A six node plane strain triangular Cosserat Point Element (CPE) for nonlinear elasticity

The objective of this paper is to develop a six node triangular Cosserat Point Element (CPE) for plane strain deformations of a nonlinear isotropic hyperelastic material. It is known that for nearly incompressible materials, full integration methods based on the Bubnov–Galerkin approximation with a quadratic ansatz predict inaccurate response and should be replaced by mixed methods. However, the mixed formulation exhibits soft response to bending. In contrast with these standard methods, the constitutive equations for the CPE are developed by treating the element as a structure with a strain energy function that models the resistance to all modes of deformation. A functional form for the strain energy function of inhomogeneous deformation (e.g. bending) is developed which eliminates this unphysical locking. Examples show that the CPE predicts accurate, robust response and retains accuracy during the transition from compressible to nearly incompressible material behavior.