Field‐gradient partitioning for fracture and frictional contact in the material point method

Homel, Michael A.; Herbold, Eric B.

doi:10.1002/nme.5317

Cited by 66 publications

(40 citation statements)

References 63 publications

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“…It should be noted that compared to the standard finite element implementation, the implicit MPM does introduce additional computational costs, as a refactorization of the stiffness matrix introduced in Equation is required when material points move across background cells. However, this results in a high‐fidelity procedure for simulating complex phenomena (see, eg, previous studies) and also provides very accurate estimates for the crack geometry as will shown in Section 5. In this work, both the displacement field and the phase field that are defined at material points are mapped at the corresponding parent cell nodes resulting in an updated MPM Lagrangian phase.…”

Section: Numerical Implementationmentioning

confidence: 96%

“…More recently, cohesive modelling approaches have been introduced in an effort to further generalize the applicability of the MPM for problems pertinent to arbitrary crack paths . A continuum damage–based approach has been introduced in Homel and Herbold also demonstrating the advantages of using domain decomposition methods to accelerate MPM.…”

Section: Introductionmentioning

confidence: 99%

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Phase‐field material point method for brittle fracture

Kakouris

Triantafyllou

2017

Numerical Meth Engineering

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The material point method for the analysis of deformable bodies is revisited and originally upgraded to simulate crack propagation in brittle media. In this setting, phase-field modelling is introduced to resolve the crack path geometry. Following a particle in cell approach, the coupled continuum/phase-field governing equations are defined at a set of material points and interpolated at the nodal points of an Eulerian, ie, non-evolving, mesh. The accuracy of the simulated crack path is thus decoupled from the quality of the underlying finite element mesh and relieved from corresponding mesh-distortion errors. A staggered incremental procedure is implemented for the solution of the discrete coupled governing equations of the phase-field brittle fracture problem. The proposed method is verified through a series of benchmark tests while comparisons are made between the proposed scheme, the corresponding finite element implementation, and experimental results. KEYWORDS fracture mechanics, material point method, phase-field model

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Section: Numerical Implementationmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Phase‐field material point method for brittle fracture

Kakouris

Triantafyllou

2017

Numerical Meth Engineering

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“…To this point, few research has been conducted in damage simulation utilizing MPM using either discrete [38,39], cohesive [40,41], or continuum damage models [42,43]. Taking advantage of the good qualities of phase field modelling in naturally resolving complex crack paths, a Phase Field Material Point Method According to Griffith's theory [47] the stored energy Ψ s of the body Ω can be expressed as…”

Section: Introductionmentioning

confidence: 99%

Phase-Field Material Point Method for dynamic brittle fracture with isotropic and anisotropic surface energy

Kakouris

Triantafyllou

2019

Computer Methods in Applied Mechanics and Engineering

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A novel phase field material point method is introduced for robust simulation of dynamic fracture in elastic media considering the most general case of anisotropic surface energy. Anisotropy is explicitly introduced through a properly defined crack density functional. The particular case of impact driven fracture is treated by employing a discrete field approach within the material point method setting. In this, the equations of motion and phase field governing equations are solved independently for each discrete field using a predictor-corrector algorithm. Contact at the interface is resolved through frictional contact conditions. The proposed method is verified using analytical predictions. The influence of surface energy anisotropy and loading conditions on the resulting crack paths is assessed through a set of benchmark problems. Comparisons are made with the standard Phase Field Finite Element Method and experimental observations. 65 3 (PF-MPM) has been successfully introduced by the authors in [44] for quasistatic brittle fracture problems while a variant accounting for anisotropy in the quasi-static regime has been developed in [45].Moving beyond the state-of-the-art, we present a phase field MPM method for the solution of dynamic fracture considering materials with anisotropic frac-70 ture energy; isotropy emerges as a special case of the proposed formulation.Following, the method is extended to also account for frictional contact fracture problems. We use as point of departure the MPM contact algorithm introduced in Bardenhagen et al. [46] where multiple fields, termed discrete fields, are introduced in the non-deforming Eulerian mesh so that each contact body 75 corresponds to a different field. We define the variational structure of our phase field implementation of impact driven fracture at each discrete field from which the coupled weak form of the contact problem naturally emerges. Finally, we develop a predictor corrector solution algorithm for the solution of the governing equations over time. 80This paper is organized as follows. In section 2 phase-field modelling is briefly described in both isotropic and anisotropic brittle fracture. The discrete field formulation for phase field fracture due to impact is presented in section 3. The Material Point Method implementation for frictional contact fracture is presented in section 4. Finally, in section 5, a set of benchmark problems are 85 examined to demonstrate the accuracy and robustness of the proposed method. Preliminaries Phase field modellingIn the following, the case of an arbitrary deformable domain Ω is considered, with an external boundary ∂Ω and a crack path Γ as shown in Fig. (1a). 90The deformable domain Ω with domain volume V , is subjected to body forces b = b 1 b 2 b 3 T . Furthermore, a set of traction/pressure loadst is applied on the boundary ∂Ωt ⊆ ∂Ω. A prescribed displacement field, denoted asū, is imposed on the boundary ∂Ωū ⊆ ∂Ω.

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“…The CPDI improves the numerical accuracy of the MPM and prevents the occurrence of the nonphysical numerical fractures in the MPM, which is possible under the large extension condition. Given these advantages, the CPDI has been applied in the MPM simulations of, among others: nanoindentation, chemical/mechanical coupling of a silicon anode, the impact of thin‐walled structures as well as being enhanced to model fracture or fluid‐driven fracture . The CPDI has also been used in simulations of geotechnical problems, such as modeling pile penetration, pile installation, soil liquefaction, and the coupled analysis of saturated porous media …”

Section: Introductionmentioning

confidence: 99%

A convected particle least square interpolation material point method

Tran

Sołowski

Berzins

et al. 2019

Numerical Meth Engineering

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Summary Applying the convected particle domain interpolation (CPDI) to the material point method has many advantages over the original material point method, including significantly improved accuracy. However, in the large deformation regime, the CPDI still may not retain the expected convergence rate. The paper proposes an enhanced CPDI formulation based on least square reconstruction technique. The convected particle least square interpolation (CPLS) material point method assumes the velocity field inside the material point domain as nonconstant. This velocity field in the material point domain is mapped to the background grid nodes with a moving least squares reconstruction. In this paper, we apply the improved moving least squares method to avoid the instability of the conventional moving least squares method due to a singular matrix. The proposed algorithm can improve convergence rate, as illustrated by numerical examples using the method of manufactured solutions.

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Field‐gradient partitioning for fracture and frictional contact in the material point method

Cited by 66 publications

References 63 publications

Phase‐field material point method for brittle fracture

Phase‐field material point method for brittle fracture

Phase-Field Material Point Method for dynamic brittle fracture with isotropic and anisotropic surface energy

A convected particle least square interpolation material point method

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