Vol. 12, No. 1, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 4, 541–746
Issue 4, 541–572
Issue 3, 303–540
Issue 2, 157–302
Issue 1, 1–156

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 1559-3959 (online)
ISSN 1559-3959 (print)
 
Author index
To appear
 
Other MSP journals
Time-adaptive finite element simulations of dynamical problems for temperature-dependent materials

Matthias Grafenhorst, Joachim Rang and Stefan Hartmann

Vol. 12 (2017), No. 1, 57–91
Abstract

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