10.1016/0020-7225(73)90109-2
[130] Hall, E. O.: The deformation and ageing of mild steel: III discussion of results, Proceedings of the physical society of London section B 64, 747-753 (1951)
[131] Halphen, B.; Nguyen, Q. S.: Sur LES materiaux standards generalizes, Journal de mecanique 14, 39-63 (1975) · Zbl 0308.73017
[132] Hammi, Y.; Horstemeyer, M. F.; Bammann, D. J.: An anisotropic damage model for ductile metals, International journal of damage mechanics 12, No. 3, 245-262 (2003)
[133] Hammi, Y.; Bammann, D. J.; Horstemeyer, M. F.: Modeling of anisotropic damage for ductile materials in metal forming processes, International journal of damage mechanics 13, No. 2, 123-147 (2004)
[134] Harley, E. J.; Bammann, D. J.: Experimental study of internal variable evolution in SS304L, at multiple rates and temperatures, Journal of engineering materials and technology – transactions of the ASME 121, No. 2, 162-171 (1999)
[135] Hart, E. W.: Constitutive relations for the non-elastic deformation of metals, Journal of engineering materials and technology – transactions of the ASME 98, 193-202 (1976)
[136] Hart, E. W.: Micromechanical basis for constitutive equations with internal state variables, American society of mechanical engineers 4, 5 (1984)
[137] Hansen, A. C.; Brown, R. L.: Internal state variable approach to constitutive theories for granular materials with snow as an example, Mechanics of materials 7, No. 2, 109-119 (1988)
[138] Harris, C.; Allen, D. H.; Nottorf, E. W.: Predictions of Poisson’s ratio in cross-ply laminates containing matrix cracks and delaminations, Journal of composites technology & research 11, No. 2, 53-58 (1989)
[139] Helmholtz, H. V.: The conservation of force: A physical memoir, Selected writings of Hermann von Helmholtz (1971), 3-55 (1847)
[140] Hencky, H., 1925. Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen Nebenspannungen. In: Waltman Jr., J., (Eds.), Proceedings of the 1st International Congress on Applied Mechanics, Delft, Technische Boekhandel en Druckerij. pp. 312 – 317. · JFM 51.0651.03
[141] Henshall, G. A.; Miller, A. K.: Simplifications and improvements in unified constitutive equations for creep and plasticity. II. behavior and capabilities of the model., Acta metallurgica et materialia 38, No. 11, 2117-2128 (1990)
[142] Herrmann, G. A.: Thermodynamic theory of damage in elastic inorganic and organic solids, Archive of applied mechanics 77, No. 2-3, 123-133 (2007) · Zbl 1151.74337 · doi:10.1007/s00419-006-0045-5
[143] Hilinski, E. J.; Lewandowski, J. J.; Wang, P. T.: Densification and flow stress evolution constitutive model for powder based discontinuously reinforced aluminum materials, Aluminum and magnesium for automotive applications, 189-207 (1996)
[144] Hill, R.: A theory of the yielding and plastic flow of anisotropic metals, Proceedings of the royal society of London series A – mathematical and physical sciences 193, 281-297 (1948) · Zbl 0032.08805 · doi:10.1098/rspa.1948.0045
[145] Hill, R.: The mathematical theory of plasticity, (1950) · Zbl 0041.10802
[146] Horstemeyer, M.F., McDowell, D.L., 1995. Stress State and History Effects in Viscoplasticity at Finite Strain. American Society of Mechanical Engineers, Materials Division (Publication) MD, 69-1, ASME Materials Division. pp. 519 – 543.
[147] Horstemeyer, M.F., Revelli, V., 1996. Stress history dependent localization and failure using continuum damage mechanics concepts. In: McDowell, D.L., (Eds.), Application of Continuum Damage Mechanics to Fatigue and Fracture, STP1315, ASTM.
[148] Horstemeyer, M. F.; Gokhale, A. M.: A void nucleation model for ductile materials, International journal of solids and structures 36, 5029-5055 (1999) · Zbl 0941.74051 · doi:10.1016/S0020-7683(98)00239-X
[149] Horstemeyer, M. F.: A numerical parametric investigation of localization and forming limits, International journal of damage mechanics 9, 255-285 (2000)
[150] Horstemeyer, M. F.; Ramaswamy, S.: On factors affecting localization and void growth in ductile metals: a parametric study, International journal of damage mechanics 9, 6-28 (2000)
[151] Horstemeyer, M. F.; Matalanis, M. M.; Sieber, A. M.; Botos, M. L.: Micromechanical finite element calculations of temperature and void configuration effects on void growth and coalescence, International journal of plasticity, 16 (2000) · Zbl 0969.74596 · doi:10.1016/S0749-6419(99)00076-5
[152] Horstemeyer, M. F.: Numerical parametric investigation of localization and forming limits, International journal of damage mechanics 9, No. 3, 255-285 (2000)
[153] Horstemeyer, M. F.; Lathrop, J.; Gokhale, A. M.; Dighe, M.: Modeling stress state dependent damage evolution in a cast al – si – mg aluminum alloy, Theoretical and applied fracture mechanics, 3331-3347 (2000)
[154] Horstemeyer, M. F.; Osborne, R.; Penrod, D.: Microstructure – property analysis and optimization of a control arm, American foundary society – AFS transactions 02-036, 297-314 (2002)
[155] Horstemeyer, M. F.; Baskes, M. I.; Prantil, V. C.; Philliber, J.; Vonderheide, S.: A multiscale analysis of fixed-end simple shear using molecular dynamics, crystal plasticity, and a macroscopic internal state variable theory, Modelling and simulation in materials science and engineering 11, No. 3, 265-286 (2003)
[156] Horstemeyer, M. F.; Wang, P.: Cradle-to-grave simulation-based design incorporating multiscale microstructure – property modeling: reinvigorating design with science, Journal of computer-aided materials design 10, 13-34 (2003)
[157] Horstemeyer, M. F.; Negrete, M.; Ramaswamy, S.: Using a micromechanical finite element parametric study to motivate a phenomenological macroscale model for void/crack nucleation in aluminum with a hard second phase, Mechanics of materials 35, 675-687 (2003)
[158] Hughes, D.: Microstructure and flow stress of deformed polycrystalline metals, Acta metallurgica 27, 969-974 (1991)
[159] Hughes, D. A.: Microstructure and flow stress of deformed polycrystalline metals, Scripta metallurgica 27, 969-974 (1992)
[160] Johnston, W. G.; Gilman, J. J.: Journal of applied physics, Journal of applied physics 30, 189 (1959)
[161] Jones, Wendell B., Rohde, R.W., Swearengen, J.C., Bammann, Douglas J., 1982. Internal State Variables For Viscoplastic Models – How Many/What Kind. Sandia Report SAND82-1955A. Sandia National Laboratories, Albuquerque, NM, 1982.
