A Blending Approach to Concurrently Couple Peridynamics and Classical Continuum Mechanics

A Blending Approach to Concurrently Couple Peridynamics and Classical Continuum Mechanics

Seleson, Pablo; Littlewood, David; Silling, Stewart

Abstract:

Peridynamics is a nonlocal reformulation of classical continuum mechanics. In contrast to classical models, governing equations in peridynamics are based on spatial integration, rather than spatial differentiation, of displacement fields. Therefore, peridynamics has been applied to the description of material failure and damage. As a nonlocal model, peridynamics is computationally more expensive than classical models; this motivates the development of concurrent multiscale methods, for which peridynamics is applied in regions where discontinuities appear or may be generated, whereas classical models are used elsewhere. A main challenge in concurrent multiscale modeling is how to couple different models without introducing spurious effects. We derive blending schemes to concurrently couple peridynamics and classical continuum mechanics, avoiding common artifacts present in these types of methods. We demonstrate the performance of the coupling schemes analytically and numerically.

Peridynamics is a nonlocal reformulation of classical continuum mechanics. In contrast to classical models, governing equations in peridynamics are based on spatial integration, rather than spatial differentiation, of displacement fields. Therefore, peridynamics has been applied to the description of material failure and damage. As a nonlocal model, peridynamics is computationally more expensive than classical models; this motivates the development of concurrent multiscale methods, for which peridynamics is applied in regions where discontinuities appear or may be generated, whereas classical models are used elsewhere. A main challenge in concurrent multiscale modeling is how to couple different models without introducing spurious effects. We derive blending schemes to concurrently couple peridynamics and classical continuum mechanics, avoiding common artifacts present in these types of methods. We demonstrate the performance of the coupling schemes analytically and numerically.

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Como citar:

Seleson, Pablo; Littlewood, David; Silling, Stewart; "A Blending Approach to Concurrently Couple Peridynamics and Classical Continuum Mechanics", p-56-56. In: Proceedings of the 13th International Symposium on Multiscale, Multifunctional and Functionally Graded Materials [=Blucher Material Science Proceedings, v.1, n.1]. São Paulo: Blucher, 2014.
ISSN 23589337, DOI