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Local-to-Nonlocal and Nonlocal-to-Nonlocal Coupling Methods: Advances in Coupling Techniques and Treatment of Interfaces in Nonlocal Mechanics and Diffusion

Marta d'Elia, Sandia National Laboratories

Pablo Seleson, Oak Ridge National Laboratory

Nonlocal models such as peridynamics and fractional equations can capture effects that classical partial differential equations (PDEs) fail to capture. These effects include multiscale behavior, material discontinuities such as cracks, and anomalous behavior such as super- and sub-diffusion. For this reason, nonlocal models provide an improved predictive capability for a large class of complex engineering and scientific applications, including fracture mechanics, subsurface flow, and turbulence, to mention a few. In many of these applications, the system under consideration exhibits heterogeneity, either in its physical composition or in its response to external stimuli. These cases often result in the need to introduce physical or virtual interfaces between different parts of the domain. The case of heterogeneity in the physical composition, such as two- or multi-material systems, normally requires the treatment of nonlocal-to-nonlocal coupling across physical interfaces. The case of heterogeneity in the system response may be benefited from local-to-nonlocal coupling across virtual interfaces; this occurs when nonlocal effects are concentrated in specific parts of the domain and the system can be partially described with a classical (local) PDE and partially described with a nonlocal model. These settings require the treatment of nonlocal-to-nonlocal or local-to-nonlocal interfaces in an accurate and physically consistent manner. The goal of this minisymposium is to bring together researchers working on the relatively new field of nonlocal interfaces, whose treatment still presents challenges, and on the well-established field of local-to-nonlocal coupling methods. As such, this minisymposium will be a way for researchers working in these two fields to benefit from each other's results and define new research directions.