[162] Jones, M. K.; Horstemeyer, M. F.; Belvin, A. D.: A multiscale analysis of void coalescence in nickel, Journal of engineering materials and technology 129, 94-104 (2007)
[163] Joule, J. P.: Philosophical magazine, Philosophical magazine 23, 263 (1843)
[164] Juhasz, L.; Andrae, H.; Hesebeck, O.: Simulation of the thermomechanical behavior of shape memory alloys under multi-axial non-proportional loading, Proceedings of SPIE – the international society for optical engineering 3992, 484-495 (2000)
[165] Kachanov, L.M., 1958. Rupture time under creep conditions. Izvestia Akademii Nauk SSSR, Otdelenie Tekhnicheskich Nauk 8, 26 – 31 (in Russian).
[166] Kanagawa, Y.; Murakami, S.; Liu, Y.; Bai, Q.; Tanaka, K.: Description of internal damage in FRP laminates by continuum damage mechanics, Zairyo/journal of the society of materials science, Japan 45, No. 2, 206-211 (1996)
[167] Karhausen, K. F.; Roters, F.: Development and application of constitutive equations for the multiple-stand hot rolling of al-alloys, Journal of materials processing technology 123, No. 1, 155-166 (2002)
[168] Kawai, M.: Constitutive model for coupled inelasticity and damage, Nippon kikai gakkai ronbunshu, A hen/transactions of the Japan society of mechanical engineers, part A 61, No. 592, 2684-2692 (1995)
[169] Kawai, M.; Morishita, M.: Damage-coupled constitutive model for metal matrix composites, Nippon kikai gakkai ronbunshu, A hen/transactions of the Japan society of mechanical engineers, part A 62, No. 597, 1180-1188 (1996)
[170] Kiefer, B.; Lagoudas, D. C.: Magnetic field-induced martensitic variant reorientation in magnetic shape memory alloys, Philosophical magazine 85, No. 33 – 35, 4289-4329 (2005)
[171] Kelly, J. M.; Gillis, P. P.: Journal of the franklin institute-engineering and applied mathematics, Journal of the franklin institute-engineering and applied mathematics 297, 59 (1974)
[172] Kelly, J. M.; Gillis, P. P.: Journal of applied physics, Journal of applied physics 45, 1091 (1974)
[173] Kestin, J.; Rice, J. R.: Paradoxes in the application of thermodynamics to strained rods, A critical review of thermodynamics (1970)
[174] Kim, J. H.; Semiatin, S. L.; Lee, C. S.: Constitutive analysis of the high-temperature deformation mechanisms of ti – 6Al – 4V and ti – 6.85Al – 1.6V alloys, Acta materialia (2004)
[175] Kocks, U. F.: The relation between polycrystal deformation and single-crystal deformation, Metallurgical transaction 1, 1121 (1970)
[176] Kohler, R.; Hofstetter, G.: A cap model for partially saturated soils, International journal for numerical and analytical methods in geomechanics 32, No. 8, 981-1004 (2008) · Zbl 1273.74256
[177] Koiter, W. T.: General theorems for elasto-plastic solids, Progress in solid mechanics, 165-221 (1960)
[178] Kondo, Y., 1952. Report on carnivorous snail experiment on Agiguan Island. Invertebrate Consultants Committee for Micronesia, Pacific Science Board, National Research Council, 50 pp. (mimeographed).
[179] Krajcinovic, D.; Foneska, G. U.: The continuum damage theory for brittle materials, Journal of applied mechanics 48, 809-824 (1981) · Zbl 0468.73124 · doi:10.1115/1.3157739
[180] Krajcinovic, D.: Constitutive equations for damaging materials, Journal of applied mechanics 50, 355-360 (1983) · Zbl 0518.73088 · doi:10.1115/1.3167044
[181] Krajcinovic, D.: Continuum damage mechanics, Applied mechanics reviews 37, 1-6 (1984)
[182] Kratochvil, J.; Dillon, O. W.: Journal of applied physics, Journal of applied physics 40, 3207 (1969)
[183] Kratochvil, J.; Deangellis, R. J.: Journal of applied physics, Journal of applied physics 42, 1097 (1971)
[184] Kratochvil, J.: Acta mechanica, Acta mechanica 16, 127 (1973)
[185] Krempl, E.: On the interaction of rate and history dependence in structural metals, Acta mechanica 22, No. 1 – 2, 53-90 (1975) · Zbl 0312.73011 · doi:10.1007/BF01170619
[186] Kröner, E.: Berechnusng der elastischen konstanten des vielkristalls aus den konstanten des einkristalls, Zeitschrift fur physik 151, 504-518 (1958)
[187] Kröner, E., 1960. How the internal state of a physically deformed body is to be described in a continuum theory. In: 4th International Congress on Rheology.
