Isotropic brittle damage and unilateral effect

This Note investigates the isotropic version of a general macroscopic model for brittle damage accounting for unilateral effects proposed by Welemane and Cormery (H. Welemane, F. Cormery, An alternative 3D model for damage induced anisotropy and unilateral effect in microcracked materials, J. Phys. IV 105 (2003) 329 13336). Built within a rigorous thermodynamic framework, the model uses a single scalar damage variable and accounts for the contribution of each set of parallel microcracks whether they are opened or closed. The consideration of unilateral effects allows to represent an anisotropic elastic behaviour induced by the closure of some microcracks and also the dissymmetric response in tension and compression which characterizes brittle materials

Microcracks closure effects in initially orthotropic materials

Microcracking is one of the basic mechanisms of inelastic deformation for a large class of anisotropic materials such as brittle matrix composites. Even at fixed microcracks density, the macroscopic behavior of these materials is very complex due to the combination of two specific features of such deteriorating phenomenon. First, the oriented nature of microcracks induces an evolution of the material symmetry (interaction between the initial anisotropy and the microcracks induced one). Secondly, a change in the elastic response of the material is expected, based on whether microcracks are open or closed in response to specific loading situations (the so-called “unilateral effect”). The present paper is devoted to a continuum micromechanics-based investigation of the resulting e generally fully e anisotropic multilinear response of orthotropic materials containing microcracks. The procedure leads to the proposal of a closed-form expression of the macroscopic free energy corresponding to 2D initially orthotropic materials weakened by arbitrarily oriented microcracks systems. The established results provide a complete quantification of both coupling effects of anisotropies and elastic moduli recovery phenomena induced by microcracks closure. A particular emphasis is put on the importance of Hill lemma for the derivation of these results which constitute a basis to the micro-macro modeling of damage process in initially orthotropic media

Micromechanical modeling of brittle damage in composite materials: primary anisotropy, induced anisotropy and opening-closure effects

Inelastic deformation of various brittle materials such as concrete, rocks or composites has been widely explained by the existence, nucleation and growth of microcracks. The oriented nature of these microdefects, coupled with the unilateral contact of their lips (i.e. microcracks can be either open or closed depending on loading), leads to a complex anisotropic behaviour notably characterized by a recovery of some effective properties at the closure of microcracks. For composite materials, the interaction of these both features with their primary (structural) anisotropy makes things even more complex. Experimental investigations through ultrasonic measures on ceramic matrix composites confirm the stiffness modifications due to degradation process, both on the amplitude (when loading axes correspond to initial material axes) and on the type of resulting material symmetry, especially in the case of off-axis loadings [3]. Concerning the unilateral effect, some authors have put in evidence the partial recovery of elastic properties at the closure of microcracks but these studies are often restricted to axial properties or to defects configurations coinciding with to the structural anisotropy of the material [1,8]. In terms of representation, the simultaneous description of the damage induced anisotropy and of the activation-deactivation process (the so-called unilateral effect) within a consistent modeling still remains a difficult and open research field, even in the context of initially isotropic materials. Indeed, mathematical or thermodynamical inconsistencies have been pointed out in existing formulations, such as discontinuities of the stress-strain response or non-uniqueness of the thermodynamic potential [4-5]. Concerning anisotropic microcracked materials, the analysis of their overall elastic properties is limited to configurations of open defects [6,7,9]. This paper aims to introduce a novel and original modeling approach for this problem within the framework of Continuum Damage Mechanics. In view of the lack of exhaustive experimental data on such aspects, we propose a micromechanics-based formulation of the resulting -generally fully- anisotropic multilinear response of orthotropic materials containing microcracks. On the basis of works by [2] for isotropic media, a strain-based homogenization approach is developed. This leads to a closed-form expression of the macroscopic free energy corresponding to 2D initially orthotropic materials weakened by arbitrarily oriented microcrack systems with account of closure effects. The consideration of such unilateral behavior constitutes one of the main contribution of the study. The explicit expressions obtained provide then a complete quantification of interaction effects both between primary and microcracks-induced anisotropies and between opening/closure states of cracks on the materials elastic properties. The thermodynamics framework finally gives a standard procedure for the formulation of the damage evolution law that ensures in all cases the verification of the thermodynamics second principle. Moreover, the association of the overall free energy expression derived with the standard evolution law introduces both oriented and closure effects due to microcracks in the material response and damage evolution. The model has been implemented within the finite-element code ABAQUS and various numerical simulations illustrate the representation capacities. Indeed, the formulation can account for the main features of brittle cracking kinetics, especially the load-induced anisotropy and the dissymmetry between initial damage thresholds in tension and compression

