STABILITY BY HOMOGENIZATION OF THERMOVISCOPLASTIC PROBLEMS
Nicolas Ch. Charalambakis, François Murat · Mathematical Models and Methods in Applied Sciences · 2010
In this paper, we study the homogenization of the system of partial differential equations describing the quasistatic shearing of heterogeneous thermoviscoplastic materials. We first present the existence and uniqueness of the solution of the above system. We then define "stable by homogenization" models as the models where the equations in both the heterogeneous problems and the homogenized one are of the same form. Finally we show that the model with non-oscillating strain-rate sensitivity which is submitted to steady boundary shearing and body force, is stable by homogenization. In this model, the homogenized (effective) coefficients depend on the initial conditions and on the boundary shearing and body force. Those theoretical results are illustrated by one numerical example.