From two- to three-dimensional continuum-kinematics-inspired peridynamics: More than just another dimension

Abstract

Continuum-kinematics-inspired Peridynamics (CPD) has been recently proposed as a geometrically exact formulation of peridynamics that is also thermodynamically and variationally consistent. Unlike the original formulation of peridynamics (PD), CPD can accurately capture the Poisson effect. For a three-dimensional analysis, CPD builds upon one-, two- and three-neighbor interactions. The isotropic three-dimensional CPD formulation of non-local elasticity therefore involves three material constants associated with length, area and volume. This manuscript aims to establish the relationships between the material parameters of CPD and isotropic linear elasticity for three-dimensional problems. In addition to addressing significant technical difficulties that arise when advancing from two- to three-dimensional problems, this contribution unravels several key features that are entirely absent in a two-dimensional analysis (Ekiz et al., 2022). It is shown that the three material parameters of CPD reduce to two independent parameters in the linearized framework, and can be expressed in terms of any pairs of isotropic linear elasticity constants, such as Lamé parameters. The analysis here provides a physical interpretation for the first Lamé constant, for the first time. Finally, we establish the admissible ranges for CPD material parameters.