Gradient damage models coupled with plasticity: Variational formulation and main properties

Alessi, Roberto; Marigo, Jean‐Jacques; Vidoli, Stefano

doi:10.1016/j.mechmat.2013.12.005

Cited by 169 publications

(159 citation statements)

References 25 publications

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“…A few very recent contributions deal with phase-field modelling of fracture in ductile materials (see e.g. Ulmer et al, 2013;Borden, 2012;Duda et al, 2015;Ambati et al, 2015;Alessi et al, 2015;Wick et al, 2015). Most relevant for the present investigation is the phase-field model for quasi-static ductile fracture proposed by Ambati et al (2015) for classical J 2 -plasticity in a kinematically linear framework and later extended by Ambati et al (2016) to large deformations and by Ambati and De Lorenzis (2016) to modelling of fracture in shells.…”

Section: Introductionmentioning

confidence: 99%

Phase‐field modelling of fracture in single crystal plasticity

2016

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We propose a phase-field model for ductile fracture in a single crystal within the kinematically linear regime, by combining the theory of single crystal plasticity as formulated in Gurtin et al. (2010) and the phase-field formulation for ductile fracture proposed by Ambati et al. (2015) . The model introduces coupling between plasticity and fracture through the dependency of the so-called degradation function from a scalar global measure of the accumulated plastic strain on all slip systems. A viscous regularization is introduced both in the treatment of plasticity and in the phase-field evolution equation. Testing of the model on two examples for face centred cubic single crystals indicates that fracture is predicted to initiate and develop in the regions of the maximum accumulated plastic strain, which is in agreement with phenomenological observations. A rotation of the crystallographic unit cell is shown to affect the test results in terms of failure pattern and corresponding global and local response.

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Section: Introductionmentioning

confidence: 99%

Phase‐field modelling of fracture in single crystal plasticity

2016

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“…In this section, we briefly recall the ingredients and the main results of the gradient damage model coupled with plasticity presented in [4,5]. The model is developed in a rate-independent framework.…”

Section: The Formulation Of a Gradient Damage Model Coupled With Plasmentioning

confidence: 99%

“…The yield function of the damage field in the regular domain includes a gradient term, while the yield function of the damage field in the singular domain establishes the relation between the displacement jump, through the singular part of the plastic strain field, and the jump of the derivative of the damage field. The explicit derivation of these laws can be found in [4,5]. The reader is also referred to [56,58,3,2,6? ]…”

Section: Evolution Lawsmentioning

confidence: 99%

“…A more general class of models for coupling damage and plasticity has been presented and analysed in [4,5]. These works introduce the regularisation only on the damage variable, through a gradient term penalised by an internal material length, while keeping plasticity local and allowing the development of sharp plastic localisations.…”

Section: Introductionmentioning

confidence: 99%

“…In Sec. 2, the main ingredients of the gradient damage-plasticity model of [4,5] are recalled. We deduce within a variational framework the evolution laws, where the displacement and the gradient of damage fields are allowed to be discontinuous in space.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples

Alessi

Marigo

Maurini

et al. 2018

International Journal of Mechanical Sciences

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104

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Plasticity and damage are two fundamental phenomena in nonlinear solid mechanics associated to the development of inelastic deformations and the reduction of the material stiffness. Alessi et al. [4] have recently shown, through a variational framework, that coupling a gradient-damage model with plasticity can lead to macroscopic behaviours assimilable to ductile and cohesive fracture. Here, we further expand this approach considering specific constitutive functions frequently used in phase-field models of brittle fracture. A numerical solution technique of the coupled elastodamage-plasticity problem, based on an alternate minimisation algorithm, is proposed and tested against semi-analytical results. Considering a one-dimensional traction test, we illustrate the properties of four different regimes obtained by a suitable tuning of few key constitutive parameters. Namely, depending on the relative yield stresses and softening behaviours of the plasticity and the damage criteria, we obtain macroscopic responses assimilable to (i) brittle fracturè a la Griffith, (ii) cohesive fractures of the Barenblatt or Dugdale type, and (iii) a sort of cohesive fracture including a depinning energy contribution. The comparisons between numerical and analytical results prove the accuracy of the proposed numerical approaches in the considered quasi-static time-discrete setting, but they also emphasise some subtle issues occurring during time-discontinuous evolutions.

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