A meshless radial point interpolation method for finite deformation analysis of hyperelasticity

Abstract

Hyperelastic materials are special materials that possess the non-linear material property. In these materials, the stress-strain relation is derived from the strain energy density function. An interesting property of these materials like rubber is the ability of elastic response when it is subjected to large deformations. That means when the load is removed, the material can easily return to the initial configuration. In addition, they also have some excellent mechanical properties like good tear and abrasion resistance, flexibility at ambient temperature. So hyperelastic materials are widely used in the industry. Due to this reason, it is needed to take a careful look at these materials, especially in the field of mechanical behavior. Because hyperelastic materials usually work under large deformation for almost all cases, their behavior is often considered in a highly non-linear elastic state. This paper presents a meshless radial point interpolation method for hyperelastic bodies with compressible and nearly-incompressible states. The weak form is obtained from the principle of minimum potential energy, and the finite deformation analysis of non-linear behavior is performed under the total Lagrange formulation. Radial point interpolation method shape functions are employed to approximate field nodes and derivatives. Due to possessing the Kronecker delta function property, the boundary conditions are imposed directly in the proposed method. Moreover, this method also shows its advantage for non-linear analysis, especially when the large deformation is considered and the highly-distorted nodal mesh is inherent in the structure. Two numerical examples are conducted with some distributed loads for both compressible and nearly-incompressible states. The obtained results show good agreement with the reference solution. That clearly demonstrates the efficiency and reliability of the proposed method for complex problems.