Phase‐Field Fracture at Finite Strains Based on Modified Invariants: A Note on its Analysis and Simulations

Thomas, Marita; Bilgen, Carola; Weinberg, Kerstin

doi:10.1002/gamm.201730004

Cited by 7 publications

(7 citation statements)

References 54 publications

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“…Our numerical experience has shown, however, that different functions are arbitrary and so we set g 0 = g 1 , which also enables a sound mathematical analysis of the positive part of (43), cf. Thomas et al (2018). Energy function (43) can also be formulated with arguments J, tr(F ) and cof(F ) and, thus, it is polyconvex in the mechanical deformation for any value of phasefield z.…”

Section: Variational Crack-driving Forces In Finite Elasticitymentioning

confidence: 99%

On the crack-driving force of phase-field models in linearized and finite elasticity

Bilgen

Weinberg

2019

Computer Methods in Applied Mechanics and Engineering

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The phase-field approach to fracture has been proven to be a mathematically sound and easy to implement method for computing crack propagation with arbitrary crack paths. Hereby crack growth is driven by energy minimization resulting in a variational crack-driving force. The definition of this force out of a tension-related energy functional does, however, not always agree with the established failure criteria of fracture mechanics. In this work different variational formulations for linear and finite elastic materials are discussed and ad-hoc driving forces are presented which are motivated by general fracture mechanical considerations. The superiority of the generalized approach is demonstrated by a series of numerical examples.

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Section: Variational Crack-driving Forces In Finite Elasticitymentioning

confidence: 99%

On the crack-driving force of phase-field models in linearized and finite elasticity

Bilgen

Weinberg

2019

Computer Methods in Applied Mechanics and Engineering

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“…Exemplarily, we formulate the strain energy function of the Mooney‐Rivlin material model

{normalΨ}^{e} false(Ī_{1}, Ī_{2}, J false) = {normalΨ}_{0}^{e} false(Ī_{1}, Ī_{2} false) + {normalΨ}_{vol} false(J false) = c_{1} false(Ī_{1} - 3 false) + c_{2} false(Ī_{2}^{3 false/ 2} - 3 \sqrt{3} false) + \frac{κ}{2} {false(J - 1 false)}^{2},

with the material constants c 1 , c 2 , the bulk modulus κ and the invariants

Ī_{1}

and

Ī_{2}

\overset{bold-italicC}{true}

. This strain energy density is based on the isochoric split of the deformation gradient, where the second term of the strain energy function has to be adapted slightly such that the strain energy function fulfils the requirements of a polyconvex function . More details about polyconvex terms and functions can be found in the literature .…”

Section: Phase‐field Fracture Modelingmentioning

confidence: 99%

“…We recommend to choose

\begin{matrix} alignleft \\ align-1 \frac{l_{c}}{M G_{c}} = O (Δ t) . & align-2 \end{matrix}

This is true for the ad hoc crack driving forces and the standard variational approach in a similar way. Another way to circumvent the choice of the mobility parameter might be decreasing the time step such that the influence of the mobility parameter becomes negligibly small …”

Section: Influence Of Various Parametersmentioning

confidence: 99%

A detailed investigation of the model influencing parameters of the phase‐field fracture approach

et al. 2019

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Phase-field approaches to fracture are gaining popularity to compute a priori unknown crack paths. In this work the sensitivity of such phase-field approaches with respect to its model specific parameters, that is, the critical length of regularization, the degradation function and the mobility, is investigated. The susceptibility of the computed cracks to the setting of these parameters is studied for problems of linear and finite elasticity. Furthermore, the convergence properties of different solution strategies are analyzed. Monolithic and staggered solution schemes for the solution of the arising nonlinear discrete systems are studied in detail. To conclude, we demonstrate the versatility of the phase-field fracture approach in a real-world problem by comparing different simulations of conchoidal fracture using structured and unstructured meshes. K E Y W O R D Scrack driving force, crack propagation, multilevel methods, phase-field fracture INTRODUCTIONCrack growth is associated with the creation of new internal surfaces of unknown size and evolution. In the literature different possibilities for simulating crack propagation can be found. Besides the cohesive zone model, [1][2][3] the extended finite element methods [4,5] or eigenfracture strategies [6] which allow for modeling the crack as a sharp interface, diffuse interface approaches gain more and more attention. More precisely, the phase-field model is becoming very popular and constitutes a reliable way to predict the crack path. [7][8][9] During the last decades phase-field methods are used to describe a number of topics, that is, thermodynamics, [10] hydraulic fracture, that is, in porous media, [11][12][13][14] ductile materials, [15,16] anisotropy, [17][18][19][20] contact problems, [21] and many more. Most of the phase-field approaches are based on the minimization of the total potential energy that leads to a crack driving force corresponding to Griffith's energy release rate. [22] However, the approach requires a detailed consideration of the fact that only tensile states are responsible for crack growth. One popular way to take this into account is to decompose the strain energy function into a positive and negative part which correspond to the tensile and compressive parts, respectively. [8,9,23] This is not always physically meaningful. Thus, crack driving forces motivated by established fracture criteria have also been introduced. [24] Nevertheless, the phase-field model depends on a series of parameters which influence the results, like the location of crack initialization. In this work we will investigate the influences of these parameters in more detail. In particular, the phase-field This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…Please note that the split is a modeling assumption, other splits result in different crack driving forces. This, in turn, influences the initiation and propagation of the cracks, for details see [2][3][4]. a Fig.…”

Section: Introductionmentioning

confidence: 99%

Phase‐field fracture simulations of a four‐point bending test

Bilgen

Schmidt

Weinberg

2021

Proc Appl Math & Mech

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Phase‐field fracture simulations have been established to simulate crack propagation in solid structures. The method employs a variational framework which has been proven to converge to Griffith' classical model for brittle fracture. Here we investigate the predictiveness of phase‐field fracture through a four‐point bending test in a mixed mode condition, and we discuss the possibilities to perform such simulation with the finite element software ABAQUS. The comparison with the experiments allows estimating the quality of the method with respect to failure loads, crack initiation angles, propagation path, and fracture surface.

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Phase‐Field Fracture at Finite Strains Based on Modified Invariants: A Note on its Analysis and Simulations

Cited by 7 publications

References 54 publications

On the crack-driving force of phase-field models in linearized and finite elasticity

On the crack-driving force of phase-field models in linearized and finite elasticity

A detailed investigation of the model influencing parameters of the phase‐field fracture approach

Phase‐field fracture simulations of a four‐point bending test

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