A micromechanical damage model for initially anisotropic materials

We propose a new model of brittle damage for initially orthotropic materials. The proposed strain energy-based formulation allows to account for the interaction between initial and induced anisotropies and to address the very challenging issue of opening-closure effects (unilateral behaviour). In order to derive the complete model including the damage growth, we take advantage of micromechanical developments suitably combined with the thermodynamics framework of the standard generalized materials. The model has been implemented within the finite-element code ABAQUS and various numerical simulations have been carried out to illustrate its predictive capabilities. In particular, emphasis is put on the evolution of the material symmetry and the influence of microcracks opening-closure states on the damage process

Caractérisation et modélisation de l'endommagement par microfissuration des composites stratifiés - Apports des mesures de champs et de l'homogénéisation

Ce travail porte sur l'endommagement des matériaux composites stratifiés utilisés notamment pour la réalisation de pièces structurales minces. La dégradation de ces matériaux induite par la création et le développement de surfaces de décohésion internes est abordée sous deux angles. Une campagne expérimentale a tout d'abord été menée sur des stratifiés en carbone-époxy réalisés par infusion de résine liquide et sollicités en traction uniaxiale. Cette étude propose une analyse originale à l'aide de trois techniques optiques permettant une caractérisation de l'endommagement par mesures de champs : cinématiques (par stéréo-corrélation d'images), thermiques (par thermographie infrarouge) et densimétriques (par tomographie à rayons X). Le second volet du travail concerne la modélisation de la microfissuration dans le contexte d'une anisotropie initiale. A cette fin, une homogénéisation bidimensionnelle de milieux orthotropes fissurés permet la prise en compte de défauts d'orientation arbitraire et des effets unilatéraux (ouverture-fermeture des microfissures) au sein d'une formulation énergétique en déformation. Sur cette base, un modèle de comportement est proposé dans le cadre de la thermodynamique des processus irréversibles avec variables internes. Des simulations numériques permettent de démontrer les capacités prédictives de la formulation, en particulier la représentation du comportement non linéaire de ces matériaux, l'interaction entre les anisotropies initiale et induite et la restitution des propriétés élastiques lors de la fermeture de défauts

Un modèle d’endommagement fragile pour les matériaux composites : couplage entre anisotropies initiale et induite et effets unilatéraux

Ce travail vise à présenter une nouvelle approche pour la modélisation de l’endommagement fragile des matériaux composites stratifiés. La formulation micromécanique proposée s’appuie sur une homogénéisation bidimensionnelle de milieux fissurés présentant une orthotropie initiale [1]. Cette démarche permet la prise en compte de défauts d’orientation arbitraire pouvant être ouverts ou fermés au sein d’une formulation énergétique en déformation. Sur cette base, un modèle de comportement est ensuite développé dans le cadre de la thermodynamique des processus irréversibles avec variables internes. En particulier, le cadre standard est retenu pour la formulation de la loi d’évolution des dommages. Des simulations numériques permettent de démontrer les capacités prédictives de la formulation, en particulier la représentation du comportement non linéaire des matériaux, l’interaction entre les anisotropies initiale et induite et la restitution des propriétés élastiques lors de la fermeture des défauts

Anisotropic unilateral damage with initial orthotropy: A micromechanics-based approach

