**Heterogeneous Materials Modeling:** Mesoscale materials modeling of irradiated materials is an important and challenging problem that is of central interest to our partner Energy Frontier Research Center (EFRC), the *Center for Materials Science of Nuclear Fuel* (CMSNF), which has the mission of developing a computationally predictive, experimentally validated, multiscale understanding of the thermo-mechanical behavior of nuclear fuel. The head image of this website shows a snapshot of radiation-generated voids in nuclear fuel. Mesoscale modeling is computationally intensive because the evolution of each diffusive boundary between a void and the surrounding matrix must be correctly predicted. We employ coupled Cahn-Hilliard and Allen-Cahn systems with a double-obstacle free-energy potential to simulate the physics. The model is discretized in time with mixed implicit-explicit integration and in space by finite elements. However, the prevailing approach approximates the dynamics of the phase variable using a smoothed potential. In turn, this (non-DVI) method results in a stiff problem and undesirable physical artifacts: the phase field variable does not have a compact support, and the boundary between phases-grains in the case of irradiated materials—is no longer localized. Therefore, we formulate a DVI, which is equivalent to a complementarity problem. This approach in turn allows us to use newly developed parallel VI solvers discussed in SOLVERS.

Preliminary results for the resolution of large-scale, heterogeneous materials problems are presented in *A Differential Variational Inequality Approach for the Simulation of Heterogeneous Materials, Preprint ANL/MCS-P1895-0511, May 2011, L. Wang, J. Lee, M. Anitescu, A. El Azab, L. C. McInnes, T. Munson, and B. Smith.*

** Applications Involving Transitional Phenomena: ** We are seeking opportunities to partner with applications teams on incorporating VI formulations, algorithms, and software to enable the consistent and efficient modeling of transitional phenomena, especially applications involving phase changes, free boundaries, and hybrid discrete-continuum behavior.