[188] Kröner, E.: Zur plastischen verformung des vielkristalls, Acta metallurgica 9, 155 (1961)
[189] Kröner, E.: Journal of mathematics and physics, Journal of mathematics and physics 42, 27 (1962)
[190] Kröner, E.: On the physical reality of torque stresses in continuum mechanics, International journal of engineering science 1, 261-278 (1963)
[191] Kröner, E., 1965. In: Lee (Ed.), Proceedings of the 4th International Congress on Rheology. Interscience, New York.
[192] Lacy, T. E.; Mcdowell, D. L.; Willice, P. A.; Talreja, R.: On representation of damage evolution in continuum damage mechanics, International journal of damage mechanics 6, 62-95 (1997)
[193] Laemmer, H.; Tsakmakis, C.: Discussion of coupled elastoplasticity and damage constitutive equations for small and finite deformations, International journal of plasticity 16, No. 5, 495-523 (2000) · Zbl 0976.74005 · doi:10.1016/S0749-6419(99)00074-1
[194] Lee, E. H.; Liu, D. T.: Finite strain elastic – plastic theory with application to plane-wave analysis, Finite strain elastic – plastic theory with application to plane-wave analysis 38, 391-408 (1967)
[195] Lee, H.; Bang, W. K.; Sung, H. J.; Chang, Y. W.: An internal variable approach to journal of applied physics the superplastic deformation of AZ31 magnesium alloy, JOM journal of the minerals metals and materials society 56, No. 11, 85 (2004)
[196] Leckie, F. A.; Onat, E. T.: Tensorial nature of damage measuring internal variables, , 140-155 (1981)
[197] Lemaitre, J.: How to use damage mechanics, Nuclear engineering and design 80, 233-245 (1984)
[198] Lemaitre, J.; Chaboche, J. L.: Mecanique des materizux solides, (1985)
[199] Lemaitre, J.: A continuous damage mechanics model for ductile fracture, Journal of engineering materials and technology 107, 83-89 (1985)
[200] Levy, M.: Memoire sur ies equations generates des mouvements intérieurs des corps solides ductiles au delà des limites ou 1’éIasticité pourrait LES ramener a leur premier état, Comptes rendus 70, 1323-1325 (1870) · JFM 02.0723.01
[201] Li, S.; Jiang, C.; Han, S.: Modeling of the characteristics of fiber-reinforced composite materials damaged by matrix-cracking, Composites science and technology 43, No. 2, 185-195 (1992)
[202] Li, X. S.; Dafalias, Y. F.: Dilatancy for cohesionless soils, Geotechnique 50, No. 4, 449-460 (2000)
[203] Li, X.; Cescotto, S.; Duxbury, P. G.: Mixed strain element method for pressure-dependent elastoplasticity at moderate finite strain, International journal for numerical methods in engineering 43, No. 1, 111-129 (1998) · Zbl 0939.74069 · doi:10.1002/(SICI)1097-0207(19980915)43:1<111::AID-NME337>3.0.CO;2-Y
[204] Lim, T. J.; Mcdowell, D. L.: Path dependence of shape memory alloys during cyclic loading, Journal of intelligent material systems and structures 6, No. 6, 816 (1995)
[205] Lim, T. J.; Mcdowell, D. L.: Mechanical behavior of a nimory alloys during cyclic loading. Journal of intelligent proportional and nonproportional loading, Journal of engineering materials and technology – transactions of the ASME 121, No. 1 (1999)
[206] Lim, T. J.; Mcdowell, D. L.: Cyclic thermomechanical behavior of a polycrystalline pseudoelastic shape memory alloy, Journal of the mechanics and physics of solids 50, No. 3, 651-676 (2002) · Zbl 1116.74401 · doi:10.1016/S0022-5096(01)00088-6
[207] Liu, Y.; Gall, K.; Dunn, M. L.; Greenberg, A. R.; Diani, J.: Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modeling:, International journal of plasticity 22, No. 2, 279-313 (2006) · Zbl 1330.74052
[208] Liu, W. K.; Karpov, E. G.; Park, H. S.: Nano mechanics and materials: theory, multiscale methods and applications, (2006)
[209] Lorentz, E.; Benallal, A.: Gradient constitutive relations: numerical aspects and application to gradient damage, Computer methods in applied mechanics and engineering 194, No. 50 – 52, 5191-5220 (2005) · Zbl 1092.74049 · doi:10.1016/j.cma.2004.12.016
[210] Lu, X.; Hangoud, S. V.: A nonequilibrium irreversible thermodynamics model for material damping, International journal of solids and structures 44, No. 10, 3278-3303 (2007) · Zbl 1121.74313 · doi:10.1016/j.ijsolstr.2006.09.021
[211] Lubliner, J.: International journal of non-linear mechanics, International journal of non-linear mechanics 7, 237 (1972) · Zbl 0265.73005
[212] Lubliner, J.: Acta mechanica, Acta mechanica 17, 109 (1973)
[213] Lubliner, J.: International journal of solids and structures, International journal of solids and structures 10, 313 (1974) · Zbl 0288.73029
[214] Lubliner, J.: Plasticity theory, (1990) · Zbl 0745.73006
[215] Luig, P.; Bruhns, O. T.: On the modeling of shape memory alloys using tensorial internal variables, Materials science and engineering A 481 – 482, No. 1 – 2C, 379-383 (2008)
[216] Lusk, M.T., Wang, W., Sun, X., Lee, Y.K., 2003. On the role of kinematics in constructing predictive models of austenite decomposition. In: Materials Science and Technology 2003 Meeting, A Symposium on the Thermodynamics, Kinetics, Characterizaion and Modeling of Austenite Formation and Decomposition, pp. 311 – 331.
