AN EFFICIENT PARTIAL DOMAIN ENRICHED ELEMENT-FREE GALERKIN METHOD CRITERION FOR CRACKS IN NONCONVEX DOMAINS

In the present work, an efficient partial domain, intrinsic, enriched element-free Galerkin criterion has been extended to simulate the cracks lying in nonconvex domains. According to this criterion, only a part of the domain near the crack tip has been enriched. A linear ramp function has been used to avoid the sudden truncation of the enrichment effect. Some cases of cracks lying in convex as well as in nonconvex domains have been solved by both full and partial domain enrichment criteria under plane stress conditions. For the cracks lying in convex domain, the results obtained by full domain enrichment criterion are found in good agreement with those obtained by partial domain enrichment criterion, whereas for cracks lying in nonconvex domain, the results obtained by full domain enrichment criterion are found to be misleading. The partial domain enrichment not only accurately simulates the cracks in nonconvex domains but also reduces the computational cost of the method.

On homotopy conditions and the existence of multiple equilibria in finite elasticity

In this paper we study homotopy classes of deformations and their properties under weak convergence. As an application, we give an analytic proof (in two and three dimensions) of the existence of infinitely many local minimisers for a displacement boundary-value problem from finite elasticity, posed on a nonconvex domain, under the constitutive assumption of polyconvexity.