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On the numerical implementation of inelastic time dependent and time independent, finite strain constitutive equations in structural mechanics. (English) Zbl 0504.73054


MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74C99 Plastic materials, materials of stress-rate and internal-variable type
74A20 Theory of constitutive functions in solid mechanics
74H99 Dynamical problems in solid mechanics
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74S99 Numerical and other methods in solid mechanics
74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids
74D10 Nonlinear constitutive equations for materials with memory

Software:

Nike2D
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Full Text: DOI

References:

[1] Truesdell, C.; Toupin, R. A., The classical field theories, (Encyclopedia of Physics, Vol. III (1960), Springer: Springer Berlin), 1
[2] Goel, R. P.; Malvern, L. E., Biaxial plastic simple waves with combined kinematic and isotropic hardening, J. Appl. Mech., 37, 1100-1106 (1970)
[3] Key, S. W.; Biffle, J. H.; Krieg, R. D., A study of the computational and theoretical differences of two finite strain elastic-plastic constitutive models, (Bathe, K. J.; Oden, J. T.; Wunderlich, W., Formulas and Computational Algorithms in Finite Element Analysis (1977), MIT: MIT Cambridge, MA)
[4] Bard, F. E., Some aspects of continuum physics used in fuel pin modeling, (Rept. No. HEDL-TME-74-30 (1975), Hanford Engineering Development Laboratory: Hanford Engineering Development Laboratory Richland, Washington, DC)
[5] Penny, R. K.; Marriott, D. L., Design for Creep (1971), McGraw-Hill: McGraw-Hill London
[6] Gittus, J. H., Creep, Viscoelasticity and Creep Fracture in Solids (1975), Wiley: Wiley New York
[7] T.J.R. Hughes and J. Winget, Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis, Internat. J. Numer. Meths. Engrg., to appear.; T.J.R. Hughes and J. Winget, Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis, Internat. J. Numer. Meths. Engrg., to appear. · Zbl 0463.73081
[8] Hallquist, J. O., NIKE2D: An implicit, finite deformation, finite-element code for analyzing the static and dynamic response of two-dimensional solids, (Rept. No. UCRL-52678 (1979), Lawrence Livermore National Laboratory: Lawrence Livermore National Laboratory Livermore, CA) · Zbl 0319.70015
[9] J.H. Biffle, JAC: A two dimensional finite element computer program which uses a nonlinear conjugate gradient technique for the solution of the nonlinear, quasistatic response of solids, Rept. Sandia National Laboratories, Albuquerque, NM, in preparation.; J.H. Biffle, JAC: A two dimensional finite element computer program which uses a nonlinear conjugate gradient technique for the solution of the nonlinear, quasistatic response of solids, Rept. Sandia National Laboratories, Albuquerque, NM, in preparation.
[10] Krieg, R. D.; Key, S. W., Implementation of a time independent plasticity theory into structural computer programs, (Stricklin, J. A.; Saczalski, K. J., Constitutive Equations in Viscoplasticity: Computational and Engineering Aspects. Constitutive Equations in Viscoplasticity: Computational and Engineering Aspects, AMD, Vol. 20 (1976), ASME: ASME New York), 125-138
[11] Krieg, R. D., An efficient numerical method for time independent plasticity, (Rept. No. SAND77-0943 (1977), Sandia National Laboratories: Sandia National Laboratories Albuquerque, NM) · Zbl 0262.70022
[12] Krieg, R. D.; Krieg, D. B., Accuracies of numerical solution methods for the elastic-perfectly plastic model (1977), J. Press: J. Press Vess. Piping
[13] Herrmann, L. R.; Peterson, F. E., A numerical procedure for viscoelastic stress analysis, (7th Meeting of ICRPG Mechanical Behavior Working Group. 7th Meeting of ICRPG Mechanical Behavior Working Group, CPIA Publication No. 177 (1968)), Orlando, FL
[14] R.D. Krieg, Numerical integration of creep equations in a finite element computer program, Rept. No. SAND80-1630, Sandia National Laboratories, Albuquerque, NM, in preparation.; R.D. Krieg, Numerical integration of creep equations in a finite element computer program, Rept. No. SAND80-1630, Sandia National Laboratories, Albuquerque, NM, in preparation. · Zbl 0555.73076
[15] Bushnell, D., A strategy for the solution of problems involving large deflections, plasticity and creep, Internat. J. Numer. Meths. Engrg., 11, 683-708 (1977) · Zbl 0354.73035
[16] Argyris, J. H.; Vaz, L. E.; Willam, K. J., Improved solution methods for inelastic rate problems, Comput. Meths. Appl. Mechs. Engrg., 16, 231-277 (1978) · Zbl 0405.73068
[17] Key, S. W., A finite element procedure for the large deformation dynamic response of axisymmetric solids, Comput. Meths. Appl. Mechs. Engrg., 4, 195-218 (1974) · Zbl 0284.73047
[18] Key, S. W.; Stone, C. M.; Krieg, R. D., Dynamic relaxation applied to the quasi-static, large deformation, inelastic response of solids, (Bathe, K. J.; Wunderlich, W., Proc. Europe-U.S. Symp. on Nonlinear Finite Element Analysis in Structural Mechanics. Proc. Europe-U.S. Symp. on Nonlinear Finite Element Analysis in Structural Mechanics, Bochum, West Germany (1980)) · Zbl 0471.73077
[19] Truesdell, C.; Noll, W., Non-linear field theories of mechanics, (Encyclopedia of Physics, Vol. III (1965), Springer: Springer Berlin), 3 · Zbl 0779.73004
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