Finite element modeling of quasi-brittle cracks in 2D and 3D with enhanced strain accuracy

Cervera, Miguel; Barbat, G. B.; Chiumenti, Michele

doi:10.1007/s00466-017-1438-8

Cited by 41 publications

(25 citation statements)

References 74 publications

(139 reference statements)

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“…It is found that the crack initially twists along the central vertical axis until the crack surface is parallel to the transversal plane, and then grows upwards along the transversal plane until the end of simulations. The simulated crack surface represented by points ( d > 0.9) is visualized in Figure 15 where the crack propagation patterns are in good agreement with reference solutions 36,53,54 . Figure 16 shows the load‐displacement curve for a three‐point bending test.…”

Section: Numerical Examplesmentioning

confidence: 59%

Phase‐field modeling of brittle fracture in a 3D polycrystalline material via an adaptive isogeometric‐meshfreeapproach

Nguyen‐Thanh

Zhou

2020

Numerical Meth Engineering

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Phase-field modeling, which introduces the regularized representation of sharp crack topologies, provides a convenient strategy for tackling 3D fracture problems. In this work, an adaptive isogeometric-meshfree approach is developed for the phase-field modeling of brittle fracture in a 3D polycrystalline material. The isogeometric-meshfree approach uses moving least-squares approximations to construct the equivalence between isogeometric basis functions and meshfree shape functions, thus inheriting the flexible local mesh refinement scheme from a meshfree method. This refinement scheme is improved by introducing an error estimator that includes both the phase field and its gradient. With the present approach, numerical implementations of the adaptive phase-field modeling that introduces the anisotropy of fracture resistance in polycrystals are proposed. In this way, propagating cracks can be dynamically tracked, and the mesh near cracks is refined in a meshfree manner without requiring a priori knowledge of crack paths. Furthermore, the intergranular and transgranular crack propagation patterns in polycrystalline materials can be simulated by the present approach. A series of numerical examples that deal with the isotropic and anisotropic fracture are investigated to demonstrate the robustness and effectiveness of the proposed approach. K E Y W O R D S adaptivity, anisotropy, isogeometric-meshfree approach, phase-field modeling, polycrystalline material 1 INTRODUCTION Fracture behaviors of engineering materials and structures, such as crack initiation, propagation, coalescence, and branching, have been extensively investigated by two types of numerical models: the discrete and diffusive models. The discrete model treats cracks as moving boundaries by constructing discontinuous displacement fields. Within the framework of a discrete model, a variety of methods have been developed, such as the extended finite element method (XFEM), 1 cohesive zone method, 2,3 extended isogeometric analysis (XIGA), 4 and extended meshfree method. 5 As a discrete model requires descriptions of crack surfaces, it suffers from low computational efficiencies induced by the tracking of complex 5042

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Section: Numerical Examplesmentioning

confidence: 59%

Phase‐field modeling of brittle fracture in a 3D polycrystalline material via an adaptive isogeometric‐meshfreeapproach

Nguyen‐Thanh

Zhou

2020

Numerical Meth Engineering

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“…These observations are in agreement with the work of Cervera et al Indeed, they mention that in order to obtain crack paths and failure strains independent of the discretization, one needs to have both a smooth strain field and a fracture criterion function of the discretization length. TLSPH provides a smooth strain field, but the fracture criterion used here is independent of the particle spacing.…”

Section: Convergencementioning

confidence: 99%

A new total‐Lagrangian smooth particle hydrodynamics approximation for the simulation of damage and fracture of ductile materials

Vaucorbeil

Hutchinson

2020

Numerical Meth Engineering

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Summary Smooth particle hydrodynamics (SPH) is gaining popularity for the simulation of solids subjected to machining, wear, and impacts. Its attractiveness is due to its abilities to simulate problems, involving large deformations resulting from the absence of mesh as well as the development of the total‐Lagrangian version of SPH (TLSPH) to solve tensile instabilities and an hourglass control algorithm to reduce rank‐deficiency problems. However, when TLSPH is used with continuum damage mechanics, nonphysical residual forces can emerge and lead to instabilities. To solve this issue, the “pseudospring” method that scales the kernel function with damage was proposed by Chakraborty and Shaw. This method preserves local linear momentum and is stable for elastic solids but can generate instabilities when solids damage after experiencing high plastic strains. In this contribution, we present a new TLSPH approximation that conserves both linear and angular momenta, which is suitable for the simulation of damage and fracture of ductile materials. Using single‐edge notched samples and tensile tests, we show that this approximation is stable whatever the stress/strain state and is in good agreement with finite element simulations and experimental results.

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“…Finally, a three-point bending test on skew notched beam has been performed. The FEM-DEM results have been compared with those obtained by Cervera et al [47]. For the 2D examples (Section 6.1) we have used 3-noded triangles.…”

Section: Numerical Examplesmentioning

confidence: 99%

Combination of an adaptive remeshing technique with a coupled FEM–DEM approach for analysis of crack propagation problems

et al. 2019

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This paper presents an enhanced coupled approach between the Finite Element Method (FEM) and the Discrete Element Method (DEM) in which an adaptative remeshing technique has been implemented. The remeshing technique is based on the computation of the Hessian of a selected nodal variable, i.e. the mesh is refined where the curvature of the variable field is greater. Once the Hessian is known, a metric tensor is defined node-wise that serves as input data for the remesher (MmgTools) that creates a new mesh. After remeshing, the mapping of the internal variables and the nodal values is performed and a regeneration of the discrete elements on the crack faces of the new mesh is carried out. Several examples of fracturing problems using the enhanced FEM-DEM formulation are presented. Accurate results in comparison with analytical and experimental solutions are obtained.

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Finite element modeling of quasi-brittle cracks in 2D and 3D with enhanced strain accuracy

Cited by 41 publications

References 74 publications

Phase‐field modeling of brittle fracture in a 3D polycrystalline material via an adaptive isogeometric‐meshfreeapproach

Phase‐field modeling of brittle fracture in a 3D polycrystalline material via an adaptive isogeometric‐meshfreeapproach

A new total‐Lagrangian smooth particle hydrodynamics approximation for the simulation of damage and fracture of ductile materials

Combination of an adaptive remeshing technique with a coupled FEM–DEM approach for analysis of crack propagation problems

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