Cohesive Fracture in 1D: Quasi-static Evolution and Derivation from Static Phase-Field Models

Bonacini, Marco; Conti, Sergio; Iurlano, Flaviana

doi:10.1007/s00205-020-01597-1

Cited by 7 publications

(2 citation statements)

References 44 publications

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“…where e(u) denotes the approximate symmetric gradient of u. In this respect, we mention results on compactness and lower semicontinuity [5,12,16,15,27,30,43], Ambrosio-Tortorelli approximations [11,13,14,23,33], dimension reduction, homogenization, atomistic derivation, and nonlocal approximations [1,3,6,10,26,28,31,38,40,41,42], linearization in elasticity [2,24,25], and modeling of fracture, epitaxially strained films, and stress-driven rearragnement instabilities [19,22,29,34]. The common feature of the above mentioned works is that the underlying ambient space is of euclidean type.…”

Section: Introductionmentioning

confidence: 99%

A new proof of compactness in G(S)BD

Almi

Tasso

2022

Advances in Calculus of Variations

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We prove a compactness result in GBD {\operatorname{GBD}} which also provides a new proof of the compactness theorem in GSBD {\operatorname{GSBD}} , due to Chambolle and Crismale. Our proof is based on a Fréchet–Kolmogorov compactness criterion and does not rely on Korn or Poincaré–Korn inequalities.

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Section: Introductionmentioning

confidence: 99%

A new proof of compactness in G(S)BD

Almi

Tasso

2022

Advances in Calculus of Variations

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“…This phase-field approximation of this scalar cohesive fracture was investigated numerically in [FI17]. A 1D cohesive quasistatic evolution (not prescribing the crack path) is presented in [BCI21] and related to the phase-field models of [CFI16]. A different approximation of (1.2), still in the scalar-valued framework, is obtained in [DMOT16] using elasto-plastic models.…”

Section: Introductionmentioning

confidence: 99%

Phase-field approximation of a vectorial, geometrically nonlinear cohesive fracture energy

Conti,

Focardi,

Iurlano

2022

Preprint

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We consider a family of vectorial models for cohesive fracture, which may incorporate SO(n)-invariance. The deformation belongs to the space of generalized functions of bounded variation and the energy contains an (elastic) volume energy, an openingdependent jump energy concentrated on the fractured surface, and a Cantor part representing diffuse damage. We show that this type of functional can be naturally obtained as Γ-limit of an appropriate phase-field model. The energy densities entering the limiting functional can be expressed, in a partially implicit way, in terms of those appearing in the phase-field approximation.

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On a phase‐field model of damage for hybrid laminates with cohesive interface

Bonetti

Cavaterra

Freddi

et al. 2021

Math Methods in App Sciences

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In this paper, we investigate a rate‐independent model for hybrid laminates described by a damage phase‐field approach on two layers coupled with a cohesive law governing the behaviour of their interface in a one‐dimensional set‐up. For the analysis, we adopt the notion of energetic evolution, based on global minimisation of the involved energy. Due to the presence of the cohesive zone, as already emerged in literature, compactness issues lead to the introduction of a fictitious variable replacing the physical one which represents the maximal opening of the interface displacement discontinuity reached during the evolution. A new strategy which allows to recover the equivalence between the fictitious and the real variable under general loading–unloading regimes is illustrated. The argument is based on time regularity of energetic evolutions. This regularity is achieved by means of a careful balance between the convexity of the elastic energy of the layers and the natural concavity of the cohesive energy of the interface.

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Cohesive Fracture in 1D: Quasi-static Evolution and Derivation from Static Phase-Field Models

Cited by 7 publications

References 44 publications

A new proof of compactness in G(S)BD

A new proof of compactness in G(S)BD

Phase-field approximation of a vectorial, geometrically nonlinear cohesive fracture energy

On a phase‐field model of damage for hybrid laminates with cohesive interface

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