Time‐adaptive non‐linear finite‐element computations for thermo‐mechanically coupled analysis in inelastic dynamical systems

Abstract

In structural dynamics the initial boundary-value problem has to be solved in the space and time domain. The spatial discretization is done using finite elements yielding systems of differential equations of second-order. Incorporating inelastic material properties, thermo-mechanical coupling and particular Dirichlet boundary conditions essentially changes the underlying mathematical problem. The main goal is to provide higher-order time integration schemes using diagonally-implicit RungeKutta methods (DIRK) and the Generalized α-method consistently applied to the semi-discretized ODE-system comprising the semi-discretized equations of motion, the unsteady semi-discrete heat equation and constitutive equations of evolutionarytype. Furthermore, we want to show the applicability of time-adaptivity by embedded schemes so that step-sizes are chosen automatically. The inelastic constitutive equations are given by a thermo-viscoplasticity model of Perzyna/Chaboche-type with non-linear kinematic hardening.