Adaptive FEM analysis of selected elastic–visco-plastic problems

Elastic–visco-plastic deformations modeled by the Bodner–Partom constitutive equations [S.R. Bodner, Y. Partom, Constitutive equations elastic viscoplastic strain-hardening materials, J. Appl. Mech. 42 (1975) 385–389] have been evaluated by the adaptive finite element method [J.M. Bass, J.T. Oden, Adaptive finite element methods for a class of evolution problems in viscoplasticity, Int. J. Engrg. Sci. 25 (623–653) (1987); L. Demkowicz, J.T. Oden, W. Rachowicz, O. Hardy, Toward a universal hp-adaptive finite element strategy. Part 1: Constrained approximation and data structure, Comput. Methods Appl. Mech. Engrg. 77 (1989) 79–112]. We use the explicit residual error estimate [I. Babuška, W.C. Rheinboldt, Error estimates for adaptive finite element computations, Int. J. Numer. Methods Engrg. 12 (1978) 1597–1615] supplemented with a special term accounting for the fact that the right hand side of the equations we use is only approximated since it depends on the inelastic strains which are computed only at the Gauss integration points. We also address the problems of adaptation strategy and the method of solution transfer to a new mesh. Results of recent tests confirm efficiency and robustness of the approach.