A ten node tetrahedral Cosserat Point Element (CPE) for nonlinear isotropic elastic materials

It is known that the standard full integration ten node tetrahedral element is inaccurate for thin nearly incompressible structures. Also, the commercial code ABAQUS recommends replacing this standard element (C3D10) with an undocumented patented modified element (C3D10M) for contact problems. The objective of this work is to develop a ten node tetrahedral Cosserat Point Element (CPE) for nonlinear isotropic hyperelastic materials. Hyperelastic constitutive equations for the CPE are developed by treating the element as a structure with a strain energy function that is restricted to satisfy a nonlinear form of the patch test. A number of examples are considered which demonstrate that the resulting CPE is accurate and robust, it does not exhibit the numerical stiffness for nearly incompressible materials observed for (C3D10) nor the unphysical instabilities observed for (C3D10M). Moreover, the CPE can be used for thin structures and three-dimensional bodies with a smooth transition from compressible to nearly incompressible material behavior.