A nonlinear correspondence model for three-dimensional continuum-kinematics-inspired peridynamics

Peridynamics (PD) is a nonlocal continuum mechanics theory that inherently allows for singularities and fracture. However, the classical PD theory restricts the Poisson ratio. This issue is rectified in continuum-kinematics-inspired peridynamics (CPD) that has been recently proposed. Because of its variational consistency and geometrically exact nature, CPD does not suffer from zero-energy modes, and thus, it furnishes an ideal nonlocal elasticity framework for large deformations. In a three-dimensional setting, CPD builds upon one-, two-, and three-neighbor interactions. One-neighbor interactions capture length-associated elasticity between pairs of points, equivalent to the original PD formalism. The two-neighbor interactions of CPD recover area-associated elasticity between triplet of points. The three-neighbor interactions of CPD recover volume-associated elasticity between quadruplet of points. This contribution provides for the first time a nonlinear correspondence material model for CPD in a three-dimensional setting such that it recovers a well-established compressible neo-Hookean energy density of nonlinear elasticity at large deformations. At small deformations, the proposed model reduces to classical isotropic linear elasticity. The current manuscript is the three-dimensional extension of the recent two-dimensional contribution of the authors.