An improved meshless method for finite deformation problem in compressible hyperelastic media

Hyperelastic materials are considered as special category of elastic solid materials because of their nonlinear complicated constitutive laws. Due to large strain state, the behaviour of such materials is often considered in finite deformation analysis. The nonlinear large deformation behavior of such materials is important. In this study, a novel meshless radial point interpolation method (RPIM) enhanced by Cartesian transformation method (CTM), an effective numerical integration, is presented for nonlinear behavior of hyperelastic media under finite deformation state with total Lagrange formulation. Unlike the mesh-based approaches, the meshless methods have shown their advantages in analysis of large deformation problems. The developed CTM-based RPIM is thus free from the need for background cells, which are often used for numerical integration in many conventional meshfree approaches. The developed meshfree method owns some desirable features of an effective technique in solving large deformation, which will be illustrated through the numerical experiments in which our computed results are validated against reference solutions derived from other approaches.