MoFEM: An open source, parallel finite element library

Kaczmarczyk, Łukasz; Ullah, Zahur; Lewandowski, Karol; Meng, Xuan; Zhou, Xiaochao; Athanasiadis, Ignatios; Nguyen, Hoang Thai; Chalons-Mouriesse, Christophe-Alexandre; Richardson, E.; Miur, Euan; Shvarts, Andrei G.; Wakeni, Mebratu F.; Pearce, CJ

doi:10.21105/joss.01441

Cited by 31 publications

(23 citation statements)

References 15 publications

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“…Two main numerical techniques are used in practice to solve the mechanical problem and find the phase-field topology: the monolithic (fully coupled) [31,32,33,34,35,36] and the staggered (weakly coupled) [27,30,37,38,39] scheme. Monolithic algorithms usually converge when the initial estimate is close to the equilibrium solution.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, we controlled the time step automatically to detect unstable propagation and reduce the change in the external loading. Since the first introduction of the method, numerous open-source implementations were proposed [32,44,39,33]. For a detailed overview on the history the reader is referred to the work of Bourdin [45].…”

Section: Introductionmentioning

confidence: 99%

“…Effective fracture toughness measured using the dynamic stress intensity factor as a function of the crack tip velocity. The simulated data are fitted using eq (33)…”

mentioning

confidence: 99%

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An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation

Molnár

Gravouil

Seghir

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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Brittle and ductile dynamic fracture in solids is a complex mechanical phenomenon which attracted much attention from both engineers and scientists due to its technological interests. Modeling cracks in dynamic cases based on a discontinuous description is difficult because it needs additional criteria for branching and widening. Due to the very short time scales and the spatial complexity of the dynamic problem, its experimental analysis is still very difficult. Therefore, researchers still have to rely on numerical simulations to find a deeper explanation for many observed phenomena. This study is set out to investigate the effect of plasticity on dynamic fracture propagation. On the other hand, the diffuse phase-field formulation makes it possible to initiate, propagate, arrest or even branch cracks while satisfying the basic principles of thermodynamics. An implicit, staggered elastoplastic version of the phase-field approach was implemented in the commercial finite element code Abaqus through the UEL option. By means of simple examples we show that localized ductile deformations first increase both resistance and toughness. Then, after a maximum value, the resistance starts to decrease with a significant increment in energy dissipation. By favoring shear deformation over tensile failure the fracture pattern changes. First the branching disappears, then the crack propagation angle changes and becomes a shear band. Finally, we observed the increment of the instantaneous dynamic stress intensity factor during the acceleration stage of the crack without introducing a rate dependent critical fracture energy. We explained this phenomenon with the increasing roughness of the fracture surface.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation

Molnár

Gravouil

Seghir

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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“…This process involves only limited changes to the volume elements, since it is restricted to the elements immediately surrounding the crack. In addition, higher-order and p -adaptive elements based on a hierarchical approximation basis framework [39,40] are adopted. Not only does this permit local enhancement of the approximation, it also mitigates the occasional existence of distorted elements in the mesh.…”

Section: Finite-element Modellingmentioning

confidence: 99%

A computational framework for crack propagation in spatially heterogeneous materials

Lewandowski

Kaczmarczyk

Athanasiadis

et al. 2021

Phil. Trans. R. Soc. A.

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This paper presents a mathematical formulation and numerical modelling framework for brittle crack propagation in heterogeneous elastic solids. Such materials are present in both natural and engineered scenarios. The formulation is developed in the framework of configurational mechanics and solved numerically using the finite-element method. We show the methodology previously established for homogeneous materials without the need for any further assumptions. The proposed model is based on the assumption of maximal dissipation of energy and uses the Griffith criterion; we show that this is sufficient to predict crack propagation in brittle heterogeneous materials, with spatially varying Young’s modulus and fracture energy. Furthermore, we show that the crack path trajectory orientates itself such that it is always subject to Mode-I. The configurational forces and fracture energy release rate are both expressed exclusively in terms of nodal quantities, avoiding the need for post-processing and enabling a fully implicit formulation for modelling the evolving crack front and creation of new crack surfaces. The proposed formulation is verified and validated by comparing numerical results with both analytical solutions and experimental results. Both the predicted crack path and load–displacement response show very good agreement with experiments where the crack path was independent of material heterogeneity for those cases. Finally, the model is successfully used to consider the real and challenging scenario of fracture of an equine bone, with spatially varying material properties obtained from CT scanning. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

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“…In the second and third studies, uncertainties in textile composites due to the variations are evaluated through statistical and reliability analyses. The numerical implementation of the proposed method is carried out on MoFEM(Kaczmarczyk et al, 2017), which is an open source finite element analysis code. Noting the studies are for illustrative purposes, only in-plane fibre misalignment and waviness are shown, but out-of-plane counterparts can be easily adopted.…”

mentioning

confidence: 99%

Influence of stochastic variations in manufacturing defects on the mechanical performance of textile composites

Zhou

Gosling

2018

Composite Structures

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MoFEM: An open source, parallel finite element library

Cited by 31 publications

References 15 publications

An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation

An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation

A computational framework for crack propagation in spatially heterogeneous materials

Influence of stochastic variations in manufacturing defects on the mechanical performance of textile composites

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