ABSTRACT
The formulations described here are implemented in the Abaqus finite-element system by way of the UMAT interface in Fortran77. In accordance with the convention provided there, in this routine, based on the current deformation gradient F and on the history data, the Cauchy stress tensor σ and the consistent module D with respect to the logarithmic deformation value ε = ln(v) of the left stretch tensor v are calculated in the current configuration and returned. Due to the nonlinearities in the constitutive law, the local solution of an equation system as an integration during the time interval [t,t + Δt] is necessary at the level of the UMAT interface, i.e. each integration point of any element formulation, see (Tsakmakis and Willuweit 2003). We perform this integration using an implicit Euler method, which, as is generally known, is not per se isochoric, see (Baaser 2004). For this reason, an additional constraint condition is included in this equation to obtain material incompressibility.
