Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids

Miehé, Christian; Schänzel, Lisa‐Marie; Ulmer, Heike

doi:10.1016/j.cma.2014.11.016

Cited by 523 publications

(259 citation statements)

References 44 publications

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“…Following Miehe et al [27,28] and Borden et al [29], to mimic the irreversibility of the crack, a strain-history field H R is introduced as a substitution of ψ e+ R , which satisfies the Kuhn-Tucker conditions…”

Section: Governing Equationsmentioning

confidence: 99%

Phase-field study of electrochemical reactions at exterior and interior interfaces in Li-ion battery electrode particles

Zhao

Stein

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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To study the electrochemical reaction on surfaces, phase interfaces, and crack surfaces in the lithium ion battery electrode particles, a phase-field model is developed, which describes fracture in large strains and anisotropic Cahn-HilliardReaction. Thereby the concentration-dependency of the elastic properties and the anisotropy of diffusivity are also considered. The implementation in 3D is carried out by isogeometric finite element methods in order to treat the high order terms in a straightforward sense. The electrochemical reaction is modeled through a modified Butler-Volmer equation to account for the influence of the phase change on the reaction on exterior surfaces. The reaction on the crack surfaces is considered through a volume source term weighted by a term related to the fracture order parameter. Based on the model, three characteristic examples are considered to reveal the electrochemical reactions on particle surfaces, phase interfaces, and crack surfaces, as well as their influence on the particle material behavior. Results show that the ratio between the timescale of reaction and the diffusion can have a significant influence on phase segregation * Corresponding author

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Section: Governing Equationsmentioning

confidence: 99%

Phase-field study of electrochemical reactions at exterior and interior interfaces in Li-ion battery electrode particles

Zhao

Stein

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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“…We mention the papers by Amor et al [7], Miehe et al [8,9], Kuhn and Müller [10], Pham et al [11], Borden et al [12], Mesgarnejad et al [13], Kuhn et al [14], Ambati et al [15], Wu et al [16], where various formulations are developed and validated. Recently, the framework has been also extended to ductile (elasto-plastic) fracture [17][18][19][20][21][22], pressurized fracture in elastic and porous media [23,24], fracture in films [25] and shells [26][27][28], and multi-field fracture [29][30][31][32][33][34][35][36]. Non-intrusive global/local approaches have also been applied to a quite large number of situations: the computation of the propagation of cracks in a sound model using the extended finite element method (XFEM) [37], the computation of assembly of plates introducing realistic non-linear 3D modeling of connectors [38], the extension to non-linear domain decomposition methods [39] and to explicit dynamics [40,41] with an application to the prediction of delamination under impact using Abaqus [42].…”

Section: Introductionmentioning

confidence: 99%

A non-intrusive global/local approach applied to phase-field modeling of brittle fracture

Gerasimov

Noii

Allix

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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This paper aims at investigating the adoption of non-intrusive global/local approaches while modeling fracture by means of the phase-field framework. A successful extension of the non-intrusive global/local approach to this setting would pave the way for a wide adoption of phase-field modeling of fracture, already well established in the research community, within legacy codes for industrial applications. Due to the extreme difference in stiffness between the global counterpart of the zone to be analized locally and its actual response when undergoing extensive cracking, the main foreseen issues are robustness, accuracy and efficiency of the fixed point iterative algorithm which is at the core of the method. These issues are tackled in this paper. We investigate the convergence performance when using the native global/local algorithm and show that the obtained results are identical to the reference phase-field solution. We also equip the global/local solution update procedure with relaxation/acceleration techniques such as Aitken's 2 -method, the Symmetric Rank One and Broyden's methods and show that the iterative convergence can be improved significantly. Results indicate that Aitken's 2 -method is probably the most convenient choice for the implementation of the approach within legacy codes, as this method needs only tools already available for the so-called sub-modeling approach, a strategy routinely used in industrial contexts.

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“…To introduce a phenomenologically motivated damage behavior [7], the crack driving force D s in Eq. (2) 1 is taken independent of the deviatoric strain.…”

Section: Governing Equations Of the Phase Field Approachmentioning

confidence: 99%

Simulation of Hertzian cone cracks using a phase field description for fracture

Strobl

Morand

Seelig

2016

Proc Appl Math and Mech

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The present contribution focuses on fracture caused by indentation loading on the surface of a brittle solid. Its theoretical prediction is a challenging task due to the fact that crack nucleation is not geometrically induced, but is caused by the stress concentration in the contact near-field. The application of the phase field model requires constitutive assumptions to ensure a tension-compression asymmetric material response and prevent damage in compressed regions. This is achieved at the cost of giving up the variational concept of brittle fracture. We simulate the indentation of a cylindrical flat-ended punch on brittle materials like silicate glass. In order to reduce the numerical effort, we exploit axisymmetric conditions for the finite element formulation. After crack initiation stable propagation of a cone crack can be observed in good agreement with experiments. Indentation fractureThe occurrence of cone cracks under indentation loading has already been described by Hertz [1] in 1881: When a cylindrical stiff punch is pressed against the surface of a brittle elastic solid a circular crack is spontaneously initiated around the contact area. Under further loading this initial ring crack grows into a cone, the so called Hertzian cone crack. The growth at this stage is stable since the radius of the cone extends with the evolving crack. A particular challenge is to compute the crack initiation from the defect-free surface. The initial crack starts some distance outside of the indenter, as known from experiments [2]. Previous studies (e.g. [3]) modeled pre-existing ring cracks in order to investigate the further progress of the cone crack. The spontaneous formation of the ring crack is a non-standard problem of fracture mechanics which requires to take strength σ c and toughness G c into account, e.g. [4]. Thus the phase field approach appears to be well suited to handle such a problem since it also comprises both parameters. Furthermore, the method does not require any assumptions concerning the unknown location of the crack initiation or crack path. Governing equations of the phase field approachPhase field models have already proven their excellent ability to reproduce situations with complex crack patterns including initiation and the determination of unknown crack paths. For the smeared description of a crack in a linear elastic body Ω, with mass density ρ and external boundary ∂Ω = ∂Ω t ∪ ∂Ω u , an additional scalar field S(x, t) is introduced to describe the state of the material between the fully broken state S = 0 and undamaged material S = 1. Thereby the crack surface energy, including Griffith's critical energy release rate G c , is approximated by a smooth function with a small regularization parameter ℓ which is related to the width of the transition zone between both states. In order to obtain the coupled Euler-Lagrange equations for dynamic brittle fracture we employ Hamilton's principle. With the choice of a quadratic degradation function, which describes the loss of stiffness in damaged ...

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Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids

Cited by 523 publications

References 44 publications

Phase-field study of electrochemical reactions at exterior and interior interfaces in Li-ion battery electrode particles

Phase-field study of electrochemical reactions at exterior and interior interfaces in Li-ion battery electrode particles

A non-intrusive global/local approach applied to phase-field modeling of brittle fracture

Simulation of Hertzian cone cracks using a phase field description for fracture

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