An energy-conserving algorithm for nonlinear elastodynamic contact problems – Extension to a frictional dissipation phenomenon

Abstract

During the last years, the construction of energy conserving time integration methods to solve nonlinear elastodynamic problems has attracted the interest of many researchers ([12, 5, 3] .). Furthermore, many works have been devoted to extend these conservative formulations to frictionless impact; more precisely, Laursen and Chawla [9] and Amero and Petocz [2] have shown the interest of the persistency condition to conserve the energy in the discrete framework. But these contributions concede a contact interpenetration which vanishing as the time step tends towards zero. Recently, this drawback is resolved by Laursen and Love [10] by introducing a discrete jump in velocity and by Hauret [6] by considering a specific penalized enforcement of the contact conditions. In this work, we present an energy-conserving algorithm for hyperelastodynamic contact problems which differs from the approaches mentionned above ([10] and [6]); this approach permits to ensure both the Kuhn- Tucker and persistency conditions at the end of each time step. These two laws are enforced during each time increment by using an extended Newton method. In section 2, we recall some general aspects of nonlinear elastodynamic problems with contact and friction. The section 3 permits also to recall the usual energy conserving frameworks used to solve nonlinear elastodynamic problems. In section 4, we present an energy-conserving algorithm to treat impact problems with an extension to frictional dissipation phenomenon. In the last section 5, representative numerical simulations are presented to assess the performance and also to underscore the conservative or dissipative behaviour of the proposed method.