A bond‐based peridynamic model considering effects of particle rotation and shear influence coefficient

Abstract

Summary The classical bond‐based peridynamic (BPD) model is limited with a fixed Poisson's ratio. To overcome this limitation, an improved BPD model is proposed to analyze the deformation and crack propagation of microelastic brittle materials with emphasis on varying Poisson's ratios. In the proposed model, the bond is subjected to axial and transverse pairwise forces, and the particle rotation angle is added to eliminate the additional bending moment caused by transverse forces, which is a key factor to satisfy the balance of angular momentum exactly. As a result, the bond not only has axial displacement but also has transverse displacement and particle rotation. This extension in the displacement mode overcomes the limitation of the fixed Poisson's ratio in the classical BPD model. The simulation results demonstrate the precision of the improved BPD model and prove its ability to predict deformations and crack propagations.

A continuum-molecular model for anisotropic electrically conductive materials

“…In fact, adopting a deformation (axial) based failure criterion, a limit value for the fiber elongation related to the mechanical behavior of the equivalent axial spring is considered. Nevertheless, in isotropic materials at atmospheric pressure, the crack front is locally associated with a mode I deformation leading to well simulated failure conditions and realistic crack paths using the critical elongation criterion even in the case of pure mode II external loading [43,44,45,46,7,47,48]. However, the situation is different in the case of anisotropic materials which need a lattice failure criterion accounting for shearing deformations to describe properly the crack nucleation and kinking phenomenon [33].…”

Bond-based peridynamics, a survey prospecting nonlocal theories of fluid-dynamics

“…Although bond-based PD is the most dated formulation of peridynamics and suffers of the discussed Poisson ratio limitation, it is yet employed in several numerical studies on peridynamics. Physical intuitiveness, less computational efforts, and crack simulation stability concerning state-based PD make the choice of bond-based integral kernel still attractive [70,71], so much that several extension of bond-based PD has been proposed (for a review, refer to [71]).…”

Anisotropic Continuum-Molecular Models: A Unified Framework Based on Pair Potentials for Elasticity, Fracture and Diffusion-Type Problems

“…the bending micromodulus), is independent of the other constitutive parameters and can be neglected if necessary (consistently with standard elasticity) [40]. Other polar formulations for classical elasticity have been proposed afterwards [41][42][43]. Most of them, however, still consider a kinematic of interacting material points inspired by beam models with non-vanishing bending micromoduli, these being function of the other micromoduli and/or abstract geometrical parameters.…”