Adaptive analysis based on error estimation for nonlocal damage models

Abstract

An adaptive finite element strategy for nonlocal damage computations is presented. The proposed approach is based on the combination of a residual-type error estimator and quadrilateral h-remeshing. A distinctive feature of the error estimator is that it consists in solving simple local problems over elements and so-called patches. The paper focuses on how the nonlocality of the constitutive model should be accounted for when solving these local problems. It is shown that the nonlocal damage models must be slightly modified. The resulting adaptive strategy is illustrated by means of some numerical examples involving the single-edge notched beam test.