A 3-D conjugated bond-pair-based peridynamic formulation for initiation and propagation of cracks in brittle solids

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.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Zheng

Shen

Xia

et al. 2019

“…Approaches based on alternative discretization techniques can also be found. Wu et al, for instance, proposed a meshfree continuous‐discontinuous approach for dynamic ductile fracture, based on the combination of a gradient‐enriched damage model with a visibility criterion for sharp cracks, whereas the meshfree approach of Wang et al for brittle solids is based on the peridynamic theory. Peridynamics grids are also used by Zaccariotto et al who combine them with the standard FE method to describe crack propagation phenomena.…”

Section: Introductionmentioning

confidence: 99%

A continuous‐discontinuous model for crack branching

Tamayo-Mas

Feliu‐Fabà

Casado‐Antolin

et al. 2019

Summary A new continuous‐discontinuous model for fracture that accounts for crack branching in a natural manner is presented. It combines a gradient‐enhanced damage model based on nonlocal displacements to describe diffuse cracks and the extended finite element method (X‐FEM) for sharp cracks. Its most distinct feature is a global crack tracking strategy based on the geometrical notion of medial axis: the sharp crack propagates following the direction dictated by the medial axis of a damage isoline. This means that, if the damage field branches, the medial axis automatically detects this bifurcation, and a branching sharp crack is thus easily obtained. In contrast to other existing models, no special crack‐tip criteria are required to trigger branching. Complex crack patterns may also be described with this approach, since the X‐FEM enrichment of the displacement field can be recursively applied by adding one extra term at each branching event. The proposed approach is also equipped with a crack‐fluid pressure, a relevant feature in applications such as hydraulic fracturing or leakage‐related events. The capabilities of the model to handle propagation and branching of cracks are illustrated by means of different two‐dimensional numerical examples.

“…The peridynamic theory redefines the mechanical problems in terms of integral equations rather than partial differential equations, which makes it mathematically compatible with crack initiation and propagation. Due to this characteristic, the peridynamic model has taken considerable attention and has been successfully applied to brittle fracture problems, heat transfer, composite, and some other nonlinear problems . The first peridynamic formulation that the researchers have widely used is bond‐based peridynamics (BPD).…”

Section: Introductionmentioning

confidence: 99%

An implicit dual‐based approach to couple peridynamics with classical continuum mechanics

Bie

She

et al. 2019

Summary A general local/nonlocal implicit coupling technique called the dual‐based approach is proposed to couple peridynamics (PD) with classical continuum mechanics. In the present method, physical information is transmitted mutually from local to nonlocal regions through the coupling elements; no transition region is introduced. For different mesh discretizations, two coupling methods are achieved with simplicity and effectivity. To obtain the stiffness matrix of the coupled model, without loss of generality, the implicit dual‐horizon ordinary state‐based peridynamic model is proposed, in which the linearization of dual‐horizon ordinary state‐based PD is derived and the dual assembly algorithm of the peridynamic stiffness matrix is developed. It will be seen that the implicit dual‐based coupling approach provides a new implicit coupling method that is easy to implement and makes full use of the internal connection between PD and classical continuum mechanics. Several numerical examples involving static crack propagation are investigated, and the satisfactory results show both quantitative and qualitative agreement with either the analytic solution or the available experiment.