Variational integration in endochronic theory for small strain elastoplastodynamics

This paper presents a basic endochronic plasticity model with isotropic hardening for small strain theory according to Valanis. The key point of this model is a convolution integral over an intrinsic time scale involving past values of the strain measure and a so-called memory kernel which leads to a smooth evolution equation for the internal variable. For the temporal discretization of the underlying constitutive equations and the resulting evolution equation we use higher order accurate variational integrators (VI). The remarkable feature is the fact that we approximate the position vector in terms of velocities according to partitioned Runge-Kutta methods (pRK). As a representative model problem serves a quasistatic, uniaxial tensile testing as well as a dynamic, elastoplastic cantilever beam with a smooth plasticity model according to the Valanis framework. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)