Phase-field modelling of brittle fracture with Smoothed Radial Point Interpolation Methods

Novelli, Larissa; Gori, Lapo; Pitangueira, Roque Luiz da Silva

doi:10.1016/j.enganabound.2022.01.011

Cited by 16 publications

(2 citation statements)

References 43 publications

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“…Second-order PFM is well established for various problems. Second-order PFM for fracture using smoothed radial point method (SPIM) is given by Novelli et al . (2022).…”

Section: Introductionmentioning

confidence: 99%

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Modeling fracture in brittle materials by higher-order phase field method using C¹ non-Sibsonian interpolants

Aurojyoti

Rajagopal

2023

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PurposeThis study implements the fourth-order phase field method (PFM) for modeling fracture in brittle materials. The weak form of the fourth-order PFM requires C1 basis functions for the crack evolution scalar field in a finite element framework. To address this, non-Sibsonian type shape functions that are nonpolynomial types based on distance measures, are used in the context of natural neighbor shape functions. The capability and efficiency of this method are studied for modeling cracks.Design/methodology/approachThe weak form of the fourth-order PFM is derived from two governing equations for finite element modeling. C0 non-Sibsonian shape functions are derived using distance measures on a generalized quad element. Then these shape functions are degree elevated with Bernstein-Bezier (BB) patch to get higher-order continuity (C1) in the shape function. The quad element is divided into several background triangular elements to apply the Gauss-quadrature rule for numerical integration. Both fourth-order and second-order PFMs are implemented in a finite element framework. The efficiency of the interpolation function is studied in terms of convergence and accuracy for capturing crack topology in the fourth-order PFM.FindingsIt is observed that fourth-order PFM has higher accuracy and convergence than second-order PFM using non-Sibsonian type interpolants. The former predicts higher failure loads and failure displacements compared to the second-order model due to the addition of higher-order terms in the energy equation. The fracture pattern is realistic when only the tensile part of the strain energy is taken for fracture evolution. The fracture pattern is also observed in the compressive region when both tensile and compressive energy for crack evolution are taken into account, which is unrealistic. Length scale has a certain specific effect on the failure load of the specimen.Originality/valueFourth-order PFM is implemented using C1 non-Sibsonian type of shape functions. The derivation and implementation are carried out for both the second-order and fourth-order PFM. The length scale effect on both models is shown. The better accuracy and convergence rate of the fourth-order PFM over second-order PFM are studied using the current approach. The critical difference between the isotropic phase field and the hybrid phase field approach is also presented to showcase the importance of strain energy decomposition in PFM.

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“…Second-order PFM is well established for various problems. Second-order PFM for fracture using smoothed radial point method (SPIM) is given by Novelli et al . (2022).…”

Section: Introductionmentioning

confidence: 99%

“…Second-order PFM is well established for various problems. Second-order PFM for fracture using smoothed radial point method (SPIM) is given by Novelli et al (2022). Crack Brittle fracture modeling via phase field method modeling in multiphase composite via a damage threshold value using PFM is studied by Li et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Modeling fracture in brittle materials by higher-order phase field method using C¹ non-Sibsonian interpolants

Aurojyoti

Rajagopal

2023

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A computational meshfree RPIM approach for phase-field modeling of brittle fracture

Saberi,

Nguyen,

Saberi

et al. 2024

Acta Mech

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A Finite-Strain Phase-Field Description of Thermomechanically Induced Fracture in Shape Memory Alloys

Hasan

Zhang²,

Baxevanis³

2022

Shap. Mem. Superelasticity

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Phase-field modelling of brittle fracture with Smoothed Radial Point Interpolation Methods

Cited by 16 publications

References 43 publications

Modeling fracture in brittle materials by higher-order phase field method using C¹ non-Sibsonian interpolants

Modeling fracture in brittle materials by higher-order phase field method using C¹ non-Sibsonian interpolants

A computational meshfree RPIM approach for phase-field modeling of brittle fracture

A Finite-Strain Phase-Field Description of Thermomechanically Induced Fracture in Shape Memory Alloys

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Phase-field modelling of brittle fracture with Smoothed Radial Point Interpolation Methods

Cited by 16 publications

References 43 publications

Modeling fracture in brittle materials by higher-order phase field method using C1 non-Sibsonian interpolants

Modeling fracture in brittle materials by higher-order phase field method using C1 non-Sibsonian interpolants

A computational meshfree RPIM approach for phase-field modeling of brittle fracture

A Finite-Strain Phase-Field Description of Thermomechanically Induced Fracture in Shape Memory Alloys

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Modeling fracture in brittle materials by higher-order phase field method using C¹ non-Sibsonian interpolants

Modeling fracture in brittle materials by higher-order phase field method using C¹ non-Sibsonian interpolants