A stiffly accurate Rosenbrock-type method of order 2 applied to FE-analyses in finite strain viscoelasticity

The numerical treatment of quasi-static problems in solid mechanics incorporating constitutive equations of evolutionary type is pursued using the method of vertical lines. The spatial discretization is carried out by means of the finite element method. This yields large systems of differential-algebraic equations. In this article a new stiffly accurate Rosenbrock-type method of second order is proposed, which is applied to this challenging test case, and comparisons to existing Rosenbrock-type and diagonally-implicit Runge–Kutta methods are carried out.