Gradient damage models: Toward full-scale computations

Lorentz, Éric; Godard, Vincent

doi:10.1016/j.cma.2010.06.025

Cited by 94 publications

(77 citation statements)

References 29 publications

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“…For this model, the damage profile can be obtained analytically in the case of uniaxial loading if the bar length is large enough so that the boundary conditions do not interfere with damage development and in the case of a prescribed displacement at both ends of the bar; this last hypothesis allows assuming a symmetrical solution for the localization band. This solution is a function of the material parameters except the elastic properties and of the maximum value of damage d max reached on the bar [25]. In is no damage.…”

Section: Fields Used In the Crack Path Searchmentioning

confidence: 99%

“…This law has been developed in the frame of the generalized standard materials (see [14] or [18]), extended to a gradient constitutive law, as shown in [23,25].…”

Section: A Brittle Gradient Damage Modelmentioning

confidence: 99%

“…In a first example, a brittle isotropic damage model is used; the regularization of the solution is obtained by enriching the formulation with the damage gradient [25]. In a second example, the Mazars' damage model [27] is employed in association with a nonlocal integral regularization.…”

Section: Continuum Models Used In the Examplesmentioning

confidence: 99%

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Topological search of the crack pattern from a continuum mechanical computation

Bottoni

Dufour

Giry

2015

Engineering Structures

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Section: Fields Used In the Crack Path Searchmentioning

confidence: 99%

“…This law has been developed in the frame of the generalized standard materials (see [14] or [18]), extended to a gradient constitutive law, as shown in [23,25].…”

Section: A Brittle Gradient Damage Modelmentioning

confidence: 99%

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Topological search of the crack pattern from a continuum mechanical computation

Bottoni

Dufour

Giry

2015

Engineering Structures

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“…When n = 2, there exists a limit value of fiber displacement before total failure and when n > 2, it takes an infinite displacement before total failure. It is interesting to note that these three regimes also exist in gradient damage models [20]. http://www.amses-journal.com/content/2/1/16…”

Section: Analysis Of the Displacement Of The Fibermentioning

confidence: 99%

Coupling local and non-local damage evolutions with the Thick Level Set model

Moës

Stolz

Chevaugeon

2014

Adv. Model. and Simul. in Eng. Sci.

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Background:The Thick Level Set model (TLS) is a recent method to delocalize local constitutive models suffering spurious localization. It has two major advantages compared to other delocalization methods. The first one is that the transition from localization to fracture is taken into account in the model. The second one is that the delocalization only acts when and where needed. In other words, the TLS has no effect when the local model is stable. The former advantage was already detailed in several papers (IJNME 86:358-380, 2011, CMAME 233:11-27, 2012, IJF 174:49-60, 2012). This paper concentrates on the latter advantage. Methods: The TLS delocalization approach is formulated as a bound on the damage gradient. The non-local zone is defined as the zone where the bound is met whereas the local zone is defined as the zone where it is not met. The boundary (localization front) between the local and non-local zone is the main unknown in the problem. Results: Based on the new model, a 1D pull-out test is solved both analytically and numerically. Different regimes are observed in the solution as the loading progresses: fully elastic, local damage, coupled local/non-local damage and, finally, purely non-local damage. Conclusions:The new model introduces delocalization as an inequality allowing local damage to develop in zones whereas non-local damage may develop in other zones. This reduces dramatically the cost of implementation of such models compared to fully non-local models.

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“…It is then presented in the form of computational recipes to enhance existing algorithms. This is for instance the case of the regularization strategy proposed for softening plasticity and damage in [9,[16][17][18][19] where the additional field equations and their coupling to the physical equations are postulated as PDEs independent of the specific form of the mechanical constitutive equations. By contrast, thermodynamically based formulations have been proposed where regularization differential operators are derived from new balance equations of generalized forces [20][21][22][23].…”

Section: Introductionmentioning

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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Gradient damage models: Toward full-scale computations

Cited by 94 publications

References 29 publications

Topological search of the crack pattern from a continuum mechanical computation

Topological search of the crack pattern from a continuum mechanical computation

Coupling local and non-local damage evolutions with the Thick Level Set model

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

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