Variational and Hemivariational Inequalities in Linear Thermoelasticity

This chapter deals with the study of certain unilateral B.V.P.s which are formulated in linear thermoelasticity. It is assumed that on the boundary of the body under consideration subdifferential relations hold, first between temperature and the heat flux vector and second between velocity and the stress vector. After deriving the corresponding variational inequalities, we prove some propositions on the existence and uniqueness of the solution. These two problems were first studied by G. Duvaut and J. L. Lions [85]. Finally, by the method of Sec. 4.1.3, some general variational inequalities are formulated. They stem from the assumption that the linear elasticity law and the well-known Fourier’s law of heat conduction are replaced by nonlinear laws described by superpotentials. This chapter closes with the study of certain hemivariational inequalities.