A plane strain quadrilateral Cosserat point element (CPE) for nonlinear orthotropic elastic materials — An extension to initially distorted geometry and general orthotropic directions

•A plane strain FE for orthotropic materials was developed based on the Cosserat point theory.•The formulation eliminates sensitivity for initially distorted meshes and material orientation.•The developed CPE is free of hourglass instabilities, robust and accurate.

The objective of the present paper is to develop a four-noded quadrilateral Cosserat point element (CPE) for the numerical solution of plane strain problems in finite elasticity of orthotropic materials with general orientation and initially distorted geometry. Generally speaking, the Cosserat point approach connects the kinetic quantities to derivatives of a strain energy function and once the strain energy of the CPE has been specified, the procedure needs no integration over the element region and it ensures that the response of the CPE is hyperelastic. In the present paper a functional form for the strain energy that controls the inhomogeneous deformations and allowing for accurate modeling of distorted meshes is proposed. A number of example problems, which compare the performance of the developed quadrilateral CPE with that of other elements based on the mixed formulation, reduced integration with enhanced hourglass control, and enhanced strains/incompatible modes methods, are considered. These examples demonstrate that CPE is free of hourglass instabilities, and it is a robust user friendly element that can be used for modeling finite deformations of orthotropic elastic materials.