Studies of Bimaterial Interface Fracture with Peridynamics

Abstract

The peridynamic is a kind of unique theory which can deal with continuous models, defect of crack and particles in a single framework. It does this by formulating problems in terms of integro-differential equation rather than partial differential equations. This theory can be used to investigate the dynamic mechanical behavior of the discontinuous material, such as the propagation, bifurcation, unstability process of crack. However, there is no reasonable force function for the interface of bimaterial. In this paper, we utilize a weight function method to establish the force function of the bimaterial interface. We discussed crack propagation along the interface in a prenotch bimaterial model by peridynamics, and analyzed the influence of different mesh shapes on the deflection angle of crack path. By comparing the peridynamic solution for these problems with the results published in the literature, we concluded that peridynamics with the proposed method is a reliable formulation for modeling the interfacial dynamic fracture of bimaterial.

Voronoi‐based peridynamics and cracking analysis with adaptive refinement

“…Rahman and Foster proposed a power‐law–based PD kernel function to mitigate the spurious wave reflection problems during multiscale modeling. Wang drew idea from one of the hybrid modeling method of PD and FEM and reduced the ghost forces by laying out virtual nodes in regions with large horizon sizes.…”

An In-depth Investigation of Bimaterial Interface Modeling Using Ordinary State-based Peridynamics

“…The red bond and black bond denote the interaction between material points in material 1 and in material 2, respectively. The blue bond represents the interaction between material points across the interface Another technique, which can be used to model the bimaterial interface in PD, is bond average as recommended by Oterkus [42], Wang et al [50], Behera et al [54]. The bond average technique can be classified into two types, e.g., arithmetic average and harmonic average.…”

“…A formal discussion about material interfaces in PD was made by Alali and Gunzburger [49], and they showed that the operator of linear PD diverges from the local solution in the limit of vanishing nonlocality when material properties are discontinuous. Bimaterial interface fracture was conducted by Wang et al [50] with the use of the weight function method for constructing the interfacial force function. Ren et al [51] applied dual-horizon PD to simulate crack propagation in heterogeneous materials.…”

A nonlocal interface approach to peridynamics exemplified by continuum‐kinematics‐inspired peridynamics

“…25,26,28 Oftentimes, the parameters are weighted with the fraction of the bond length associated with the respective material. These approaches can further be classified into arithmetic averaging 6,[35][36][37] and harmonic averaging. 6,7,9,38 Cheng et al 26 used the proportion of the material coefficients to identify a weighting factor.…”