Modelling brittle impact failure of disc particles using material point method

Li, Fan; Pan, Jia-Yu; Sinka, Csaba

doi:10.1016/j.ijimpeng.2011.02.004

Cited by 31 publications

(13 citation statements)

References 30 publications

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“…The Material Point Method (MPM) [30] has been introduced as a promis- 50 ing alternative to computationally expensive particle based methods that can efficiently deal with contact and large displacement problems. MPM is an extension of Particle-In-Cell (PIC) methods that efficiently treats history-dependent variables.…”

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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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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“…The in-plane damage model takes into account the load path redistribution due to through ply cracking and delamination rates, through a coupling matrix between five bases ruin modes and intrinsic damage variables, but in a passive way. If we compare with the very interesting work of Li [39] who uses the MPM method for brittle materials, it can be noticed that our model does not need any distribution default neither to initiate nor to propagate cracks, even if the coupling is weak. Indeed the transient dynamics introduces enough (and probably too much) differences in the integration points states of stresses and strains.…”

Section: Discussionmentioning

confidence: 99%

“…But the treatment of explicit cracks needs to set discontinuous velocities in the support grid [36,37]. New developments have been done to compute stress concentrations in 3D structures containing a crack placed between the particles [38], or multiple cracks supported by the particles for brittle materials [39]. Keeping in mind the idea that local stresses must be correctly computed to create and propagate cracks, and that the rupture can be supported by particles instead of being supported by surfaces between the particles, recent research activities have been devoted to the quality of numerical integration of meshess methods [40].…”

Section: Introductionmentioning

confidence: 99%

Coupling continuous damage and debris fragmentation for energy absorption prediction by cfrp structures during crushing

et al. 2014

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Energy absorption during crushing is evaluated using a thermodynamic based continuum damage model inspired from the Matzenmiller-Lubliner-Taylors model. It was found that for crash-worthiness applications, it is necessary to couple the progressive ruin of the material to a representation of the matter openings and debris generation. Element kill technique (erosion) and/or cohesive elements are efficient but not predictive. A technique switching finite elements into discrete particles at rupture is used to create debris and accumulated mater during the crushing of the structure. Switching criteria are evaluated using the contribution of the different ruin modes in the damage evolution, energy absorption, and reaction force generation.

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“…The problem is solved using the material point numerical method, which has previous been employed to model multiple cracking during impact of brittle materials . We have recently further extended the method for the analysis of sintering deformation and multiple cracking .…”

Section: De‐sintering and Healing Of A Cubic Defect In A Film Constramentioning

confidence: 99%

Defect Healing and Cracking in Ceramic Films During Constrained Sintering

Pan

Cocks

2012

J. Am. Ceram. Soc.

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Cracking is a major problem during constrained sintering of ceramic films. A local variation of density in a green film, referred to as a defect in this work, is the leading cause for cracking. This article presents analytical and numerical studies of the behavior of such defects during constrained sintering. An interesting behavior of de-sintering and healing of the defects is revealed. It is demonstrated that the healing process can be made to start earlier during sintering by using (a) larger particles, (b) lower sintering temperature, and (c) lower initial density. However, a uniform distribution of initial density in the film is shown to be the most effective means to avoid cracking. It is realized that most of the factors beneficial to defect healing are detrimental to sintering a film to high density because the driving force for sintering also drives cracking. The analytical and numerical studies also offer some simple explanations to why thin films are less susceptible to cracking than thick ones. Finally, the constitutive model has been combined with a simple empirical failure criterion, to simulate the initiation and propagation of multiple cracks in a sintering film. The cracking patterns predicted by the simulations resemble those observed during sintering experiments.

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Modelling brittle impact failure of disc particles using material point method

Cited by 31 publications

References 30 publications

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

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

Coupling continuous damage and debris fragmentation for energy absorption prediction by cfrp structures during crushing

Defect Healing and Cracking in Ceramic Films During Constrained Sintering

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