Elastoplastic-damage modelling including the gradient of damage: formulation and computational aspects

This paper describes the formulation of an implicit gradient damage model for ÿnite strain elastoplasticity problems including strain softening. The strain softening behavior is modeled through a variant of Lemaitre's damage evolution law. The resulting constitutive equations are intimately coupled with the ÿnite element formulation, in contrast with standard local material models. A 3D ÿnite element including enhanced strains is used with this material model and coupling peculiarities are fully described. The proposed formulation results in an element which possesses spatial position variables, nonlocal damage variables and also enhanced strain variables. Emphasis is put on the exact consistent linearization of the arising discretized equations.A numerical set of examples comparing the results of local and the gradient formulations relative to the mesh size in uence is presented and some examples comparing results from other authors are also presented, illustrating the capabilities of the present proposal. ?

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“…Further discussion of diagnostic and remedies for this behavior have been addressed in Refs. [9,2,10,40,12,8,1,41], for example.…”

Section: Constitutive Equations For Elastoplasticity Including Isotromentioning

confidence: 99%

“…Both these works, although in di erent contexts, use an implicit gradient model (see also Ref. [9] for a small strain brittle case and [10] for the small strain elastoplastic case).…”

Section: Introductionmentioning

confidence: 99%

A gradient model for finite strain elastoplasticity coupled with damage

Areias

Sá

Curnis

2003

Finite Elements in Analysis and Design

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“…Similar works linking gradient damage with plasticity (c.f. Nedjar [28]), as well assuming large deformation (c.f. Aslan et al [29], Saanouni and Hamed [30], and references cited therein), have been previously published in the literature.…”

Section: Introductionmentioning

confidence: 99%

A phase-field/gradient damage model for brittle fracture in elastic–plastic solids

Duda

Ciarbonetti

Sánchez

et al. 2015

International Journal of Plasticity

210

106

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The formulation of a phase-field continuum theory for brittle fracture in elastic-plastic solids and its computational implementation are presented in this contribution. The theory is based on a virtual-power formulation in which two additional and independent kinematical descriptors are introduced, namely the phase-field and the accumulated plastic strain. Further, it incorporates irreversibility of both phase-field and plastic strain evolutions by introducing suitable constraints and by carefully heeding the influence of those constraints on the kinetics underlying microstructural changes associated with plasticity and fracture.The numerical implementation employs the finite-element method for spatial discretization and a splitting scheme with sub-stepping for the time integration. To illustrate its potential utility, we apply the model to a number of well known linear, as well as non-linear, fracture mechanics problems.The described phase-field model, coupled with plasticity, provides a feasible technique to analyzing crack initiation and the subsequent crack growth resistance only if the length scale parameter included in the phase-field model is finite and treated as a material parameter which should be properly characterized.

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“…Since the local action (ii) and the material simplicity (iv) (see Section 2.1) are not necessarily satisfied and their relevance is therefore questionable [27], the nonlocal continuum theory can be used to integrate the weighted averages [28] and higher-order gradients of state variables, such as the observable variables (strain, temperature) or internal variables (characteristic of the dissipative processes under consideration) [12,29]. Gradient theories are therefore widely used to model the localization of the strain and damage in a large class of solid materials [30][31][32][33][34][35][36][37][38][39].…”

Section: Nonlocal Approach: Gradient Modelling With the Temperature Amentioning

confidence: 99%

On a New Kinetic Modelling Approach of the Irreversible Quasi-Surface Metallurgical Phase Transformations

Antoni

2014

Journal of Solid State Physics

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Irreversible quasi-surface metallurgical phase transformations are the specific response of some metallic materials-such as metals and alloys-subjected to high thermomechanical loads applied very near their surface during the manufacturing processes or after being put into operation. These solid/solid phase transformations can be observed, for example, on the tread of many rails in railroad networks frequented by freight trains. The severe thermal and mechanical loads imposed on the surface of the rails and in the immediate vicinity of the surface by the wheel/rail contact often result in highly localized irreversible metallurgical transformations. A new kinetic model based on a previous study is presented here, which accounts more realistically for the nucleation and growth of these irreversible solid/solid phase transformations resulting from high thermomechanical loads. This metallurgical behavioral model was developed in the framework of continuum thermodynamics with gradients of temperature and internal variables.

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Elastoplastic-damage modelling including the gradient of damage: formulation and computational aspects

Cited by 92 publications

References 12 publications

A gradient model for finite strain elastoplasticity coupled with damage

A gradient model for finite strain elastoplasticity coupled with damage

A phase-field/gradient damage model for brittle fracture in elastic–plastic solids

On a New Kinetic Modelling Approach of the Irreversible Quasi-Surface Metallurgical Phase Transformations

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