A phase-field crack model based on directional stress decomposition

2019

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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.

Section: Introductionmentioning

confidence: 99%

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

Qinami

Pandolfi

2019

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“…In Strobl and Seelig and Steinke and Kaliske, an idealized discrete model for the crack with contact is considered (Figure 5). Isotropic, linear elasticity and small deformations are assumed.…”

Section: Crack Kinematics Of Phase‐field Formulations For Fracturementioning

confidence: 99%

“…The introduction of a crack orientation is not unique and requires a concept, also for its evolution and irreversibility. The models in Section 2, which rely on the information about the crack orientation, use one of the following three approaches: direction of phase‐field gradient, maximum absolute principle stress direction, direction by principle of maximum dissipated energy …”

Section: Crack Irreversibility and Crack Orientationmentioning

confidence: 99%

The concept of representative crack elements for phase‐field fracture: Anisotropic elasticity and thermo‐elasticity

Storm

Supriatna

2019

Summary The realistic representation of material degradation at a fully evolved crack is still one of the main challenges of the phase‐field method for fracture. An approach with realistic degradation behavior is only available for isotropic elasticity in the small deformation framework. In this paper, a variational framework is presented for the standard phase‐field formulation, which allows to derive the kinematically consistent material degradation. For this purpose, the concept of representative crack elements (RCE) is introduced to analyze the fully degraded material state. The realistic material degradation is further tested using the self‐consistency condition, where the behavior of the phase‐field model is compared to a discrete crack model. The framework is applied to isotropic elasticity, anisotropic elasticity and thermo‐elasticity, but not restricted to these constitutive formulations.

“…This problem does not exist for the quadratic degradation function Equation due to

\frac{\partial g false(d false)}{\partial d} {false|}_{d = 0} = - 2

. In order to achieve more brittle fracture without the initial perturbation of the phase‐field, the exponential function

g false(d, β false) = \frac{\exp false(β \cdot d false) - false(β \cdot d + false(1 - β false) false) \cdot \exp false(β false)}{false(β - 1 false) \cdot \exp false(β false) + 1}

is studied, where the parameter β is introduced in order to control the shape of the degradation function. A comparison of the aforementioned degradation functions is shown in Figure .…”

Section: Phase‐field Model For Quasi‐viscous Fracturementioning

confidence: 99%

“…Another approach is proposed by Miehe et al, where the strain tensor is spectrally decomposed and the tensile energy is identified for the driving force. A recent approach considers the crack's orientation to define the driving stress and the corresponding driving strain potential …”

Section: Introductionmentioning

confidence: 99%

Formulation and implementation of strain rate‐dependent fracture toughness in context of the phase‐field method

Yin

Steinke

2019

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Summary The phase‐field approach is a promising technique for the realistic simulation of brittle fracture processes, both in quasi‐static and transient analysis. Considering fast loading, experimental evidence indicates a strong relationship between the rate of strain and the material's resistance against fracture, which can be considered by a dynamic increase factor for the strength of the material. The paper at hand presents a novel approach within the framework of phase‐field models for brittle fracture. A rate‐dependent fracture toughness is formulated as a function of the rate of crack driving strain components, which results in higher strength for faster loading. Beside the increased amount of energy necessary to evolve a crack at a high strain rate loading situation, the model incorporates quasi‐viscous stress‐type quantities that are not directly related to the formation of the crack and exist only in the phase‐field transition zone between broken and sound material. The governing strong form equations for a transient simulation are derived and the relevant information for an implementation of the model into a finite element code is outlined in detail. The performance of the model is demonstrated for static and dynamic benchmark simulations and for a comparison to experimental findings.