The Extended Meshfree Method for Crack Analysis in Hyperelastic Bodies

The extended meshfree method is adopted herein for analyzing hyperelastic solids with an initial crack which are considered to be incompressible. This method is developed based on the extended radial point interpolation method (XRPIM), in which the Heaviside function and the asymptotic function are utilized to describe the displacement discontinuity along the crack line and the singularity of the stresses near the crack tip, respectively. Unlike mesh-based mesh methods, the proposed method does not require any mesh for the approximation. But instead, field nodes are generated within the problem domain and field variables are approximated via radial point interpolation method (RPIM) in local support domains. For the implementation, formulations of the proposed method are performed by using the total Lagrangian formulation. A number of numerical examples are given to investigate the accuracy and efficiency of the developed method by comparing our computed results with reference solutions derived from other approaches.