Iterative LCP solvers for non-local loading-unloading conditions

This paper deals with the nite element analysis of a certain class of non-local dissipative constitutive models, where the canonical pointwise backward-Euler scheme cannot be employed for satisfying the loading-unloading conditions. In the presence of a non-local dissipation, the admissibility conditions in a point depend on the inelastic strain increment of the surrounding points and can be cast as a linear complementarity problem (LCP) involving all Gauss points of the process zone. In order to actually solve the LCP, the use of iterative algorithms that can be easily embodied into existing FE codes is discussed. The performance of the proposed algorithms is tested in 1D and 2D examples for both elastoplastic and damaging materials.