Stability of peridynamic correspondence material models and their particle discretizations

• Published in: Computer methods in applied mechanics and engineering Vol. 322; no. C; pp. 42 - 57
• Main Author: Silling, S.A.
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01.08.2017; Elsevier
• Subjects: Elasticity; Meshless methods; Nonlocal; Particle methods; Peridynamic; Peridynamic; Elasticity; Nonlocal; Particle methods; Meshless methods
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2017.03.043

Peridynamic correspondence material models provide a way to combine a material model from the local theory with the inherent capabilities of peridynamics to model long-range forces and fracture. However, correspondence models in a typical particle discretization suffer from zero-energy mode instability. These instabilities are shown here to be an aspect of material stability. A stability condition is derived for state-based materials starting from the requirement of potential energy minimization. It is shown that all correspondence materials fail this stability condition due to zero-energy deformation modes of the family. To eliminate these modes, a term is added to the correspondence strain energy density that resists deviations from a uniform deformation. The resulting material model satisfies the stability condition while effectively leaving the stress tensor unchanged. Computational examples demonstrate the effectiveness of the modified material model in avoiding zero-energy mode instability in a peridynamic particle code.