On the development of thermodynamically consistent algorithms for thermomechanical frictional contact
In simulations of contact/impact phenomena using finite element techniques, spurious oscillations and/or numerical instabilities continue to pose considerable difficulty for many analysts. Recently, the combination of thermodynamically based stability estimates and energy-momentum numerical approaches has proven to be useful in developing effective, unconditionally stable algorithms for mechanical contact/impact in fully nonlinear regime. In this paper, these ideas are extended to coupled interface problems by developing a new a priori stability estimate for fully coupled thermomechanical contact problems in large deformations. The model framework encompasses inelastic heating and thermal softening within the contacting bodies, as well as frictional heating and thermal softening of coefficient of friction on sliding interfaces. Also, incorporated are pressure-dependent heat transfer across these interfaces, and a fully coupled treatment of conductive heat transfer occurring within the bodies. The obtained stability estimate can extend energy-momentum approaches to dissipative and thermally coupled phenomena, providing an unconditionally stable adiabatic splitting of coupled problems. The latter is shown to be useful in developing partitioned integration schemes for coupled equations of evolution.
thermodynamically based unconditionally stable algorithms
unconditionally stable adiabatic splitting
scientific article; zbMATH DE number 1436264
scientific article