An accurate numerical algorithm for stress integration with finite rotations. (English) Zbl 0614.73035

An accurate numerical algorithm for the integration of constitutive equations under both large deformations and/or large rotations is presented. The algorithm is based on the choice of the unrotated configuration as the frame of reference for all constitutive equations. The algorithms does not entail excessive computational time or memory expense. The accuracy of the method is demonstrated by several numerical examples.


74B20 Nonlinear elasticity
74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids
74S30 Other numerical methods in solid mechanics (MSC2010)
74A20 Theory of constitutive functions in solid mechanics


Full Text: DOI


[1] Truesdell, C., The elements of continuum mechanics, (1966), Springer New York · Zbl 0188.58803
[2] Dienes, J.K., On the analysis of rotation and stress rate in deforming bodies, Acta mech., 32, 217-232, (1979) · Zbl 0414.73005
[3] Johnson, G.C.; Bammann, D.J., A discussion of stress rates in finite deformation problems, Internat. J. solids and structures, 20, 8, 725-737, (1984) · Zbl 0546.73031
[4] Reed, K.W.; Atluri, S., Constitutive modeling and computational implementation for finite strain plasticity, Internat. J. plasticity, 1, 1, 63-88, (1985) · Zbl 0612.73050
[5] Nagtegaal, J.C.; De Jong, J.E., Some aspects of nonisotropic work-hardening in finite strain plasticity, (), 65
[6] Prager, W., Introduction to mechanics of continua, (1961), Ginn Boston · Zbl 0094.18602
[7] Taylor, L.M.; Flanagan, D.P., PRONTO 2D, A two-dimensional transient solid dynamics program, ()
[8] Hughes, T.J.R.; Winget, J., Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis, Internat.J. numer. meths. engrg., 15, 12, 1862-1867, (1980) · Zbl 0463.73081
[9] Simo, J.C.; Ortiz, M., A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations, Comput. meths. appl. mech. engrg., 49, 221-245, (1985) · Zbl 0566.73035
[10] Kim, S.J.; Oden, J.T., Finite element analysis of a class of problems in finite elastoplasticity based on the thermodynamical theory of materials of type N, Comput. meths. appl. mech. engrg., 53, 277-307, (1985) · Zbl 0552.73066
[11] Hughes, T.J.R., Theoretical foundation for large-scale computations of nonlinear material behavior, ()
[12] Rubinstein, R.; Atluri, S.N., Objectivity of incremental constitutive relations over finite time steps in computational finite deformation analyses, Comput. meths. appl. mech. engrg., 36, 277-290, (1983) · Zbl 0486.73081
[13] Reed, K.W.; Atluri, S.N., Analyses of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm, Comput. meths. appl. mech. engrg., 39, 245-295, (1983) · Zbl 0505.73045
[14] Atluri, S.N., Alternate stress and conjugate strain measures, and mixed variational formulations involving rigid rotations, for computational analyses of finitely deformed solid, with applications to plates and shells—I, Theory, comput. & structures, 18, 1, 93-116, (1984) · Zbl 0524.73043
[15] Atluri, S.N., On constitutive relations at finite strain: hypo-elasticity and elasto-plasticity with isotropic or kinematic hardening, Comput. meths. appl. mech. engrg., 137-171, (1984) · Zbl 0571.73001
[16] Goodbody, A.M., Cartesian tensors: with applications to mechanics, fluid mechanics and elasticity, (1982), Wiley New York · Zbl 0584.73005
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.