Publication 26-CNA-011

Solving the Dissipation Inequality not as a Constitutive Restriction

Maximiliano Larrain Silva
Department of Civil & Environmental Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
maximill@andrew.cmu.edu

Amit Acharya
Department of Civil & Environmental Engineering
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
acharyaamit@cmu.edu

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.

Get the paper in its entirety as  26-CNA-011.pdf

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