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Center for Nonlinear Studies |
In classical equilibrium statistical mechanics, there is a formula for the entropy of a finite dimensional, constrained Hamiltonian system. It seems that this idea can be combined in a systematic way with space-time averaged, kinematically rigorous PDE models of dislocations or voids to produce mesoscale models physical phenomena. In doing so, the idea of ‘local equilibrium’ in non-equilibrium thermodynamics of extended systems can be given a specific operational meaning at the level of generating useful algorithms from it. The energetics and driving forces for dissipative mechanisms in these models can be precisely linked to atomistic behavior through well-defined, material- specific, one-time calculations that are expected to be possible on modern computers. This presentation will discuss the details of this formalism and illustrate it in the context of mesoscale void damage and dislocation plasticity.