Rate-independent elastoplasticity at finite strains and its numerical approximation

0464549 - ÚT 2017 RIV SG eng J - Článek v odborném periodiku
Mielke, A. - Roubíček, Tomáš
Rate-independent elastoplasticity at finite strains and its numerical approximation.
Mathematical Models and Methods in Applied Sciences. Roč. 26, č. 12 (2016), s. 2203-2236. ISSN 0218-2025. E-ISSN 1793-6314
Grant CEP: GA ČR GA14-15264S
Institucionální podpora: RVO:61388998
Klíčová slova: plasticity * quasistatic evolution * energetic solutions
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 2.860, rok: 2016
http://www.worldscientific.com/doi/abs/10.1142/S0218202516500512

Gradient plasticity at large strains with kinematic hardening is analyzed as quasistatic rate-independent evolution. The energy functional with a frame-indifferent polyconvex energy density and the dissipation is approximated numerically by finite elements and implicit time discretization, such that a computationally implementable scheme is obtained. The nonself-penetration as well as a possible frictionless unilateral contact is considered and approximated numerically by a suitable penalization method which keeps polyconvexity and simultaneously bypasses the Lavrentiev phenomenon. The main result concerns the convergence of the numerical scheme toward energetic solutions. In the case of incompressible plasticity and of nonsimple materials, where the energy depends on the second derivative of the deformation, we derive an explicit stability criterion for convergence relating the spatial discretization and the penalizations.
Trvalý link: http://hdl.handle.net/11104/0266072