Higher order continuous approximation for the assessment of nonlocal-gradient based damage model

In this work we present an implicit nonlocal gradient damage model. A scalar damage variable which is a function of monotonically increasing function of history parameter is introduced to account for damage. The nonlocal model accounts for spatial interaction of neighboring material element at different length scales. The history parameter accounting for damage is obtained by considering nonlocal equivalent strains. To study the influence of nonlocal nature of approximation method on the proposed damage model, for numerical implementation, in a Galerkin framework, the influence of Cp − 1 and C0 continuous approximation schemes are explored. Cp − 1 approximations are achieved by using Bezier and B-spline basis functions. C0 approximations are achieved by using standard Lagrangian basis functions. From numerical examples, it is observed that Cp − 1 approximations are more nonlocal and results in better results than C0 approximations