Multiscale Models of Materials: Linking Microstructure and Macroscopic Behavior

Michael Ortiz, California Institute of Technology

The fidelity of computational capability is central to the credibility of the certification of the nuclear stockpile. In particular, the engineering models in the weapon's codes are a major source of uncertainty in computed performance margins. Within this framework, multiscale modeling may be understood as a paradigm for reducing or, ideally, eliminating uncertainty and empiricism, especially in simulations involving complex materials systems and behavior. The main two strategies of multiscale modeling are: i) Bottom-up: Coarsening of first principles descriptions of material behavior; and ii) Top-down: Informing macroscopic models with physics gleaned from the lower scales. An example of a bottom-up approach is provided by mixed continuum-atomistic models such as the quasi-continuum. Bottom-up approaches seek to extend the range of fundamental theories by systematically weeding out inactive or redundant degrees of freedom and by averaging out fluctuations. Top-down approaches seek to strengthen the physical grounding of engineering models by the systematic consideration of microstructure. Top-down approaches are exemplified by homogenization, relaxation and gamma-convergence methods. I shall review a number of avenues that are currently being pursued at Caltech's Center for the Simulation of the Dynamic Behavior of Materials in order to implement these strategies, with a particular focus on: strength and spallation; and on concurrent multiscale computing.

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