Publications / SAND Report

Mathematical Foundations for Nonlocal Interface Problems: Multiscale Simulations of Heterogeneous Materials (Final LDRD Report)

D'Elia, Marta D.; Bochev, Pavel B.; Foster, John E.; Glusa, Christian A.; Gulian, Mamikon G.; Gunzburger, Max G.; Trageser, Jeremy T.; Kuhlman, Kristopher L.; Martinez, Mario A.; Najm, H.N.; Silling, Stewart A.; Tupek, Michael T.; Xu, Xiao X.

Nonlocal models provide a much-needed predictive capability for important Sandia mission applications, ranging from fracture mechanics for nuclear components to subsurface flow for nuclear waste disposal, where traditional partial differential equations (PDEs) models fail to capture effects due to long-range forces at the microscale and mesoscale. However, utilization of this capability is seriously compromised by the lack of a rigorous nonlocal interface theory, required for both application and efficient solution of nonlocal models. To unlock the full potential of nonlocal modeling we developed a mathematically rigorous and physically consistent interface theory and demonstrate its scope in mission-relevant exemplar problems.