[217] Malinan, N. N.; Khadjinsky, G. M.: Theory of creep with anisotropic hardening, International journal of mechanical sciences 14, 235 (1972) · Zbl 0244.73025 · doi:10.1016/0020-7403(72)90065-3
[218] Mandel, J.: Plasticite classique et viscoplasticite, (1971) · Zbl 0285.73018
[219] Mandel, J.: Equations constitutives et directeurs dans LES milieux plastiques et viscoplastiques, International journal of solids and structures 9, 725-740 (1973) · Zbl 0255.73004 · doi:10.1016/0020-7683(73)90120-0
[220] Maniatty, A. M.; Dawson, P. R.; Weber, G. G.: Eulerian elasto-viscoplastic formulation for steady-state forming processes, International journal of mechanical sciences 33, No. 5, 361-377 (1991) · Zbl 0755.73044 · doi:10.1016/0020-7403(91)90075-E
[221] Marchand, N. J.; Moosbrugger, J. C.: Critical evaluation and extension of internal state variables constitutive models nonlinear structural modeling for life predictions. Physical mechanisms and continuum theories., International journal of pressure vessels and piping 47, No. 1, 79-112 (1991)
[222] Marin, E. B.; Mcdowell, D. L.: Associative versus non-associative porous viscoplasticity based on internal state variable concepts, International journal of plasticity 12, No. 5, 629-669 (1996) · Zbl 0884.73021 · doi:10.1016/S0749-6419(96)00023-X
[223] De Sciarra, F. Marotti: Nonlocal and gradient rate plasticity, International journal of solids and structures 41, No. 26, 7329-7349 (2004) · Zbl 1076.74013 · doi:10.1016/j.ijsolstr.2004.05.026
[224] De Sciarra, F. Marotti: A general theory for nonlocal softening plasticity of integral-type, International journal of plasticity 24, No. 8, 1411-1439 (2008) · Zbl 1388.74018
[225] De Sciarra, F. Marotti: Novel variational formulations for nonlocal plasticity, International journal of plasticity 25, No. 2, 302-331 (2009) · Zbl 1159.74007 · doi:10.1016/j.ijplas.2008.02.002
[226] Maugin, G. A.: Thermomechanical equations of magnetic fluids, International journal of engineering science 31, No. 1, 27-39 (1993) · Zbl 0770.76070 · doi:10.1016/0020-7225(93)90062-Y
[227] Maugin, G. A.: Thermodynamics with internal variables. Part I. General concepts, Journal of non-equilibrium thermodynamics 19, No. 3, 217-249 (1994) · Zbl 0808.73006
[228] Maugin, G. A.: Thermomechanics of heterogeneous materials with weakly nonlocal microstructure, Periodica polytechnica, chemical engineering 41, No. 2, 163-173 (1997)
[229] Maugin, G. A.: On the thermomechanics of continuous media with diffusion and/or weak nonlocality, Archive of applied mechanics 75, No. 10-12, 723-738 (2006) · Zbl 1168.74305 · doi:10.1007/s00419-006-0062-4
[230] Maxwell, J. C.: On the dynamical evidence of molecular constitution of matter, Journal of the chemical society – London 28, 493-508 (1875)
[231] Mccartney, L. N.: Constitutive relations describing creep deformation for multiaxial time-dependent stress states, Journal of the mechanics and physics of solids 29, No. 1, 13-33 (1981) · Zbl 0453.73001 · doi:10.1016/0022-5096(81)90013-2
[232] Mcclintock, F. A.: A criterion for ductile fracture by the growth of holes, Journal of applied mechanics – transactions of the ASME 35, 363 (1968)
[233] Mcdowell, D. L.: An experimental study of the structure of constitutive equations for nonproportional cyclic plasticity, Journal of engineering materials and technology – transactions of the ASME 107, 307-315 (1985)
[234] Mcdowell, D. L.: A two surface model for transient nonproportional cyclic plasticity: part I – development of appropriate equations, Journal of applied mechanics – transactions of the ASME 52, 298-302 (1985) · Zbl 0571.73038 · doi:10.1115/1.3169044
[235] Mcdowell, D. L.: Multiaxial fatigue modeling based on microcrack propagation, American society of mechanical engineers, pressure vessels and piping division PVP 290, 69-83 (1994)
[236] Mcdowell, D. L.: Internal state variable theory, Handbook of materials modeling (2005)
[237] McMeeking, R.M., 1992. Constitutive Laws for Sintering and Pressing of Powders. American Society of Mechanical Engineers, Materials Division (Publication) MD, 37, Mechanics of Granular Materials and Powder Systems. pp. 51 – 61.
