Peridynamic bond‐associated correspondence model: Stability and convergence properties. (6th November 2018)

• Record Type: Journal Article
• Authors: Chen, Hailong; Spencer, Benjamin W.
• Is Part Of: International journal for numerical methods in engineering. Volume 117:Number 6(2019)
• Page Start: 713
• Page End: 727
• Publication Date: 2018-11-06
• Subjects: bond‐associated deformation gradient -- correspondence model -- material instability -- Peridynamics -- zero‐energy modes; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5973
• Languages: English
• ISSNs: 0029-5981

Abstract

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.