Static solution of crack propagation problems in Peridynamics

Ni, Tao; Zaccariotto, Mirco; Zhu, Qi‐Zhi; Galvanetto, Ugo

doi:10.1016/j.cma.2018.11.028

Cited by 146 publications

(60 citation statements)

References 31 publications

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“…The idea of allowing part of the crack body to appear within Ω F E has already been considered in some studies. For instance, in a recent publication [28], Ni et al used the FE-PD coupling proposed in [22,23] to study crack propagation problems. The dimensions of Ω P D are selected such that both the current and the final locations of the crack tip are included.…”

Section: Introductionmentioning

confidence: 99%

Coupling XFEM and peridynamics for brittle fracture simulation—part I: feasibility and effectiveness

et al. 2020

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A peridynamics (PD)-extended finite element method (XFEM) coupling strategy for brittle fracture simulation is presented. The proposed methodology combines a small PD patch, restricted near the crack tip area, with the XFEM that captures the crack body geometry outside the domain of the localised PD grid. The feasibility and effectiveness of the proposed method on a Mode I crack opening problem is examined. The study focuses on comparisons of the J integral values between the new coupling strategy, full PD grids and the commercial software Abaqus. It is demonstrated that the proposed approach outperforms full PD grids in terms of computational resources required to obtain a certain degree of accuracy. This finding promises significant computational savings when crack propagation problems are considered, as the efficiency of FEM and XFEM is combined with the inherent ability of PD to simulate fracture. Keywords Bond-based peridynamics • Extended finite element method • Nonlocal J integral • XFEM-PD coupling • Crack propagation B Ilias N. Giannakeas

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Section: Introductionmentioning

confidence: 99%

Coupling XFEM and peridynamics for brittle fracture simulation—part I: feasibility and effectiveness

et al. 2020

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“…where jn represents the bond status between the node j and the node n, and which can be given by jn = { 1 for an active bond 0 for a broken bond (50) There are several failure criteria for PD model. 10,19,31,35,36,38,[43][44][45][46][47][48][49][50] The most popular failure criterion in PD is the bond stretch criterion. 10,19,[45][46][47] The bond is broken if the stretch is over the critical stretch, that is where, s 0 represents the critical stretch, and s is the stretch of the bond between the node j and the node n, which is given by…”

Section: Failure Criteria For Laminated Composite Materialsmentioning

confidence: 99%

“…There are several failure criteria for PD model 10,19,31,35,36,38,43‐50 . The most popular failure criterion in PD is the bond stretch criterion 10,19,45‐47 .…”

Section: Nosbpd With Zero‐energy Modes Controlling Scheme For Laminatmentioning

confidence: 99%

A stable non‐ordinary state‐based peridynamic model for laminated composite materials

Liu

Liang

et al. 2020

Numerical Meth Engineering

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Non-ordinary state-based peridynamics (NOSBPD) has instability issue due to zero-energy modes during nodal integration. A zero-energy mode controlling scheme of NOSBPD for laminated composite materials is derived by using the linearized bond-based peridynamics, which forms a stable force state formulation corresponding to the non-uniform deformation. The proposed controlling scheme does not include any controlling parameter to avoid the complex parametric adjustment. A critical stretch continuously varying with the angle between fiber and bond directions is further proposed for the failure analysis of laminated composite materials with arbitrary fiber angles. The improved NOSBPD model adopts the explicit integration method to solve static problems. Several numerical examples are conducted to validate the proposed scheme suppressing the oscillation caused by zero-energy modes. K E Y W O R D S failure analysis, laminated composite materials, non-ordinary state-based peridynamics, stabilization, zero-energy modes 1 INTRODUCTION Peridynamics (PD) is a powerful non-local theory using integro-differential equations for differential equations. 1-5 The damage at any position in materials initiates spontaneously and can propagate along any paths. Based on these characteristics, PD has been widely used in damage and failure analysis of materials. 6-9 Generally, PD formulations have three types: bond-based peridynamics (BBPD), 10-13 ordinary state-based peridynamics (OSBPD), 14-16 and non-ordinary state-based peridynamics (NOSBPD). 17,18 BBPD has the restriction on the Poisson's ratio, and cannot distinguish the distortional and volumetric deformations. 4,19 OSBPD removes the restriction on the Poisson's ratio. Furthermore, NOSBPD uses the non-local approximate deformation gradient tensor to define strain. However, NOSBPD has inherent instability issues on displacement, stress, and strain fields due to zero-energy modes. 20,21 Recently, several zero-energy modes controlling methods have been developed for NOSBPD. 20-29 Littlewood 22 proposed a penalty approach to control zero-energy modes, in which the penalty force is proportional to the difference

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“…Although the peridynamic governing equation is in dynamic form, it can still be used to solve quasi-static or static problems [29][30][31]. Adaptive dynamic relaxation (ADR) method [29] is currently the most widely used method to solve quasi-static or static problems for PD.…”

Section: Numerical Implementationmentioning

confidence: 99%

“…Adaptive dynamic relaxation (ADR) method [29] is currently the most widely used method to solve quasi-static or static problems for PD. ADR method is particularly effective for solving highly nonlinear problems, including geometric and material nonlinearities [31].…”

Section: Numerical Implementationmentioning

confidence: 99%

Peridynamic Modeling of Mode-I Delamination Growth in Double Cantilever Composite Beam Test: A Two-Dimensional Modeling Using Revised Energy-Based Failure Criteria

Jiang

Guo

et al. 2019

Applied Sciences

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This study presents a two-dimensional ordinary state-based peridynamic (OSB PD) modeling of mode-I delamination growth in a double cantilever composite beam (DCB) test using revised energy-based failure criteria. The two-dimensional OSB PD composite model for DCB modeling is obtained by reformulating the previous OSB PD lamina model in x–z direction. The revised energy-based failure criteria are derived following the approach of establishing the relationship between critical bond breakage work and energy release rate. Loading increment convergence analysis and grid spacing influence study are conducted to investigate the reliability of the present modeling. The peridynamic (PD) modeling load–displacement curve and delamination growth process are then quantitatively compared with experimental results obtained from standard tests of composite DCB samples, which show good agreement between the modeling results and experimental results. The PD modeling delamination growth process damage contours are also illustrated. Finally, the influence of the revised energy-based failure criteria is investigated. The results show that the revised energy-based failure criteria improve the accuracy of the PD delamination modeling of DCB test significantly.

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Static solution of crack propagation problems in Peridynamics

Cited by 146 publications

References 31 publications

Coupling XFEM and peridynamics for brittle fracture simulation—part I: feasibility and effectiveness

Coupling XFEM and peridynamics for brittle fracture simulation—part I: feasibility and effectiveness

A stable non‐ordinary state‐based peridynamic model for laminated composite materials

Peridynamic Modeling of Mode-I Delamination Growth in Double Cantilever Composite Beam Test: A Two-Dimensional Modeling Using Revised Energy-Based Failure Criteria

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