[238] Mecking, H.; Kocks, U. F.: Kinetics of flow and strain-hardening, Acta metallurgica 29, 1865-1875 (1981)
[239] Mehling, V., Tsakmakis, C., Gross, D., 2005. Fully Coupled 3-D Modelling of Ferroelectric Polycrystalline Material Behavior, Materials Research Society Symposium Proceedings, Coupled Nonlinear Phenomena: Modeling and Simulation for Smart, Ferroic, and Multiferroic Materials, vol. 881. pp. 101 – 106.
[240] Mehling, V.; Tsakmakis, C.; Gross, D.: Thermodynamical modeling of ferroelectric polycrystalline material behavior, WSEAS transactions on mathematics 5, No. 4, 429-434 (2006)
[241] Mehling, V.; Tsakmakis, C.; Gross, D.: Phenomenological model for the macroscopical material behavior of ferroelectric ceramics, Journal of the mechanics and physics of solids 55, No. 10, 2106-2141 (2007) · Zbl 1170.74021 · doi:10.1016/j.jmps.2007.03.008
[242] Militzer, M.; Poole, W. J.; Wells, M. A.: Microstructure engineering for continuous annealing of steels and aluminum alloys, Materials science forum 426 – 432, No. 5, 3783-3788 (2003)
[243] Miller, M. P.; Harley, E. J.; Bammann, D. J.: Reverse yield experiments and internal variable evolution in polycrystalline metals, International journal of plasticity 15, No. 1, 93-117 (1999) · Zbl 0988.74500 · doi:10.1016/S0749-6419(98)00046-1
[244] Mohite, P.M., Upadhyay, C.S., 2008. Static damage signatures for laminated composite plates. In: 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, vol. 3, 7 – 10 April 2008, Schaumburg, IL, USA, pp. 1602 – 1628.
[245] Moteff, J., 1980. Deformation induced microstructure changes in metals. In: Stouffer, D.C., (Ed.), Proceedings of a Workshop on a Continuum Mechanics Approach to Damage and Life Prediction, Carrollton, KY, 1980.
[246] Murakami, S., Ohno, N., 1981. A continuum theory of creep and creep damage. In: Proceedings of the 3rd IUTAM Symposium on Creep in Structures. Springer, Berlin. pp. 422 – 444.
[247] Murakami, A.: Notion of continuum damage mechanics and its application to anisotropic creep damage theory, Journal of engineering materials and technology 105, 99-105 (1983)
[248] Nabarro, F.: Mathematical theory of stationary dislocations, Advances in physics 1, 269 (1952) · Zbl 0046.44804
[249] Naghdi, P. M.: Stress – strain relations in plasticity and thermoplasticity, , 121-167 (1960)
[250] Narayanan, V., Lu, X., Hanagud, S., A domain evolution model for the ferroelastic hysteresis of piezoceramic materials. In: Proceedings of the ASME Aerospace Division – 2003, American Society of Mechanical Engineers, Aerospace Division (Publication) AD, vol. 68, pp. 181 – 187.
[251] Näser, B.; Kaliske, M.; Müller, R.: Material forces for inelastic models at large strains: application to fracture mechanics, Computational mechanics 40, No. 6, 10 (2007) · Zbl 1160.74003 · doi:10.1007/s00466-007-0159-9
[252] Needleman, A.: The analysis of localized plastic flow, Computer simulation in materials science, 537-561 (1996)
[253] Nemat-Nasser, S.; Shokooh, A.: On finite plastic flows of compressible materials with internal friction, International journal of solids structures 16, 495-514 (1980) · Zbl 0433.73091 · doi:10.1016/0020-7683(80)90002-5
[254] Neu, R. W.; Scott, D. T.; Woodmansee, M. W.: Measurement and modeling of back stress at intermediate to high homologous temperatures, International journal of plasticity 16, No. 3, 283-301 (2000) · Zbl 0948.74501 · doi:10.1016/S0749-6419(99)00055-8
[255] Obataya, Y.; Itoh, T.; Kato, T.: New development of the multiple strata plasticity model, JSME international journal, series A: solid mechanics and material engineering 44, No. 1, 64-70 (2001)
[256] Olson, G. B.: Systems design of hierarchically structured materials: advanced steels, Journal of computer-aided materials design 4, 143-156 (1998)
[257] Olson, G. B.: New age of design, Journal of computer-aided materials design 7, 143-144 (2000)
[258] Onat, E.T., 1991. Group theory and representation of microstructure and mechanical behavior of materials. In: Lowe, T.C., Rollett, A.D., Follensbee, P.S., Daehn, G.S. (Eds.), Modeling the Deformation of Crystalline Solids. The Minerals, Metals and Materials Society.
[259] Onsager, L.: Physical review, Physical review 37, 405-426 (1931)
[260] Onsager, L.: Reciprocal relations in irreversible processes, Physical review 38, 2265-2279 (1931) · Zbl 0004.18303
[261] Orowan, E.: Zur kristallplastizität I, Z. phys 89, 605-659 (1934)
[262] Orowan, E.: Causes and effects of internal stresses, In internal stresses and fatigue in metals (1958)
[263] Park, S. W.; Schapery, R. A.: Viscoelastic constitutive model for particulate composites with growing damage, International journal of solids and structures 34, No. 8, 931-947 (1997) · Zbl 0947.74511 · doi:10.1016/S0020-7683(96)00066-2
[264] Parks, D.M., Argon, A.S., Bagepalli, B., 1985. Large Elastic – Plastic Deformation of Glassy Polymers. Part 1: Constitutive modeling. MIT, Program in Polymer Science and Technology Report.
