A strong-form meshfree method for stress analysis of hyperelastic materials

Abstract

A strong-form based meshfree method for stress analysis of hyperelastic materials under large deformations is presented in this research. The non-linear elastic response of hyperelastic materials is modeled by the compressible Mooney–Rivlin strain energy function. Simple implementation and truly meshfree nature are some of the advantages of strong-form meshfree methods. In the presented meshfree formulation, second derivatives of the strain energy function with respect to the components of the deformation gradient tensor appear. These second derivatives are obtained analytically. Various plane stress and plane strain problems with different boundary conditions are considered. The effects of the value of the shape parameter, the number of the nodes in the support domain, and the total number of nodes on the performance of the method are investigated. Various techniques for applying boundary conditions such as the direct collocation method and the use of fictitious nodes are examined, and an alternative method is presented to apply boundary conditions in the proposed meshfree method.