A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach

Heister, Timo; Wheeler, Mary F.; Wick, Thomas

doi:10.1016/j.cma.2015.03.009

Cited by 351 publications

(369 citation statements)

References 38 publications

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“…Additionally, some of the challenges associated with a non-convex energy functional require careful developments as outlined and addressed in [7,14,15].…”

Section: Introductionmentioning

confidence: 99%

Numerical simulations of crack propagation in screws with phase-field modeling

Wick

Hellmig

et al. 2015

Computational Materials Science

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“…Additionally, some of the challenges associated with a non-convex energy functional require careful developments as outlined and addressed in [7,14,15].…”

Section: Introductionmentioning

confidence: 99%

Numerical simulations of crack propagation in screws with phase-field modeling

Wick

Hellmig

et al. 2015

Computational Materials Science

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“…< TOL GL − TOL Stag , which is stipulated by (44), (45), and the already prescribed above magnitudes of TOL GL and TOL Stag . Since the quantity η naturally stems from the global/local solution accuracy check E z (z n ; y) = 0, it represents not only the iterative convergence indicator, but also the solution accuracy indicator-a very desired property, since the former is only suitable for tracing the convergence of the corresponding iterative solution process, but, clearly, is not adequate for stopping criterion.…”

Section: Staggered Process For the Local Problemmentioning

confidence: 99%

“…Also, the finite element treatment of the phase-field formulation of brittle fracture is known to be computationally demanding, mainly due to the non-convexity of the energy functional to be minimized with respect to both arguments (the displacement and the phase field) simultaneously [45][46][47]. As a result, the so-called monolithic approach manifests major iterative convergence issues of the Newton-Raphson procedure.…”

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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“…A primal-dual active set strategy has been proposed by Heister et al [38] to enforce crack irreversibility as a constraint. An alternative approach has been suggested by Bourdin et al [39], in which Dirichlet boundary conditions are imposed on the phase field variable.…”

Section: Phase Field Model For Rate-dependent Ductile Fracturementioning

confidence: 99%

A Phase Field Model for Rate-Dependent Ductile Fracture

Badnava¹,

Etemadi

Msekh

2017

Metals

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Abstract:In this study, a phase field viscoplastic model is proposed to model the influence of the loading rate on the ductile fracture, as one of the main causes of metallic alloys' failure. To this aim, the effects of the phase field are incorporated in the Peric's viscoplastic model; the model can efficiently be converted to a standard rate-independent model. The novel aspects of this work include: Describing a coupling between rate-dependent plasticity and phase field formulation by defining an energy function that contains the energy dissipation caused by plastic deformation as well as the fracture process and elastic energy. In addition, the equations required to develop the numerical solution are presented. The governing equations are determined by a minimization principle that results in balance laws for the coupled displacement-phase field problem. Furthermore, an implicit integration algorithm for a viscoplasticity model coupled with a phase field is presented for a three-dimensional stress state. The proposed algorithm can be utilized for different constitutive models of rate-dependent and rate-independent plasticity models coupled with fracture by changing the definition of the plastic multiplier. In addition, to control the influence of the plastic deformation and its work on the crack propagation, a threshold variable is defined in the model. Finally, using the proposed model, the influence of the loading rate on the responses of the different specimens in one-dimensional and multi-dimensional cases is investigated and the accuracy of the results was verified by comparing them with existing experimental and numerical results. The obtained result proves that the model can simulate the impact of the loading rate on the material response, and the gradual change of the fracture phase from ductile to brittle, caused by increasing the loading rate.

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A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach

Cited by 351 publications

References 38 publications

Numerical simulations of crack propagation in screws with phase-field modeling

Numerical simulations of crack propagation in screws with phase-field modeling

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

A Phase Field Model for Rate-Dependent Ductile Fracture

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