9 Viscoplastic Contact

Abstract

We describe contact problems for viscoplastic materials in which once the stress reaches the so-called yield limit the deformation becomes irreversible. Metals behave as viscoplastic materials, for instance, during metal-forming, and so do some polymers and other materials when hot or under large loads. Such problems are common in industrial processes and deserve considerable attention, both analytical and computational. We use rate-type constitutive laws of the form (6.4.7), and note that unlike the elastic or viscoelastic cases, the variational formulations of viscoplastic contact problems involve both the displacements and the stress fields. Indeed, this feature arises from the fact that, essentially, the stress field can not be eliminated from the constitutive law and, therefore, derivation of a variational formulation in terms of the displacements only leads to considerable mathematical difficulties.