On stress resultant plasticity and viscoplasticity for metal plates

In this work we derive elastoplastic and elastoviscoplastic finite element formulations for stress resultant bending analysis of thin metal plates. The principle of maximum plastic dissipation is used to obtain the ingredients of the small strain stress resultant plate elastoplasticy with state variables describing general isotropic and linear kinematic hardening. The ingredients of the plate stress resultant elastoviscoplasticy are further obtained by using the penalty-like form of the principle of maximum plastic dissipation. Such an approach enables single framework for numerical implementation of both considered inelastic stress resultant plate material models. The implementation is based on the spectral decomposition algorithm. For spatial discretization we use simple and robust quadrilateral finite element. A set of numerical examples is presented to illustrate the approach and to discuss the accuracy of the stress resultant inelastic plate formulations.