On the relation between phase-field crack approximation and gradient damage modelling

Steinke, Christian; Zreid, Imadeddin; Kaliske, Michael

doi:10.1007/s00466-016-1369-9

Cited by 34 publications

(21 citation statements)

References 25 publications

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“…The similarities to gradient-enhanced damage models [11] [12] [13] [14] [15] are obvious and highlighted in [16] and [17]. [1] was, according to the best of the authors' knowledge, the first to introduce phase-field modeling for fracture of rubbery polymers.…”

Section: Introductionmentioning

confidence: 95%

Rate-dependent phase-field damage modeling of rubber and its experimental parameter identification

Loew

Peters

Beex

2019

Journal of the Mechanics and Physics of Solids

102

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Phase-field models have the advantage in that no geometric descriptions of cracks are required, which means that crack coalescence and branching can be treated without additional effort. Miehe et al. [1] introduced a rate-independent phase-field damage model for finite strains in which a viscous damage regularization was proposed. We extend the model to depend on the loading rate and time by incorporating rubber's strain-rate dependency in the constitutive description of the bulk, as well as in the damage driving force. The parameters of the model are identified using experiments at different strain rates. Local strain fields near the crack tip, obtained with digital image correlation (DIC), are used to help identify the length scale parameter. Three different degradation functions are assessed for their accuracy to model the rubber's rate-dependent fracture. An adaptive time-stepping approach with a corrector scheme is furthermore employed to increase the computational efficiency with a factor of six, whereas an active set method guarantees the irreversibility of damage. Results detailing the energy storage and dissipation of the different model constituents are included, as well as validation results that show promising capabilities of rate-dependent phase-field modeling.

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Section: Introductionmentioning

confidence: 95%

Rate-dependent phase-field damage modeling of rubber and its experimental parameter identification

Loew

Peters

Beex

2019

Journal of the Mechanics and Physics of Solids

102

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“…Standard gradient damage models are regularly used to model failure . Even though, from the algorithmic and structural point of view, these models are similar to the variational approaches, the physical background is relatively different . A distinctive drawback of gradient damage models is the lack of the Γ‐convergence property.…”

Section: Introductionmentioning

confidence: 99%

“…[33][34][35] Even though, from the algorithmic and structural point of view, these models are similar to the variational approaches, the physical background is relatively different. 36 A distinctive drawback of gradient damage models is the lack of the Γ-convergence property. In this way, no minimizers are sought via the damage models, but just an extra boundary value problem is solved.…”

Section: Introductionmentioning

confidence: 99%

Variational eigenerosion for rate‐dependent plasticity in concrete modeling at small strain

Qinami

Pandolfi

Kaliske

2019

Numerical Meth Engineering

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Summary In the context of eigenfracture scheme, the work at hand introduces a variational eigenerosion approach for inelastic materials. The theory seizes situations where the material accumulates large amounts of plastic deformations. For these cases, the surface energy entering the energy balance equation is rescaled to favor fracture, thus energy minimization delivers automatically the crack‐tracking solution also for inelastic cases. The minimization approach is sound and preserves the mathematical properties necessary for the Γ‐limit proof, thus the existence of (local) minimizers is guaranteed by the Γ‐convergence theory. Although it is not possible to demonstrate that the obtained minimizers are global, satisfactory results are obtained with the local minimizers provided by the method. Furthermore, with the goal of addressing the constitutive behavior of concrete, a Drucker‐Prager viscoplastic consistency model is introduced in the microplane setting. The model delivers a rate‐dependent three‐surface smooth yield function that requires hardening and hardening‐rate parameters. The independent evolution of viscoplasticity in different microplanes induces anisotropy in the mechanical response. The sound performance of the model is illustrated via numerical examples for both rate‐independent and rate‐dependent plasticity.

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“…We want to note that coupling the extended finite element method (XFEM, [9], [10], [11]) with a cohesive zone model can deal with cracks not known in advance ( [12]). Phase-field models are similar to gradient-enhanced damage models ( [13], [14], [15]), as both rely on a length scale parameter to obtain mesh independent results ( [16], [17], [18]). Miehe and Schänzel [19] were the first to extend phasefield damage models to finite strains and rubber, while its extension to ratedependency, with experimental identification and validations can be found in [20].…”

Section: Introductionmentioning

confidence: 99%

Accelerating fatigue simulations of a phase-field damage model for rubber

Loew

Poh

Peters

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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Phase-field damage models are able to describe crack nucleation as well as crack propagation and coalescence without additional technicalities, because cracks are treated in a continuous, spatially finite manner. Previously, we have developed a phase-field model to capture the rate-dependent failure of rubber, and we have further enhanced it to describe failure due to cyclic loading. Although the model accurately describes fatigue failure, the associated cyclic simulations are slow. Therefore, this contribution presents an acceleration scheme for cyclic simulations of our previously introduced phase-field damage model so that the simulation speed is increased to facilitate large-scale simulations of industrially relevant problems. We formulate an explicit and implicit cycle jump method, which, depending on the selected jump size, reduces the calculation time up to 99.5%. To circumvent the manual tuning of the jump size, we also present an adaptive jump size selection procedure. Thanks to the implicit adaptive scheme, all material parameters are identified from experiments, which include fatigue crack nucleation and crack growth. Finally, the model and its parameters are validated with additional measurements of the fatigue crack growth rate.

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On the relation between phase-field crack approximation and gradient damage modelling

Cited by 34 publications

References 25 publications

Rate-dependent phase-field damage modeling of rubber and its experimental parameter identification

Rate-dependent phase-field damage modeling of rubber and its experimental parameter identification

Variational eigenerosion for rate‐dependent plasticity in concrete modeling at small strain

Accelerating fatigue simulations of a phase-field damage model for rubber

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