A new adaptive integration method for the peridynamic theory

Abstract

Peridynamics is a new formulation of solid mechanics based on direct interactions between material points in a continuum separated by a finite distance. Integration of interactions between material points plays a crucial role in the formulation of peridynamics. To overcome the deficiencies in numerical integration methods for peridynamics in the literature, the work presented here focuses on a new method of numerical integration for the peridynamic theory. In this method, the continuum is discretized into cubic cells, and different geometric configurations over the cell and the horizon of interaction are classified in detail. Integration of the peridynamic force over different intersection volumes are calculated accurately using an adaptive trapezoidal integration scheme with a combined relative-absolute error control. Numerical test examples are provided to demonstrate the accuracy of this new method. The bond-based peridynamic constitutive model is used in the calculation but this new method is also applicable to state-based peridynamics.