Time-adaptive finite element simulations of dynamical problems for temperature-dependent materials

Dynamical systems in finite elements yield systems of second-order differential equations. Incorporating inelastic material properties, thermomechanical coupling and particular Dirichlet boundary conditions essentially changes the underlying mathematical problem. In this respect, we investigate the behavior of a number of subproblems such as reaction force computation, high-order time-integration, time-adaptivity, etc., which yield (depending on the underlying problem) systems of differential-algebraic equations or a mixture of systems of second-order and first-order ordinary differential equations (especially if the constitutive equations are of evolutionary-type, as in the case of viscoelasticity and viscoplasticity). The main goals are to provide higher-order time integration schemes using diagonally implicit Runge–Kutta methods and the generalized- $α$ method so that they may be applied to the constitutive equations, and to apply time-adaptivity via embedded schemes so that step-sizes are chosen automatically. The constitutive equations are given by a thermoviscoplasticity model of Perzyna/Chaboche-type with nonlinear kinematic hardening.

Keywords

dynamics, DIRK methods, finite elements, generalized-alpha method, time-adaptivity, thermoviscoplasticity

Milestones

Received: 28 February 2016

Revised: 21 May 2016

Accepted: 13 June 2016

Published: 26 November 2016

Authors

Matthias Grafenhorst
Institute of Applied Mechanics Clausthal University of Technology Adolph-Roemer-straße 2A D-38678 Clausthal–Zellerfeld Germany

Joachim Rang
Institute of Scientific Computing Technical University Braunschweig Hans–Sommer–Str. 65 D-38106 Braunschweig Germany

Stefan Hartmann
Institute of Applied Mechanics Clausthal University of Technology Adolph–Roemer–Straße 2A D-38678 Clausthal–Zellerfeld Germany

Vol. 12, No. 1, 2017

Matthias Grafenhorst, Joachim Rang and Stefan Hartmann

Abstract

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Authors