Phase-field finite deformation fracture with an effective energy for regularized crack face contact

Hakimzadeh, Maryam; Agrawal, Vaibhav; Dayal, Kaushik; Mora-Corral, Carlos

doi:10.1016/j.jmps.2022.104994

Cited by 5 publications

(2 citation statements)

References 55 publications

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“…The magnitude of the crack vector field encapsulates the degree of damage at a material point, while its orientation reflects that of the crack face normal at that point. An independent vector-valued field representing the crack-face normal as a fundamental kinematic ingredient in a PDE model of fracture was introduced in Acharya (2018); Steinke et al (2019), and is beginning to be used (Morin and Acharya 2021;Hakimzadeh et al 2022;Steinke et al 2022). The dislocation and crack-tip velocity fields are relative velocities of the motion of the dislocation density field α and the crack-tip field t, respectively, w.r.t.…”

Section: Governing Equations: Mechanicsmentioning

confidence: 99%

Coupled dislocations and fracture dynamics at finite deformation: model derivation, and physical questions

Acharya

2024

J Mater. Sci: Mater. Theory

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Section: Governing Equations: Mechanicsmentioning

confidence: 99%

Coupled dislocations and fracture dynamics at finite deformation: model derivation, and physical questions

Acharya

2024

J Mater. Sci: Mater. Theory

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“…This idea is adopted in Royer-Carfagni 2010, 2011;De Lorenzis and Maurini 2022;Navidtehrani et al 2022), justified through structured deformation theory. Other contributions are inspired by anisotropic materials (van Dijk et al 2020;He and Shao 2019;Vu et al 2022), propose cohesive fracture Lorentz (2017), introduce plasticity (Ulloa et al 2022;You et al 2020;Fei and Choo 2021) or propose an explicit treatment of the crack direction (Hakimzadeh et al 2022;Steinke and Kaliske 2019;Storm et al 2020). Unfortunately, the available variational models implicitly prioritize either nucleation or propagation, and (as we will show in this paper, at least for the most popular ones) none of them can describe both aspects correctly without introducing excessive complexity with respect to the original model.…”

Section: Introductionmentioning

confidence: 99%

On the energy decomposition in variational phase-field models for brittle fracture under multi-axial stress states

Vicentini,

Zolesi,

Carrara

et al. 2024

Int J Fract

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Phase-field models of brittle fracture are typically endowed with a decomposition of the elastic strain energy density in order to realistically describe fracture under multi-axial stress states. In this contribution, we identify the essential requirements for this decomposition to correctly describe both nucleation and propagation of cracks. Discussing the evolution of the elastic domains in the strain and stress spaces as damage evolves, we highlight the links between the nucleation and propagation conditions and the modulation of the elastic energy with the phase-field variable. In light of the identified requirements, we review some of the existing energy decompositions, showcasing their merits and limitations, and conclude that none of them is able to fulfil all requirements. As a partial remedy to this outcome, we propose a new energy decomposition, denoted as star-convex model, which involves a minimal modification of the volumetric-deviatoric decomposition. Predictions of the star-convex model are compared with those of the existing models with different numerical tests encompassing both nucleation and propagation.

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Phase‐Field Modeling of Fracture Under Compression and Confinement in Anisotropic Geomaterials

Hakimzadeh,

Mora‐Corral,

Walkington

et al. 2024

Num Anal Meth Geomechanics

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Strongly anisotropic geomaterials, such as layered shales, have been observed to undergo fracture under compressive loading. This paper applies a phase‐field fracture model to study this fracture process. While phase‐field fracture models have several advantages—primarily that the fracture path is not predetermined but arises naturally from the evolution of a smooth non‐singular damage field—they provide unphysical predictions when the stress state is complex and includes compression that can cause crack faces to contact.Building on a recently developed phase‐field model that accounts for compressive traction across the crack face, this paper extends the model to the setting of anisotropic fracture. The key features of the model include the following: (1) a homogenized anisotropic elastic response and strongly anisotropic model for the work to fracture; (2) an effective damage response that accounts consistently for compressive traction across the crack face, that is derived from the anisotropic elastic response; (3) a regularized crack normal field that overcomes the shortcomings of the isotropic setting, and enables the correct crack response, both across and transverse to the crack face.To test the model, we first compare the predictions to phase‐field fracture evolution calculations in a fully resolved layered specimen with spatial inhomogeneity, and show that it captures the overall patterns of crack growth. We then apply the model to previously reported experimental observations of fracture evolution in laboratory specimens of shales under compression with confinement, and find that it predicts well the observed crack patterns in a broad range of loading conditions. We further apply the model to predict the growth of wing cracks under compression and confinement. Prior approaches to simulate wing cracks have treated the initial cracks as an external boundary, which makes them difficult to apply to general settings. Here, the effective crack response model enables us to treat the initial crack simply as a nonsingular damaged zone within the computational domain, thereby allowing for easy and general computations.

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Phase-field finite deformation fracture with an effective energy for regularized crack face contact

Cited by 5 publications

References 55 publications

Coupled dislocations and fracture dynamics at finite deformation: model derivation, and physical questions

Coupled dislocations and fracture dynamics at finite deformation: model derivation, and physical questions

On the energy decomposition in variational phase-field models for brittle fracture under multi-axial stress states

Phase‐Field Modeling of Fracture Under Compression and Confinement in Anisotropic Geomaterials

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