Computational inelasticity for loading conditions on multiple time scales by adaptive step size control

This contribution proposes an algorithm based on adaptive step size control for the simulation of inelastic solids and structures undergoing loading conditions at multiple time scales. Adaptivity in time integration of viscoelastic constitutive laws is directed by an refinement indicator which is constructed from integrators of different order, here a fourth-order Runge-Kutta (RK) method and linear Backward-Euler. The key novel aspect is that by virtue of an recently established consistency condition the higher order methods, p ≥ 2, can achieve their full nominal order without fulfilling the weak form of balance of linear momentum in the RK stages, but only at the end of the time interval. A representative numerical example illustrates the performance of the present adaptive method and underpins the computational savings compared with uniform time step sizes. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)