[265] Perzyna, P.; Wojno, W.: Archiwum mechaniki stosowanej, Archiwum mechaniki stosowanej 20, 499 (1968)
[266] Perzyna, P.: Internal state variable description of dynamic fracture of ductile solids, International journal of solids and structures 22, No. 7, 797-818 (1985)
[267] Petch, N. J.: The cleavage strength of polycrystals, Journal of the iron and steel institute 174, 25 (1953)
[268] Phillips, A.; Gray, G.: Experimental investigations of corners in the yield surface, Journal of basic engineering – transactions of the ASME 83, 275 (1961)
[269] Phillips, R.: Crystals, defects and microstructures: modeling across scales, (2001)
[270] Polyani, M. Z.: &Udblac;ber eine art gilterstorung die einen kristall plastisch machen konnte, Zeitschrift fur physik 89, 660-664 (1934)
[271] Polizzotto, C.; Borino, G.: Thermodynamics-based formulation of gradient-dependent plasticity, European journal of mechanics, A – solids 17, No. 5, 741-761 (1998) · Zbl 0937.74013 · doi:10.1016/S0997-7538(98)80003-X
[272] Potirniche, G. P.; Hearndon, J. L.; Horstemeyer, M. F.; Ling, X. W.: Lattice orientation effects on void growth and coalescence in fcc single crystals, International journal of plasticity 22, No. 5, 921-942 (2006) · Zbl 1177.74108 · doi:10.1016/j.ijplas.2005.06.003
[273] Potirniche, G. P.; Horstemeyer, M. F.; Wagner, G. J.; Gullett, P. M.: A molecular dynamics study of void growth and void coalescence in single crystal nickel, International journal of plasticity 22, No. 2, 257-278 (2006) · Zbl 02240061
[274] Potirniche, G. P.; Horstemeyer, M. F.: On the growth of nanoscale fatigue cracks, Philosophical magazine letters 86, No. 3, 185-193 (2006)
[275] Potirniche, G.P., Horstemeyer, M.F., Gullett, P.M., Jelinek, B., 2006d. Atomistic modeling of fatigue crack growth and dislocation structuring in FCC single crystals. Proceedings of the Royal Society of London Series A – Mathematical and Physical Sciences, 462, 3707 – 3731 · Zbl 1149.74306 · doi:10.1098/rspa.2006.1746
[276] Prager, W.: Applied physics, Applied physics 15, 64 (1945)
[277] Prandtl, L., Spannungsverteilung in plastischen Koerpern. In: Proceedings of the 1st International Congress on Applied Mechanics, Delft. pp. 43 – 54. · JFM 51.0649.02
[278] Rabotnov, Y. N.: On the equations of state of creep, Progress in applied mechanics (1963)
[279] Radayev, Y. N.: Thermodynamical model of anisotropic damage growth. Part I. Canonical damage state variables of continuum damage mechanics and thermodynamical functions of three-dimensional anisotropic damage state, Journal of non-equilibrium thermodynamics 21, 129-152 (1996) · Zbl 0864.73053 · doi:10.1515/jnet.1996.21.2.129
[280] Raeisinia, B.; Poole, W. J.; Wang, X.; Lloyd, D. J.: A model for predicting the yield stress of AA6111 after multistep heat treatments, Metallurgical and materials transactions A: physical metallurgy and materials science 37, No. 4, 1183-1190 (2006)
[281] Rahouadi, R.; Ganghoffer, J. F.; Cunat, C.: A thermodynamic approach with internal variables using Lagrange formalism. Part I: General framework, Mechanics research communications 30, No. 2, 109-117 (2003) · Zbl 1022.80001 · doi:10.1016/S0093-6413(02)00360-9
[282] Read, W. T.: Dislocations in crystals, (1953) · Zbl 0051.23003
[283] Ricci, S.; Brünig, M.: Numerical analysis of nonlocal anisotropic continuum damage, International journal of damage mechanics 16, No. 3, 283-299 (2007)
[284] Rice, J. R.: Journal of applied mechanics – transactions of the ASME, Journal of applied mechanics – transactions of the ASME 37, 728 (1970)
[285] Rice, J. R.: Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity, Journal of the mechanics and physics of solids 9, 433-455 (1971) · Zbl 0235.73002 · doi:10.1016/0022-5096(71)90010-X
[286] Rist, M. A.; Plumbridge, W. J.; Cooper, S.: Creep-constitutive behavior of sn-3.8Ag – 0.7Cu solder using an internal stress approach, Journal of electronic materials 35, No. 5, 1050-1058 (2006)
[287] Roberts-Austen, W. C.: On certain mechanical properties of metals considered in relation to the periodic law, Philosophical transactions of the royal society of London series A – mathematical and physical sciences 179, 339-349 (1888)
[288] Saint-Venant, B.: Memoire sur i’établissement des equations differentielles des mouvements intérieurs opérés dans LES corps solides ductiles au dela des limites 1’éIasticité pourrait LES ramener à leur premier état, Comptes rendus 70, 473-480 (1870) · JFM 02.0722.02
[289] Sanders, D. R.; Kim, Y. I.; Stubbs, N.: Nondestructive evaluation of damage in composite structures using modal parameters, Experimental mechanics 32, No. 3, 240-251 (1992)
[290] Santaoja, K.: Gradient theory from the thermomechanics point of view, Engineering fracture mechanics 71, No. 4-6, 557-566 (2004)
[291] Sawczuk, A.: On modelling of creep and damage at steady state of internal variables change, Bulletin of the Polish Academy of sciences: technical sciences 32, No. 5 – 6, 249-256 (1984) · Zbl 0556.73026
[292] Schapery, R. A.: Nonlinear viscoelastic and viscoplastic constitutive equations with growing damage, International journal of fracture 97, No. 1 – 4, 33-66 (1999)
[293] Schmid, E.: Ueber die schubverfestigung von einkristallen bei plasticher deformation, Zeitschrift fur physik 40, 54-74 (1926)
[294] Sellars, C. M.; Zhu, Q.: Microstructural modelling of aluminum alloys during thermomechanical processing, Materials science and engineering A: structural materials: properties, microstructure and processing 280, No. 1, 1-7 (2000)
[295] Sellars, C. M.; Abbod, M. F.; Zhu, Q.; Linkens, D. A.: Hybrid modelling methodology applied to microstructural evolution during hot deformation of aluminium alloys, Materials science forum 426 – 432, No. 1, 27-34 (2003)
[296] Shenoy, M.; Tjiptowidjojo, Y.; Mcdowell, D. L.: Microstructure-sensitive modeling of polycrystalline IN 100, International journal of plasticity 24, No. 10, 1694-1730 (2008) · Zbl 1207.74028 · doi:10.1016/j.ijplas.2008.01.001
[297] Shiau, Y.C., Fong, C.K., 1991. Validation of Two-Internal-State-Variable Constitutive Model for Processing of Purity Aluminum at Elevated Temperature. American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED, 124, Recent Developments in Non-Newtonian Flows and Industrial Applications. pp. 39 – 45.
