Peridynamic bond‐associated correspondence model: Reformulation and comparison study

Abstract

AbstractThe peridynamic bond‐associated formulation has been shown to be effective in stabilizing the conventional correspondence model for both two‐dimensional and three‐dimensional, static, and dynamic problems. However, recent study revealed the persistence of material instability in the bond‐associated formulation for one‐dimensional problems for majority combinations of the bond associated horizon size and material point horizon size and two‐dimensional problems when both the bond‐associated horizon size and the material point horizon size are twice of mesh spacing. In addition, it was found that the bond‐associated formulation has instability in dynamic problems when the bond‐associated horizon size is close to the material point horizon size. In this article, a reformulation of the bond‐associated correspondence formulation is presented. Distinct from the original formulation, the proposed reformulation derives the force density states of a bond as a volume weighted average of all bond‐associated force density states whose bond‐associated horizons include the material points of the bond. Similar to the original bond‐associated formulation, the proposed reformulation recovers the conventional formulation when the bond‐associated horizon size is at least twice as large as the material point horizon size. Detailed numerical study on wave dispersion relations, static deformation, and dynamic wave propagation problems are performed to investigate and compare the two bond‐associated formulations. It is found that for all these three types of problems, the proposed reformulation significantly improves the model instability compared to the original bond‐associated formulation, especially when the bond‐associated horizon size is small relative to the material point horizon size. Based on numerical study, small bond‐associated horizon is recommended for use in the proposed reformulation.