Peridynamics: Introduction

Abstract

The peridynamic theory is a nonlocal extension of continuum mechanics that is compatible with the physical nature of cracks as discontinuities. It avoids the need to evaluate the partial derivatives of the deformation with respect to the spatial coordinates, instead using an integro-differential equation for the linear momentum balance. This chapter summarizes the peridynamic theory, emphasizing the continuum mechanical and thermodynamic aspects. Formulation of material models is discussed, including details on the statement of models using mathematical objects called peridynamic states that are nonlocal and nonlinear generalizations of second-order tensors. Damage evolution is treated within a nonlocal thermodynamic framework making use of the dependence of free energy on damage. Continuous, stable growth of damage can suddenly become unstable, leading to dynamic fracture. Peridynamics treats fracture and long-range forces on the same mathematical basis as continuous deformation and contact forces, extending the applicability of continuum mechanics to new classes of problems.