Solving the Dissipation Inequality not as a constitutive restriction

Abstract

A solution procedure is formulated and solved for treating the nonlinear Dissipation Inequality
as a constraint equation within continuum mechanics, and allowing for incomplete knowledge
of constitutive behavior. The scheme is demonstrated in the context of the rate-dependent,
elastoplastic response of a bar, resulting in a nonlinear problem of constrained optimization.
Both closed form and computational results are developed. The computational solutions utilize
a sequence of convex optimization problems, and are shown to be accurate. In the example
considered, the approach is shown to automatically correct an (intentionally) faulty constitutive
specification, resulting in the solution to be in accord with the fundamental postulates of
continuum mechanics.