Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments

Amor, Hanen; Marigo, Jean‐Jacques; Maurini, Corrado

doi:10.1016/j.jmps.2009.04.011

Cited by 1,215 publications

(807 citation statements)

References 55 publications

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“…This is typically done by splitting the elastic energy density into 2 additive parts related to tension Ψ + and compression Ψ − , respectively, and degrading only Ψ + by (s 2 + k). Different splitting approaches are possible, either by considering the principal strain direction (Miehe et al, 2010) or via a decomposition of the strain energy in volumetric and deviatoric components (Amor et al, 2009), see Ambati et al (2015) for a more detailed discussion. The extension to poroelastic media is possible (Miehe et al, 2015;Mikelic et al, 2015;Lee et al, 2016;Wilson and Landis, 2016), although details in the regularization differ among the various published approaches.…”

Section: Phase Field Methodsmentioning

confidence: 99%

Numerical methods for hydraulic fracture propagation: A review of recent trends

Lecampion

Bunger

Zhang

2018

Journal of Natural Gas Science and Engineering

350

172

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Section: Phase Field Methodsmentioning

confidence: 99%

Numerical methods for hydraulic fracture propagation: A review of recent trends

Lecampion

Bunger

Zhang

2018

Journal of Natural Gas Science and Engineering

350

172

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“…Dissipative higher order contributions remain to be explored from the viewpoint of regularization, as started in [21]. Constitutive models of that kind are already available for plasticity, damage and fracture [101,102]. The gradient of the anisotropic norm is calculated in a similar way:…”

Section: Resultsmentioning

confidence: 99%

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Forest¹

2016

Proc. R. Soc. A.

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International audienceThe construction of regularization operators presented in this work is based on the introduction of strain or damage micromorphic degrees of freedom in addition to the displacement vector and of their gradients into the Helmholtz free energy function of the constitutive material model. The combination of a new balance equation for generalized stresses and of the micromorphic constitutive equations generates the regularization operator. Within the small strain framework, the choice of a quadratic potential w.r.t. the gradient term provides the widely used Helmholtz operator whose regularization properties are well known: smoothing of discontinuities at interfaces and boundary layers in hardening materials, and finite width localization bands in softening materials. The objective is to review and propose nonlinear extensions of micromorphic and strain/damage gradient models along two lines: the first one introducing nonlinear relations between generalized stresses and strains; the second one envisaging several classes of finite deformation model formulations. The generic approach is applicable to a large class of elastoviscoplastic and damage models including anisothermal and multiphysics coupling. Two standard procedures of extension of classical constitutive laws to large strains are combined with the micromorphic approach: additive split of some Lagrangian strain measure or choice of a local objective rotating frame. Three distinct operators are finally derived using the multiplicative decomposition of the deformation gradient. A new feature is that a free energy function depending solely on variables defined in the intermediate isoclinic configuration leads to the existence of additional kinematic hardening induced by the gradient of a scalar micromorphic variable

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“…Numerical experiments illustrate that setting 2h ∼ still gives reasonable results. However, the computed surface energy will be slightly overestimated [28,45].…”

Section: Phase-field Model For Thin Shellmentioning

confidence: 96%

Phase-field modeling of fracture in linear thin shells

Amiri

Millán

Shen

et al. 2014

Theoretical and Applied Fracture Mechanics

285

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We present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximumentropy (LME) meshfree method. Since the crack is a natural outcome of the analysis it does not require an explicit representation and tracking, which is advantage over techniques as the extended finite element method that requires tracking of the crack paths. The geometric description of the shell is based on statistical learning techniques that allow dealing with general point set surfaces avoiding a global parametrization, which can be applied to tackle surfaces of complex geometry and topology. We show the flexibility and robustness of the present methodology for two examples: plate in tension and a set of open connected pipes.

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Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments

Cited by 1,215 publications

References 55 publications

Numerical methods for hydraulic fracture propagation: A review of recent trends

Numerical methods for hydraulic fracture propagation: A review of recent trends

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Phase-field modeling of fracture in linear thin shells

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