Effect of material viscosity on the response of elasto-frictional multi-layered contact systems

A general and efficient computational two-dimensional model capable of analyzing the nonlinear response of the quasistatic viscoelastic multiphase frictional contact of multilayered bodies is presented. The incremental convex programming method, which has been proved to be superior, is modified to accommodate viscoelastic frictional contact problems. The Lagrange multiplier method is used to incorporate the contact conditions into the global equilibrium equations. In the developed procedure, local and nonlinear friction model, which represents effectively the microscopic slipping between the two contacting surfaces, is adopted. This in turn eliminates the difficulties associated with the classical laws of friction. The friction effect is represented by nonlinear tangential contact stiffness. Wiechert model, as a general and effective model, is adopted to describe the linear viscoelastic behavior of the contacting bodies. The constitutive equations are incrementalized to replace the requirements of solving a set of integrals by the requirements solving a set of algebraic equations. The finite element method, as a numerical tool, is adopted to discretize the space domain of the problem. On the other hand the time domain is discretized in such a way that both convergence and stability of the solution can be satisfied. Finally, and based on the contact events, the presented formulations are implemented into an adaptive procedure capable of investigating the nonlinear response of the multilayered viscoelastic frictional contact problems.