ON ERROR-ESTIMATES AND ADAPTIVITY IN ELASTOPLASTIC SOLIDS - APPLICATIONS TO THE NUMERICAL-SIMULATION OF STRAIN LOCALIZATION IN CLASSICAL AND COSSERAT CONTINUA

The a posteriori error estimates based on the post-processing approach are introduced for elastoplastic solids. The standard energy norm err or estimate established for linear elliptic problems is generalized he re to account for the presence of internal variables through the norm associated with the complementary free energy, This is known to repres ent a natural metric for the class of elastoplastic problems of evolut ion. In addition, the intrinsic dissipation functional is utilized as a basis for a complementary a posteriori error estimates. A posteriori error estimates and adaptive refinement techniques are applied to the finite element analysis of a strain localization problem. As a model problem, the constitutive equations describing a generalization of sta ndard J2-elastoplasticity within the Cosserat continuum are used to ov ercome serious limitations exhibited by classical continuum models in the post-instability region. The proposed a posteriori error estimates are appropriately modified to account for the Cosserat continuum mode l and linked with adaptive techniques in order to simulate strain loca lization problems. Superior behaviour of the Cosserat continuum model in comparison to the classical continuum model is demonstrated through the finite element simulation of the localization in a plane strain t ensile test for an elastoplastic softening material, resulting in conv ergent solutions with an h-refinement and almost uniform error distrib ution in all considered error norms.