Effective Constitutive Algorithms in Elastoplasticity and Elastoviscoplasticity

摘要

The basic constitutive relations for elastoplasticity and elastoviscoplasticityare shown to form a typical boundary layer-type stiff system of ordinary differential equations. Three numerical algorithms are discussed. The singular perturbation method, which yields accurate results for both the rate-independent and rate-dependent cases, where in the former case, the algorithm is explicit, whereas in the latter case, it is implicit and requires the solution of a nonlinear equation; therefore it is impractical as a constitutive algorithm for large-scale finite-element applications, where the constitutive algorithm is used a great number of times at each finite-element node. The new constitutive algorithm which is explicit and accurate for both the rate-independent and rate-dependent cases; the underlying mathematical feature of this new method is investigated, and it is shown that it can be classified as a simplified perturbation method; computable error bounds for this algorithm are obtained, and when the flow rule is given by the commonly used power law, it is shown that the errors are very small. A modified outer-solution method, which combines the above two techniques, and is simple, explicit, and accurate. (AN).