An energy-based coupling approach to nonlocal interface problems

Giacomo Capodaglio; Marta D'Elia; Pavel Bochev; Max Gunzburger

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arXiv · 2001.03696

An energy-based coupling approach to nonlocal interface problems

Giacomo Capodaglio·Marta D'Elia·Pavel Bochev·Max Gunzburger

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Abstract

Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, where traditional partial differential equations fail to capture effects caused by long-range forces at the microscale and mesoscale. However, the application of nonlocal models to problems involving interfaces such as multimaterial simulations and fluid-structure interaction, is hampered by the lack of a rigorous nonlocal interface theory needed to support numerical developments. In this paper, we use an energy-based approach to develop a mathematically rigorous nonlocal interface theory which provides a physically consistent extension of the classical perfect interface PDE formulation. Numerical examples validate the proposed framework and demonstrate the scope of our theory.

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BibTeX RIS

Giacomo Capodaglio, Marta D'Elia, Pavel Bochev, Max Gunzburger. 2020-01-11. An energy-based coupling approach to nonlocal interface problems. https://arxiv.org/abs/2001.03696

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