Tykhonov well-posedness of a rate-type viscoplastic constitutive law

Abstract

We consider a rate-type constitutitve law given by an implicit nonlinear differential equation in the space of second order symmetric tensors on Rd, in which the unknowns are the stress and the linearized strain fields. We list the assumptions on the constitutive functions then we state and prove its well-posedness with respect to two different Tykhonov triples. We use these well-posedness properties in order to deduce two convergence results. Finally, we provide the mechanical interpretation of these results as well as some concluding remarks.