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On the numerical integration of three-invariant elastoplastic constitutive models. (English) Zbl 1036.74007
Summary: We investigate the performance of a numerical algorithm for the integration of isotropically hardening three-invariant elastoplastic constitutive models with convex yield surfaces. The algorithm is based on a spectral representation of stresses and strains for infinitesimal and finite deformation plasticity, and on a return mapping in principal stress directions. Smooth three-invariant representations of Mohr-Coulomb model, such as Lade-Duncan and Matsuoka-Nakai models, are implemented within the framework of the proposed algorithm. Among the specific features incorporated into the formulation are the hardening/softening responses and the tapering of the yield surfaces toward the hydrostatic axis with increasing confining pressure. Isoerror maps are generated to study the local accuracy of the numerical integration algorithm. Finally, a boundary value problem involving loading of a strip foundation on a soil is analyzed with and without finite deformation effects to investigate the performance of the integration algorithm in a full-scale nonlinear finite element simulation.

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74S05 Finite element methods applied to problems in solid mechanics
Full Text: DOI
[1] Jiang, J.; Pietruszczak, S., Convexity of yield loci for pressure sensitive materials, Comput. geotech., 5, 51-63, (1988)
[2] Lade, P.V.; Duncan, J.M., Elastoplastic stress – strain theory for cohesionless soil, J. geotech. engrg. div., ASCE, 101, 1037-1053, (1975)
[3] Matsuoka, H.; Nakai, T., Stress-deformation and strength characteristics of soil under three different principal stresses, Proc. JSCE, 232, 59-70, (1974)
[4] Argyris, J.H.; Faust, G.; Szimmat, J.; Warnke, E.P.; Willam, K.J., Recent developments in the finite element analysis of prestressed concrete reactor vessel, Nuclear engrg. des., 28, 42-75, (1974)
[5] K.J. Willam, E.P. Warnke, Constitutive model for the triaxial behaviour of concrete, ISMES Seminar on Concrete Structures Subjected to Triaxial Stresses, Bergamo, Italy, 1975, pp. 1-30
[6] Boswell, L.F.; Chen, Z., A general failure criterion for plain concrete, Int. J. solids struct., 23, 621-630, (1987) · Zbl 0609.73067
[7] Lade, P.V., Elasto-plastic stress – strain theory for cohesionless soil with curved yield surfaces, Int. J. solids struct., 13, 1019-1035, (1977) · Zbl 0365.73098
[8] Simo, J.C., Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory, Comput. meth. appl. mech. engrg., 99, 61-112, (1992) · Zbl 0764.73089
[9] Simo, J.C., Numerical analysis and simulation of plasticity, (), 183-499 · Zbl 0930.74001
[10] Koiter, W.T., Stress – strain relations, uniqueness and variational theorems for elastic – plastic materials with a singular yield surface, Quart. appl. math., 11, 350-354, (1953) · Zbl 0053.14003
[11] Ogden, R.W., Nonlinear elastic deformations, (1984), Chichester Ellis Horwood · Zbl 0541.73044
[12] Ting, T.C.T., Determination of C1/2, \bfc−1/2 and more general isotropic functions of \bfc, J. elasticity, 15, 319-323, (1985) · Zbl 0587.73002
[13] Morman, K.N., The generalized strain measure with application to non-homogeneous deformation in rubber-like solids, J. appl. mech., 53, 726-728, (1986)
[14] Miehe, C., Aspects of the formulation and finite element implementation of large strain isotropic elasticity, Int. J. numer. meth. engrg., 37, 1981-2004, (1994) · Zbl 0804.73067
[15] Miehe, C., Comparison of two algorithms for the computation of fourth-order isotropic tensor functions, Comput. struct., 66, 37-43, (1998) · Zbl 0929.74128
[16] Hughes, T.J.R., The finite element method, (1987), Prentice-Hall Englewood Cliffs, NJ
[17] Parlett, B.N., The symmetric eigenvalue problem, (1980), Prentice-Hall Englewood Cliffs, NJ · Zbl 0431.65016
[18] Smith, B.T.; Boyle, J.M.; Ikebe, Y.; Klema, V.C.; Moler, C.B., Matrix eigensystem routines: EISPACK guide, Lecture notes in computer science, vol. 6, (1976), Springer New York · Zbl 0325.65016
[19] Tamagnini, C.; Castellanza, R.; Nova, R., A generalized backward Euler algorithm for the numerical integration of an isotropic hardening elastoplastic model for mechanical and chemical degradation of bonded geomaterials, Int. J. numer. anal. meth. geomech., 26, 963-1004, (2002) · Zbl 1151.74427
[20] Simo, J.C.; Kennedy, J.G.; Govindjee, S., Non-smooth multisurface plasticity and viscoplasticity. loading/unloading conditions and numerical algorithms, Int. J. numer. meth. engrg., 26, 2161-2185, (1988) · Zbl 0661.73058
[21] Borja, R.I.; Wren, J.R., Discrete micromechanics of elastoplastic crystals, Int. J. numer. meth. engrg., 36, 3815-3840, (1993) · Zbl 0812.73055
[22] Borja, R.I., Plasticity modeling and computation, lecture notes, (2001), Stanford University California
[23] Sulem, J.; Vardoulakis, I.; Papamichos, E.; Oulahna, A.; Tronvoll, J., Elasto-plastic modelling of red wildmoor sandstone, Mech. cohesive-frictional mater., 4, 215-245, (1999)
[24] Ortiz, M.; Martin, J.B., Symmetry-preserving return mapping algorithms and incrementally extremal paths: a unification of concepts, Int. J. numer. meth. engrg., 28, 1839-1853, (1989) · Zbl 0704.73030
[25] Simo, J.C.; Hughes, T.J.R., Computational inelasticity, (1998), Springer New York · Zbl 0934.74003
[26] Lade, P.V.; Jakobsen, K.P., Incrementalization of a single hardening constitutive model for frictional materials, Int. J. numer. anal. meth. geomech., 26, 647-659, (2002) · Zbl 1011.74045
[27] Jakobsen, K.P.; Lade, P.V., Implementation algorithm for a single hardening constitutive model for geomaterials, Int. J. numer. anal. meth. geomech., 26, 661-681, (2002) · Zbl 1068.74089
[28] Borja, R.I.; Tamagnini, C., Cam-Clay plasticity. part III. extension of the infinitesimal model to include finite strains, Comput. meth. appl. mech. engrg., 155, 73-95, (1998) · Zbl 0959.74010
[29] Borja, R.I.; Lin, C.H.; Montáns, F.J., Cam-Clay plasticity. part IV. implicit integration of anisotroic bounding surface model with nonlinear hyperelasticity and ellipsoidal loading function, Comput. meth. appl. mech. engrg., 190, 3293-3323, (2001) · Zbl 1059.74038
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