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Jacob Fish

Civil Engineering, Mechanical Engineering, Aerospace Engineering, Information Technology, Rensselaer Polytechic Institute

Multiscale Multiphysics Computational Solid Mechanics

This short course will summarize the information-passing and concurrent ultiscale-multiphysics computational techniques in solid mechanics. In the concurrent approach both the fine and coarse scales are simultaneously resolved, whereas in the information-passing multiscale methods, fine scales are modeled and their ross response is infused into the coarse scale. Among the information-passing techniques, the unified mathematical homogenization, the multiscale enrichment based on partition of unity, and the variational multiscale methods will be described. Mathematical homogenization theory in space will be applied to elasticity, plasticity, damage and fatigue. A unified continuum-to-continuum and continuum-to-discrete (atomistic) scale bridging methodology based on the generalization of the space-time mathematical homogenization will be presented. Temporal homogenization theory will be derived and applied to problems of viscoelasticity , viscoplasticity and fatigue. Among the concurrent multiscale computational techniques to be described are: the multigrid (multilevel), the composite grid and the mesh superposition approaches. For multiphysics applications multiscale staggering methods will be discussed.