Key, Samuel W.; Krieg, Raymond D. On the numerical implementation of inelastic time dependent and time independent, finite strain constitutive equations in structural mechanics. (English) Zbl 0504.73054 Comput. Methods Appl. Mech. Eng. 33, 439-452 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 16 Documents 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 Keywords:incorporation of finite strain; inelastic material behavior; piecewise numerical construction of solutions in solid mechanics; elementary time dependent creep model; viscoelastic model; constitutive equations suitable for problems involving large deformations and finite strains; rate form; symmetric part of velocity gradient; stretching; co-rotational time derivative of Cauchy stress; current value of Cauchy stress from hereditary integral of materially invariant; current configuration selected for evaluation of equilibrium; process of strain incrementation; conversion of rotation rates based on spin into incremental orthogonal rotations Software:Nike2D PDFBibTeX XMLCite \textit{S. W. Key} and \textit{R. D. Krieg}, Comput. Methods Appl. Mech. Eng. 33, 439--452 (1982; Zbl 0504.73054) 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. 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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 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.