[298] Solanki, K., Acar, E., Rais-Rohan, M., Eamon, C., Horstemeyer, M.F., 2007. Reliability-based structural optimization using a multiscale material model. In: Collection of Technical Papers – AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, vol. 8. pp. 7684 – 7702.
[299] Spearot, D. E.; Jacob, K. I.; Mcdowell, D. L.: Nonlocal separation constitutive laws for interfaces and their relation to nanoscale simulations, Mechanics of materials 36, No. 9, 825-847 (2004)
[300] Stone, D. S.: Scaling laws in dislocation creep, Acta metallurgica et materialia 39, No. 4, 599-608 (1991)
[301] Sunder, S. S.; Wu, M. S.: Multiaxial differential model of flow in orthotropic polycrystalline ice, Cold regions science and technology 16, No. 3, 223-235 (1989)
[302] Sunder, S. S.; Wu, M. S.: On the constitutive modeling of transient creep in polycrystalline ice, Cold regions science and technology 18, No. 3, 267-294 (1990)
[303] Swearengen, J. C.; Holbrook, J. H.: Internal variable models for rate-depedent plasticity: analysis of theory and experiment, International journal of structural mechanics and materials science 13, No. 2, 93-128 (1985)
[304] Talreja, R., 1987. Modeling of Damage Development in Composites Using Internal Variables Concepts. ASME Aerospace Division (Publication) AD, vol. 12, pp. 11 – 16.
[305] Talreja, R.: Mechanics of materials, Mechanics of materials 12, 165 (1991) · Zbl 0561.73090
[306] Talreja, R.: Am. soc. Mech. engn. Appl. mech. Div. AMD, Am. soc. Mech. engn. Appl. mech. Div. AMD 166, 89 (1993)
[307] Talreja, R., 1997. American Society of Mechanical Engineers, Materials Division, MD, 80, Composites of Functionally Graded Materials.
[308] Tanaka, K.; Nagaki, S.: Thermomechanical description of materials with internal variables in the process of phase transitions, Ingenieur archiv 51, No. 5, 287-299 (1982) · Zbl 0495.73098 · doi:10.1007/BF00536655
[309] Tanner, A. B.; Mcdowell, D. L.: Deformation, temperature and strain rate sequence experiments on OFHC cu, International journal of plasticity 15, No. 4, 375-399 (1999)
[310] Tanner, A. B.; Mcginty, R. D.; Mcdowell, D. L.: Modeling temperature and strain rate history effects in OFHC cu, International journal of plasticity 15, No. 6, 575-603 (1999) · Zbl 0986.74502 · doi:10.1016/S0749-6419(98)00062-X
[311] Taylor, G. I.: The mechanism of plastic deformation of crystals. Part I. Theoretical, Proceedings of the royal society of London series A – mathematical and physical sciences 145, No. 855, 362-387 (1934) · JFM 60.0712.02 · doi:10.1098/rspa.1934.0106
[312] Teodosiu, C., 1969. A Dynamic Theory of Dislocations and Its Application to the Theory of Elastic – Plastic Continuum, Fundamental Aspects of Dislocation Theory. NBS Special Publication 317, US Government Printing Office, Gaithersburg, MD. pp. 837 – 876.
