A bond-based micropolar peridynamic model with shear deformability: Elasticity, failure properties and initial yield domains

Abstract

A generalized micropolar bond-based Peridynamic model with shear deformability for linear and non-linear problems is proposed. The analytical implicit formulation is derived from the definition of a specific microelastic energy function for micropolar nonlocal lattices, giving particular attention to numerical implementation aspects of the model. We investigate the effectiveness of this formulation, empathizing the importance of considering particle’s rotations in enriched bond-based peridynamic models with arbitrary Poisson’s ratios. Numerical analyses show that a microelastic energy function dependent on a shear deformation measure in which rotational degrees of freedom of the particles are not included, leads to a model not capable to describe properly the elastic behavior of isotropic solids subjected to non-homogeneous deformation fields. Moreover two novel deformation-based failure criteria for micropolar peridynamics accounting for bond shear deformation, associated or not with the corresponding stretch of the ligament, are proposed. A deep investigation is carryied out on the direction dependency of the failure response of the lattice, considering different horizon/grid spacing ratios. In this way the maximum errors are estimated and the effective initial yield domains corresponding to the failure criteria presented are identified in two dimensional principal s1−s2 and generalized s−γ deformations space.