Meshless Radial Point Interpolation Method for Hyperelastic Materials

Abstract

Hyperelastic materials are special types of material that tends to behavior elastically when they are subjected to very large strains. These materials show not only the nonlinear material behavior but also the large deformation and stress-strain relationship is derived from a strain energy density function. Hyperelastic materials are widely used in many applications such as biological tissues, polymeric foams, and moreover. Neo - Hookean is a material model for hyperelastic solid which contains only two material parameters: bulk modulus and shear modulus. In the field of numerical analysis, the radial point interpolation method (RPIM) is a well-known meshfree method based on Garlekin's weak form. With the property of “free of mesh”, the RPIM approach shows its advantage for large deformation problems. In this study, a meshless radial point interpolation method is applied to demonstrate the elastic response of rubber-like materials based on the Mooney- Rivlin model. The obtained results are compared with the reference solutions given by other methods to verify the accuracy of the proposed method.

Buckling analysis of functionally graded plates in thermal environment by using a meshfree method

“…Besides FEM and its variance, several methods have been introduced and implemented for buckling analysis of FGPs [9 -14] and one of which is the group of meshfree methods. A typical method in this group is radial point interpolation method (RPIM) [15,16]. Among several meshfree methods, RPIM is one of which satisfied the Kronecker delta property, which allows to directly imposed essential boundary conditions on its field nodes like FEM.…”