A micromechanics-based damage model able to describe the brittle response of initially anisotropic materials is presented. A special emphasis is put on the account of damage-induced anisotropy and unilateral behaviour related to microcracks closure effects. These both features clearly influence the inelastic deformation of microcracked materials and lead to even more complex consequences in the context of initial anisotropy. The aim of this work is then to derive a new strain-based formulation which allows representing the related interactions between all these phenomena. This is achieved through a recent two-dimensional energy-based micromechanical analysis that accounts for the fully anisotropic multilinear response of orthotropic materials weakened by arbitrarily oriented microcracks. On the other hand, the thermodynamics framework gives a standard procedure for the development of the damage evolution law. Throughout the paper, attention is put on the mathematical and thermodynamical consistency of the model to avoid difficulties usually associated to the simultaneous description of damageinduced anisotropy and unilateral effects. In addition to elastic constants, the model requires the identification of only two parameters related to damage evolution. The model has been implemented within the commercial finite-element code ABAQUS, and various numerical simulations are presented to illustrate its capabilities. Especially, evolution of the material symmetry and influence of opening-closure states of microcracks on the damage process are illustrated in the case of brittle matrix composites subjected to different loading cases (axis and off-axis loads, tension and compression, tension followed by compression)

Brittle damage in initially anisotropic materials: a model accounting for the induced anisotropy and unilateral effects

A new micromechanical modelling approach for brittle damage in initially orthotropic materials is presented. The proposed strain-based energy formulation allows to derive a fully anisotropic multilinear model for microcracked materials with arbitrary oriented defects. The thermodynamics framework provides a standard procedure for the damage evolution law. The new model explicitly accounts for the interaction between primary and induced anisotropies. Moreover, the very challenging issue of opening-closure effects (unilateral behavior) is addressed in this framework

Cardiovascular Risk Evaluation in Patients with Critical Leg Ischemia before Vascular Surgery

Assessment of the role and investigation particularities (comparative and complementary aspects, hierarchies, preferential indication) adapted to the context of a global cardiovascular (CV) evaluation, including clinical elements, non-invasive and invasive imagistic examination in order to estimate the cardiovascular risk (CVR) and to define the revascularization therapeutic strategy in patients with critical leg ischemia (CLI). Complete and accessible evaluation involves accessible means of investigation like clinical exam, electrocardiogram, cardiac biomarkers, arterial, cardiac, and carotid ultrasonography which could be affordable in all cardiovascular departments. Non-invasive stress tests, coronary and arterial cervical angiography imaging leads in selected cases and where is possible to the identification of significant coronary and/or carotid lesions potential responsible for cardiac and cerebrovascular events after vascular surgery. The evaluation algorithm allows better risk stratification of patients with CLI in high and intermediate CVR. The “poly-arterial” status in patients with CLI changes the intervention management with a more intensive pre-operative medical treatment, while the coronary and the carotid arteries revascularization might precedes the peripheral arterial revascularization procedures, in order to reduce the CV risk status

Damage investigation in CFRP composites using full-field measurement techniques: combination of digital image stereo-correlation, infrared thermography and X-ray tomography

The present work is devoted to damaging process in carbon–fiber reinforced laminated composites. An original experimental approach combining three optical measurement techniques is presented. Image stereo-correlation and infrared thermography, that respectively provide the kinematic and thermal fields on the surface of the composites, are used in live recording during axis and off-axis tensile tests. Special attention is paid to simultaneously conduct these two techniques while avoiding their respective influence. On the other hand, X-ray tomography allows a post-failure analysis of the degradation patterns within the laminates volume. All these techniques are non-destructive (without contact) and offer an interesting full-field investigation of the material response. Their combination allows a coupled analysis of different demonstrations of same degradation mechanisms. For instance, thermal events and densimetric fields show a random location of damage in the early stages of testing. The influence of the material initial anisotropy on damage growth, localization and failure mode can also be clearly put in evidence through various data. In addition to such characterization, this study illustrates at the same time the capabilities of the different full-field techniques and the damage features they can best capture respectively