Large deformation analysis of rubber based on a reproducing kernel particle method
A nonlinear formulation of the reproducing kernel particle method (RKPM) is presented for the large deformation analysis of rubber materials which are considered to be hyperelastic and nearly incompressible. In this approach, the global nodal shape functions derived on the basis of RKPM are employed in the Galerkin approximation of the variational equation to formulate the discrete equations of a boundary-value hyperelasticity problem. Existence of a solution in RKPM discretized hyperelasticity problem is discussed. A Lagrange multiplier method and a direct transformation method are presented to impose essential boundary conditions. The characteristics of material and spatial kernel functions are discussed. Several numerical examples are presented.
Galerkin approximation of variational equation
scientific article; zbMATH DE number 1066658