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Consistent tangent operators for rate-independent elastoplasticity

1985; Elsevier BV; Volume: 48; Issue: 1 Linguagem: Inglês

10.1016/0045-7825(85)90070-2

1879-2138

J.C. Simo, Robert L. Taylor,

Elasticity and Material Modeling

It is shown that for problems involving rate constitutive equations, such as rate-independent elastoplasticity, the notion of consistency between the tangent (stiffness) operator and the integration algorithm employed in the solution of the incremental problem, plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon Newton's method. Within the framework of closest-point-projection algorithms, a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed. To wit, associative J2 flow rules with general nonlinear kinematic and isotropic hardening rules, as well as a class of non-associative flow rules are considered. The resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of Newton's method, whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm, a procedure often employed, results in Newton type of algorithms with suboptimal rate of convergence. Application is made to a set of numerical examples which include saturation hardening laws of exponential type.