Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 137, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2019.103862
Keywords
Peridynamics; Semi-Lagrangian; Correspondence modeling; Extreme events; Nonlocal
Funding
- AFOSR MURI Center for Materials Failure Prediction through Peridynamics [ONRBAA12-020]
- University of Texas at Austin
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Lagrangian formulations, in which material models are established upon a mapping from a deformed domain back to an undeformed reference configuration, have traditionally been employed in most previous developments of the peridynamic theory. In this paper, a semi-Lagrangian constitutive framework for peridynamics is proposed, in which peridynamic material point interactions depend only on their current properties (e.g. position and stress values) in the deformed configuration. A nonlocal version of the velocity gradient is proposed to determine the Cauchy stress rate, using local constitutive theories, as an intermediate quantity in computing peridynamic bond forces. It is shown that a pure state based peridynamic approach would involve material instabilities. A bond-associated formulation is presented to benefit from both bond-based and state-based views, resulting in an enhanced stability. A bond-associated, correspondence damage modeling is introduced to incorporate classical failure criteria in a convenient way. The proposed framework opens up new pathways in modeling extreme events, where excessive material deformation and damage make the Lagrangian formulation unsuitable. Capabilities of the new theory is showcased in a handful of illustrative scenarios. (C) 2020 Elsevier Ltd. All rights reserved.
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