A phase field model for cohesive fracture in micropolar continua

Suh, Hyoung Suk; Sun, WaiChing; O’Connor, Devin

doi:10.1016/j.cma.2020.113181

Cited by 44 publications

(14 citation statements)

References 67 publications

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“…Similar to [22], we attempt to employ a diffuse approximation for the sharp interface between two regions via implicit function. By adopting a phase field approach which is widely used in modeling fracture [3,14,23,24], we approximate the interfacial area as , which can be expressed in terms of volume integration of surface density over :…”

Section: Diffuse Representation Of Stokes-darcy Systemmentioning

confidence: 99%

An immersed phase field fracture model in fluid-infiltrating porous media with evolving Beavers-Joseph-Saffman condition

Suh

Sun

2020

E3S Web Conf.

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This study presents a phase field model for brittle fracture in fluid-infiltrating vuggy porous media. While the state-of-the-art in hydraulic phase field fracture considers Darcian fracture flow with enhanced permeability along the crack, in this study, the phase field not only acts as a damage variable that provides diffuse representation of cracks or cavities, but also acts as an indicator function that separates the domain into two regions where fluid flows are governed by Stokes and Darcy equations, respectively. Since the phase field and its gradient can be respectively regarded as smooth approximations of the Heaviside function and Dirac delta function, our new approach is capable of imposing interfacial transmissibility conditions without explicit interface parametrizations. In addition, the interaction between solid and fluid constituents is modeled by adopting the concept of mixture theory, where the fluid velocities in Stokes and Darcy regions are considered as relative measures compared to the solid motion. This model is particularly attractive for coupled flow analysis in geological materials with complex microstructures undergoing brittle fracture often encountered in energy geotechnics problems, since it completely eliminates the needs to generate specific enrichment function, integration scheme, or meshing algorithm tailored for complex geological features.

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Section: Diffuse Representation Of Stokes-darcy Systemmentioning

confidence: 99%

An immersed phase field fracture model in fluid-infiltrating porous media with evolving Beavers-Joseph-Saffman condition

Suh

Sun

2020

E3S Web Conf.

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“…Equal amount of displacement along and on top of the plate is applied by Dirichlet boundary conditions in order to displace the top 45 • tilted and cause a mixed mode crack analogous in the Iosipescu specimen [128]. The implementation is done by using Dirichlet boundaries for |  D = ( , ) with an amplitude = 0.01 mm leading to 0.1 mm in and directions after 10 s. Therefore, the results are comparable with results in [78] and the asymmetric start of the crack is devoted to the mixed mode loading as demonstrated in Figure 3.…”

Section: Simulationmentioning

confidence: 78%

“…Especially for the damage mechanism modeled by defining , there are different formulations in the literature [76]. We apply a so-called non-standard approach resulting in a diffusive localization band [77,78] by defining as follows:…”

Section: Damage In Brittle Materialsmentioning

confidence: 99%

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A novel phase‐field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable

et al. 2021

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Metamaterials response is generally modeled by generalized continuum based theories. Their inherent substructure leads to a necessity for higher-order theories, and especially in damage mechanics, such a generalization is difficult to acquire. We exploit the action formalism in order to obtain the governing equations in generalized damage mechanics for metamaterials. Additionally, by using auxilliary variables, the variational formulation is endowed with the first rate of damage variable that is missing in standard approaches. The presented action formalism with auxilliary variables leads directly to the weak form. We implement a finite element method based approach by using open-source computing platform called FEniCS and solve this weak in order to obtain the deformation and damage numerically. Metamaterials simulations are demonstrated for simple geometries in mixed mode (I and II) as well as in mode III.

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“…The coupled mechanics and phase field problems, for example, the deformation-twinning phase field problem 21 and the phase field fracture problem, [22][23][24][25][26][27] are usually solved in an alternating minimization way. The displacement field and the phase field are updated alternatively with fixing the other field until both residuals vanish eventually.…”

Section: Solution Techniques For Phase Field Models: Alternating Minimentioning

confidence: 99%

Phase field modeling of coupled crystal plasticity and deformation twinning in polycrystals with monolithic and splitting solvers

Sun

2020

Numerical Meth Engineering

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For some polycrystalline materials such as austenitic stainless steel, magnesium, TATB, and HMX, twinning is a crucial deformation mechanism when the dislocation slip alone is not enough to accommodate the applied strain. To predict this coupling effect between crystal plasticity and deformation twinning, we introduce a mathematical model and the corresponding monolithic and operator splitting solvers that couple the crystal plasticity material model with a phase field twining model such that the twinning nucleation and propagation can be captured via an implicit function. While a phase field order parameter is introduced to quantify the twinning induced shear strain and corresponding crystal reorientation, the evolution of the order parameter is driven by the resolved shear stress on the twinning system. To avoid introducing an additional set of slip systems for dislocation slip within the twinning region, we introduce a Lie algebra averaging technique to determine the Schmid tensor throughout the twinning transformation. Three different numerical schemes are proposed to solve the coupled problem, including a monolithic scheme, an alternating minimization scheme, and an operator splitting scheme. Three numerical examples are utilized to demonstrate the capability of the proposed model, as well as the accuracy and computational cost of the solvers.

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A phase field model for cohesive fracture in micropolar continua

Cited by 44 publications

References 67 publications

An immersed phase field fracture model in fluid-infiltrating porous media with evolving Beavers-Joseph-Saffman condition

An immersed phase field fracture model in fluid-infiltrating porous media with evolving Beavers-Joseph-Saffman condition

A novel phase‐field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable

Phase field modeling of coupled crystal plasticity and deformation twinning in polycrystals with monolithic and splitting solvers

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