A variational formulation for nonlocal damage models

Lorentz, Éric; Andrieux, Stéphane

doi:10.1016/s0749-6419(98)00057-6

Cited by 111 publications

(89 citation statements)

References 27 publications

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“…For instance, in the context of plastic fracture mechanics, [9] proposed to deÿne an energy release rate which relies on such an energetic property. Another example is the non-local extension of constitutive laws [10] to deal with scale e ects and strain localization. As it is also based on this energetic property, a framework is available to derive ÿnite strain non-local constitutive laws, which can prove to be an adequate way to model ductile fracture.…”

Section: Resultsmentioning

confidence: 99%

“…The integration of this constitutive relation, i.e. solving the non-linear system (10), is now classical, see again Reference [5] Based on the integration procedure described in Table I and the integration formula (20), von Mises plasticity for ÿnite strain is introduced into the ÿnite element software Code Aster J . The stress state and the cumulated plastic strain are reported in for ÿve Gauss points whose location, labelled from 1 to 5, are deÿned in Table II and Figure 1.…”

Section: Numerical Applicationmentioning

confidence: 99%

See 1 more Smart Citation

A minimization principle for finite strain plasticity: incremental objectivity and immediate implementation

Lorentz

Cano

2002

Commun. Numer. Meth. Engng.

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SUMMARYA ÿnite strain plasticity formulation is proposed which meets several requirements that often appear contradictory. On a physical ground, it is based on a multiplicative split of the deformation, hyperelasticity for the reversible part of the behaviour and the maximal dissipation principle to deÿne the evolution laws. On a numerical ground, it is incrementally objective and the integration over a time increment can be expressed as a minimization problem, a proper framework to examine the questions of existence and uniqueness of the solutions. Last but not least, the implementation is immediate since it relies on the same equations for ÿnite and inÿnitesimal transformations. Finally, the formulation is applied to von Mises plasticity with isotropic linear hardening and introduced in the ÿnite element software Code Aster J . The numerical computation of a cantilever beam shows that it leads to results in good agreement with those obtain with common approaches.

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Section: Resultsmentioning

confidence: 99%

Section: Numerical Applicationmentioning

confidence: 99%

A minimization principle for finite strain plasticity: incremental objectivity and immediate implementation

Lorentz

Cano

2002

Commun. Numer. Meth. Engng.

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“…Practically, in order to avoid the direct computation of Eq. (1) in a finite element framework, this expression can be substituted by an explicit gradient enhanced approximated solution as in [59] e.g., or by an implicit form preserving the high order accuracy. In the latter a non-local internal variable is computed through the resolution of a new boundary value problem.…”

Section: Anisotropic Non-local Gradient Modelmentioning

confidence: 99%

A study of composite laminates failure using an anisotropic gradient-enhanced damage mean-field homogenization model

Sket

Molina-Aldareguia

et al. 2015

Composite Structures

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The failure of carbon fiber reinforced epoxy laminates is studied using an anisotropic gradient-enhanced continuum damage model embedded in a mean-field homogenization scheme. In each ply, a homogenized material law is used to capture the intra-laminar failure. The anisotropy of the homogenized material model results from the homogenization method and from the reformulation of the non-local continuum damage theory to account for the material anisotropy. As a result the damage propagation direction in each ply is predicted with accuracy as compared to the experimental results, while the problems of losing uniqueness and strain localization, which occur in classical finite element simulations when strain softening of materials is involved, can be avoided. To model the delamination process, the hybrid discontinuous Galerkin/extrinsic cohesive law method is introduced at the ply interfaces. This hybrid method avoids the need to propagate topological changes in the mesh with the propagation of the delamination while it preserves the consistency and stability in the un-cracked interfaces. As a demonstration, open-hole coupons with different stacking sequences are studied numerically and experimentally. Both the intra-and inter-laminar failure patterns are shown to be well captured by the computational framework.

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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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A variational formulation for nonlocal damage models

Cited by 111 publications

References 27 publications

A minimization principle for finite strain plasticity: incremental objectivity and immediate implementation

A minimization principle for finite strain plasticity: incremental objectivity and immediate implementation

A study of composite laminates failure using an anisotropic gradient-enhanced damage mean-field homogenization model

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

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