On the solution of LCP in nonlocal problems

This paper deals with a certain class of nonlocal dissipative constitutive models, for which the canonical pointwise backward-Euler scheme cannot be employed for satisfying the loading-unloading conditions. It is shown that, in the presence of a nonlocal 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 Gaussian points of the f.e. discretized structure. In order to actually solve the LCP, the use of iterative algorithms is discussed with reference to a one-dimensional model of nonlocal quasi-brittle material.