A finite element model for 2D elastic–plastic contact analysis of multiple Cosserat materials

In this paper, a finite element model is reported for 2D elastic–plastic contact analysis of Cosserat materials. Based on the parametric virtual work principle, a quadratic programming method is developed to solve the elastic–plastic contact problem of Cosserat materials. Both the elastic–plastic problem and the contact problem with friction between two Cosserat materials are studied by using the parametric variational principle, which can greatly simplify the solution process of the original double nonlinear problem. The penalty factors, which are introduced into the algorithm for contact problem, are eliminated by using a definite numerical technique, resulting in high accuracy of the numerical results. Numerical examples are performed to demonstrate the accuracy and feasibility of the proposed algorithm. It can be found that sometimes the contact forces are strongly dependent on the material parameters of Cosserat materials.