Peridynamic Modeling of Fracture in Elastomers and Composites

The peridynamic model of solid mechanics is a mathematical theory designed to provide consistent mathematical treatment of deformations involving discontinuities, especially cracks. Unlike the partial differential equations (PDEs) of the standard theory, the fundamental equations of the peridynamic theory remain applicable on singularities such as crack surfaces and tips. These basic relations are integro-differential equations that do not require the existence of spatial derivatives of the deformation, or even continuity of the deformation.

In the peridynamic theory, material points in a continuous body separated from each other by finite distances can interact directly through force densities. The interaction between each pair of points is called a bond. The dependence of the force density in a bond on the deformation provides the constitutive model for a material. By allowing the force density in a bond to depend on the deformation of other nearby bonds, as well as its own deformation, a wide spectrum of material response can be modelled. Damage is included in the constitutive model through the irreversible breakage of bonds according to some criterion. This criterion determines the critical energy release rate for a peridynamic material.

In this talk, we present a general discussion of the peridynamic method and recent progress in its application to penetration and fracture in nonlinearly elastic solids. Constitutive models are presented for rubbery materials, including damage evolution laws. The deformation near a crack tip is discussed and compared with results from the standard theory. Examples demonstrating the spontaneous nucleation and growth of cracks are presented. It is also shown how the method can be applied to anisotropic media, including fiber reinforced composites. Examples show prediction of impact damage in composites and comparison against experimental measurements of damage and delamination.