In addition to providing a more general capability for reproducing material response, the new framework provides a means to incorporate a constitutive model from the conventional theory of solid mechanics directly into a peridynamic model. The relation between the deformation state and force state is the constitutive model for the material. A similar object called a force state is defined, which contains the forces within bonds of all lengths and orientation.

To accomplish this generalization, a mathematical object called a deformation state is defined, a function that maps any bond onto its image under the deformation. This extends the types of material response that can be reproduced by peridynamic theory to include an explicit dependence on such collectively determined quantities as volume change or shear angle. This generalization permits the response of a material at a point to depend collectively on the deformation of all bonds connected to the point. Abstract: A generalization of the original peridynamic framework for solid mechanics is proposed.

Meshfree methods in solid mechanics