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Peridynamic bond‐associated correspondence model: Stability and convergence properties
Author(s) -
Chen Hailong,
Spencer Benjamin W.
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5973
Subject(s) - convergence (economics) , stability (learning theory) , instability , mathematics , computer science , statistical physics , mathematical optimization , mechanics , physics , economics , machine learning , economic growth
Summary The correspondence approach is a powerful technique that permits the usage of standard constitutive models from local theory within a peridynamic formulation. However, the conventional correspondence formulation suffers from material instability, ie, zero‐energy modes, which must be controlled for it to be applied in practice. The recently‐introduced correspondence reformulation based on the use of a bond‐associated deformation gradient can inherently remove the material instability. In this paper, we show how the bond‐associated correspondence model satisfies the requirement for material stability. The convergence behavior is also examined. The accuracy of this approach is further demonstrated by comparing model predictions against local reference solutions and results from the conventional correspondence model with penalty stabilization for both two‐dimensional and three‐dimensional problems.