[313] Teodosiu, C.; Sidoroff, F.: Finite theory of the elastoviscoplasticity of single crystals, International journal of engineering science 14, No. 8, 713 (1976) · Zbl 0346.73069 · doi:10.1016/0020-7225(76)90027-6
[314] Teodosiu, C.; Sidoroff, F.: Theory of the elastoviscoplasticity of single crystals, International journal of engineering science 14, No. 2, 165 (1976) · Zbl 0329.73037 · doi:10.1016/0020-7225(76)90085-9
[315] Thomson, W.: On the dynamical theory of heat, with numerical results deduced from mr.joule’s equivalent of a thermal unit and M. Regnault’s observations on steam, Mathematical and physical papers 1, 175-183 (1851)
[316] Tjiptowidjojo, Y.; Przybyla, C.; Shenoy, M.; Mcdowell, D. L.: Microstructure-sensitive notch root analysis for Dwell fatigue in ni-base superalloys, International journal of fatigue 31, No. 3, 515-525 (2009)
[317] To, A. C.; Liu, W. K.; Olson, G. B.; Belytschko, T.; Chen, W.: Materials integrity in microsystems: a framework for a petascale predictive-science based multiscale modeling and simulation system, Computational mechanics (2008) · Zbl 1421.74084
[318] Tresca, H.: Sur l’ecoulement des corps solids soumis a de fortes pression, Comptes rendus 59, 754 (1864)
[319] Valanis, K. C.: Journal of mathematics and physics, Journal of mathematics and physics 45, 197-212 (1966) · Zbl 0146.21503
[320] Von Mises, R.: Mechanik der festen koerper im plastisch deformablen zustant, Goettingen nachrichten mathematisch – physikalische klasse, 582-592 (1913) · JFM 44.0918.06
[321] Von Mises, R.: Mechanik der plastischen formanderung von kristallen, Zeitschrift fur angewandte Mathematik und mechanik 8, 161 (1928) · JFM 54.0877.01 · doi:10.1002/zamm.19280080302
[322] Voyiadjis, G. Z.; Kattan, P. I.: A plasticity-damage theory for large deformation of solids, part I: Theoretical formulation, International journal of engineering science 30, No. 9, 1089-1108 (1992) · Zbl 0756.73038 · doi:10.1016/0020-7225(92)90059-P
[323] Voyiadjis, G. Z.; Venson, A. R.; Kattan, P. I.: Experimental determination of damage parameters in uniaxially-loaded metal matrix composites using the overall approach, International journal of plasticity 11, No. 8, 895-926 (1995)
[324] Voyiadjis, G. Z.; Park, T.: Anisotropic damage for the characterization of the onset of macro – crack initiation in metals, International journal of damage mechanics 5, No. 1, 68-92 (1996)
[325] Voyiadjis, G. Z.; Kattan, P. I.: Advances in damage mechanics: metals and metal matrix composites, (1999) · Zbl 0936.74004
[326] Voyiadjis, G. Z.: Model of inelastic behavior coupled to damage, Handbook of materials behavior models, 814 (2001)
[327] Voyiadjis, G. Z.; Dorgan, R. J.: Framework using functional forms of hardening internal state variables in modeling elasto-plastic-damage behavior, International journal of plasticity 23, No. 10 – 11, 1826-1859 (2007) · Zbl 1139.74047 · doi:10.1016/j.ijplas.2007.03.012
[328] Voyiadjis, G. Z.; Deliktas, B.: Formulation of strain gradient plasticity with interface energy in a consistent thermodynamic framework, International journal of plasticity 25, No. 10, 1997-2024 (2009)
[329] Wang, P. T.: Evolution of matrix strength and porosity during hot deformation of aluminum metals, Recent advances in heat transfer and micro-structure modelling for metal processing 70 (1995)
[330] Wang, B.; Xiao, Z. M.: General constitutive equations of an ER suspension based on the internal variable theory, Applied mathematics and mechanics (English edition) 22, No. 2, 190-209 (2001) · Zbl 1143.76592 · doi:10.1023/A:1015536716651
[331] Webster, G. A.: Philosophical magazine, Philosophical magazine 14, 475 (1966)
[332] Webster, G. A.: Philosophical magazine, Philosophical magazine 14, 1303 (1966)
[333] Wei, C.; Dewoolkar, M. M.: Formulation of capillary hysteresis with internal state variables, Water resources research 42, No. 7, W07405 (2006)
[334] Wei, P. J.; Chen, J. K.: A viscoelastic constitutive model with nonlinear evolutionary internal variables, Acta mechanica 164, No. 3 – 4, 217-225 (2003) · Zbl 1064.74030 · doi:10.1007/s00707-002-1013-y
[335] Westergaard, H. M.: Theory of elasticity and plasticity, (1952) · Zbl 0048.42103
[336] Wooley, R. L.: The bauschinger effect in some face-centered and body centered cubic metals, Philosophical magazine series 7, No. 44, 597-618 (1953)
[337] Yang, Q.; Engblom, J. J.: Finite element based sub-laminate damage model for intraply cracking, Journal of reinforced plastics and composites 14, No. 3, 233-254 (1995)
[338] Yin, X.; Lee, S.; Chen, W.; Liu, W. K.; Horstemeyer, M. F.: Efficient random field uncertainty propagation in design using multiscale analysis, ASME journal of mechanical design 131, No. 2 (2009)
[339] Yin, X.; Chen, W.: A hierarchical statistical sensitivity analysis method for complex engineering systems, ASME journal of mechanical design 130, No. 7 (2008)
[340] Yoon, C.; Allen, D. H.: Damage dependent constitutive behavior and energy release rate for a cohesive zone in a thermoviscoelastic solid, International journal of fracture 96, No. 1, 55-74 (1999)
[341] Zarka, J.: Generalisation de la theorie du potentiel plastique multiple en viscoplasticite, Journal of the mechanics and physics of solids 20, 179 (1972) · Zbl 0243.73060 · doi:10.1016/0022-5096(72)90010-5
[342] Ziefle, M.; Nackenhorst, U.: An internal variable update procedure for the treatment of inelastic material behavior within an ALE-description of rolling contact, Applied mechanics and materials 9, 157-171 (2008) · Zbl 1161.74043
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.