A novel two-parameter linear elastic constitutive model for bond based peridynamics

Abstract

A novel linear elastic constitutive model is developed for bond based peridynamics. For a peridynamic constitutive model, the relevant material parameters are derived from energy equivalence to a classical linear elastic continuum mechanics model. The commonly used microelastic model is a central force model characterized by a single micromodulus constant, and hence the effective Poisson’s ratio of the isotropic peridynamic material is found to always be 1/3 in 2D and 1/4 in 3D. The elastic modulus of the peridynamic material is also dependant on the input Poisson’s ratio and as a result, the strain energy for simple loading conditions, for eg. a uniaxial tension test, is not correctly estimated by the microelastic bond model. This originates from the fact that typically a bulk expansion test is used to calibrate the peridynamic model which relates the micromodulus to the bulk modulus of the material only. In the present work, a novel linear elastic constitutive model incorporating two peridynamic material parameters is proposed, analogous to the idea of two material constants used to describe linear isotropic materials in classical theory. Numerical results are presented to demonstrate that after initial calibration using a simple biaxial test, the material model shows correct Poisson’s contraction and strain energies for a range of Poisson’s ratios. A damage model based on an energy criterion is implemented, and a dynamic crack propagation and crack branching problem is considered. Results are compared with both the microelastic model and other numerical methods from published literature. It is observed that the two parameter model shows a significant improvement in predicting displacements as a result of the inclusion of a tangential stiffness parameter.