Modeling of nonlinear viscoelastic–viscoplastic frictional contact problems

Abstract

This paper presents a nonlinear time-dependent computational model for analyzing the quasistatic response of viscoelastic–viscoplastic frictional contact problems. Both material and geometrical nonlinearities are considered in the framework of the Lagrangian description. The material nonlinearity is due to the time–stress-dependency of the constitutive equation, while the geometrical nonlinearity is due to large displacements and rotations, but small strains. The model is derived based on an implicit time-integration method within a general displacement-based finite element analysis. The nonlinear Schapery’s single integral model is used to model the viscoelastic part, while the Perzyna model is adopted model the viscoplastic part. The exponential form of the Prony series is used to represent the transient component of the viscoelastic creep compliance, since it permits hereditary effects to be computed recursively. In addition, an incremental form of the viscoplastic strain component is derived in the framework of associative viscoplasticity based on implicit integration scheme. Throughout the contact interface, friction is simulated using a local-nonlinear friction law, while the Lagrange multiplier method is adopted to model the inequality contact constraints. In a presented case study, the complete contact configuration and internal stresses are analyzed. Results show the significant effects of material nonlinearity, viscoplastic flow, and friction on the response of contact problems.