Finite Element Analysis of Quasi-static Contact Problems Using Minimum Dissipation of the Energy Principle

There are many practical situations where two bodies are directly in contact and are subjected to dynamic or varying loads. The contact area and the contact conditions are functions of load and load history and are not known a priori at any load thus making the problems nonlinear. The conditions of contact are determined by the kinematic constraints and the Coulomb’s law of friction. Direct solutions do not give unique results if the load steps are large and the finite element mesh is coarse. In the present work a method using the principle of minimum dissipation of energy is proposed and is applied to finite element analysis of a two-dimensional elastic contact problem under quasi-static loading. A combined incremental and iterative procedure is adopted to solve this problem. The results obtained are in good agreement with physical reasoning. The proposed method obtains new results apart from greatly reducing computational time and efforts.