An isogeometric enriched quasi-convex meshfree formulation with application to material interface modeling

An isogeometric enriched quasi-convex meshfree method is presented with particular application to the material interface modeling. The current quasi-convexity of the meshfree approximation is achieved by introducing the mixed reproducing points of isogeometric B-spline basis functions into the meshfree consistency conditions. The resulting new meshfree shape functions have a similar form as the standard reproducing kernel meshfree shape functions, while the negative portions of the shape functions are significantly reduced. It is shown that this quasi-convex meshfree scheme yields better accuracy compared with the conventional meshfree method. Furthermore, in order to accurately model the material interface where the strain jump needs to be properly treated, a coupled isogeometric–meshfree approximation with a unified format of reproducing conditions is devised. The problem geometry and strain jump for the material interface are described by the isogeometric basis functions with repeated knots in the interface normal direction, while the rest regions are discretized by the isogeometric enriched quasi-convex meshfree approximation. This approach encompasses the geometry exactness of isogeometric analysis as well as the model refinement robustness of meshfree formulation. The effectiveness of the proposed method is thoroughly demonstrated by several typical numerical examples.