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

Vicentini, F.; Zolesi, C.; Carrara, P.; Maurini, C.; De Lorenzis, L.

doi:10.1007/s10704-024-00763-w

Cited by 11 publications

(2 citation statements)

References 50 publications

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“…in which 𝑘𝑘 is a small parameter used for ensuring some residual stiffness as 𝛼𝛼 = 1, and both 𝜎𝜎 𝐷𝐷 and R σ represent the damageable and residual parts of the stress tensor. In particular, the so-called Cleavage-Deviatoric model proposed by Amor et al (2009) was reported by Vicentini et al (2024) to be able to exactly reproduce the behavior above mentioned as ℓ → 0. In particular, this model defines the damageable and residual parts of the stress tensor as:…”

Section: Particularization Of the Phase Field Fracture Model For Mana...mentioning

confidence: 88%

“…Such a feature renders implicit the PFM representation of a crack, hence potentially allowing any crack pattern, regardless of its complexity, to be represented over a certain non-conforming mesh. Furthermore, the PFM has been reported by Vicentini et al (2024) to be able to asymptotically reproduce unilateral contact conditions upon a proper choice of the function that modulates the stiffness based on the value of the phase field. Therefore, the PFM poses a powerful contender for assessing the residual behaviour of fractured glass components, in both PFLS I and PFLS II cases, especially when these are multiply fragmented.…”

Section: Introductionmentioning

confidence: 99%

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Phase Field Fracture Model for Assessing the Load Bearing Capacity of Fractured Glass

Corrado,

Chao Correas,

Ventura

2024

CGC

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The use of glass as structural material has highlighted the need for more reliable numerical approaches to analyze its mechanical behavior, especially in the accidental eventuality of fracture. Modelling the behavior of fractured laminated glass, in fact, is fundamental to assess the Post-Fracture load-bearing capacity. However, this is a highly challenging task because of the many interplaying factors, such as the viscoelastic and thermal-dependent behavior of the interlayer, the presence of a highly complex and variable crack pattern and the interaction among fragments. The objective of the present work is the development and testing of a robust numerical model that can naturally introduce the generated crack pattern into virtual specimens and manage the interaction among many fragments. The phase field fracture model is herein explored, by assigning the damage variable to fit the pre-existing crack pattern. Then, the specimen is loaded letting the phase field managing the fragments interaction. The dependence of the stress tensor with the damage variable is herein defined through the Cleavage-Deviatoric model, since it prevents fully damaged regions from transmitting tensile and shear stresses yet keeping their ability to bear compressive forces. Indeed, this model can asymptotically reproduce unilateral and frictionless contact conditions between the existing crack lips. Preliminary case studies are discussed to check the potentiality of the proposed approach.

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Section: Particularization Of the Phase Field Fracture Model For Mana...mentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Phase Field Fracture Model for Assessing the Load Bearing Capacity of Fractured Glass

Corrado,

Chao Correas,

Ventura

2024

CGC

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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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Simulating the onset of damage in DCDC tests using a novel gradient‐extended damage model for tension‐compression asymmetry

Zhang,

Reese

et al. 2024

Proc Appl Math and Mech

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In the present work, an existing framework for gradient‐extended damage is extended to simulate the damage onset in double cleavage drilled compression (DCDC) tests. The main idea is to consider the different evolution of the damage variable under tensile and compressive loading. More specifically, the star‐convex decomposition is exploited to split the strain energy into an active part and an inactive part, and only the active part drives the evolution of the damage variable in the compressive regime. A parameter adopted in the star‐convex decomposition is applied to calibrate the compressive strength independently from the tensile strength, such that the current model can simulate different types of the damage onset. Furthermore, the strengthening effect induced by damage hardening is discussed in this work.

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

Cited by 11 publications

References 50 publications

Phase Field Fracture Model for Assessing the Load Bearing Capacity of Fractured Glass

Phase Field Fracture Model for Assessing the Load Bearing Capacity of Fractured Glass

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

Simulating the onset of damage in DCDC tests using a novel gradient‐extended damage model for tension‐compression asymmetry

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