An alternative 3D model for damage induced anisotropy and unilateral effect in microcracked materials

A three-dimensional model of damage by microcrack growth is proposed to account for the mechanical behavior of quasi brittle materials (especially for concrete and rocks). The emphasis is put on the induced anisotropy and on the elastic moduli dependence on the opening and closure of microcracks (unilateral effect). This formulation is based first on a damage characterization throught the microcracked density distribution, and secondly avoids the use of spectral decompositions generally adopted in literature and which induce some major inconsistencies

Some remarks on the damage unilateral effect modelling for microcracked materials

This study deals with the macroscopic modelling of the mechanical behaviour of microcracked materials and particularly with the unilateral aspect of such damage which leads, at the closure of microcracks, to a partial damage deactivation. By means of a micromechanical analysis, the aim of this article is first to point out the influence of the opening-closure of microdefects on the effective elastic properties of a microcracked medium. According to these considerations, a new elastic moduli recovery condition at damage deactivation is proposed. The introduction of this condition within the anisotropic damage model proposed by Halm and Dragon, 1996 allows to extend its micromechanical background while preserving its main advantages, in particular the continuity of the stress-strain response and the symmetry of the stiffness tensor

A critical review of some damage models with unilateral effect

The concern here is the macroscopic modeling of the brittle damage unilateral effect (due to the opening-closure of microcracks). Several formulations have been proposed in recent years to solve the problems pointed out by Chaboche (Int. J. Damage Mech. 1 (1992) 148). In this paper, we examine precisely two of these new formulations (Int. J. Damage Mech. 2 (1993) 311; Int. J. Damage Mech. 5 (1996) 384) and show that they still exhibit some major inconsistencies

A stress-based macroscopic approach for microcracks unilateral effect

The question of the nonlinear response of brittle materials undergoing elastic damage is investigated here. Owing to the specific nature of microcracking, the macroscopic behaviour of these materials is complex, generally anisotropic owing to the possible preferential orientation of defects and multilinear because of the unilateral effect due to the transition between open and closed state of microcracks. A new three-dimensional macroscopic model outlined by Welemane and Cormery [1] has been proposed to account simultaneously for these both aspects. This paper intends to present in details the principles of such approach and to demonstrate its applicability to a stress-based framework. Based on a fabric tensor representation of the damage density distribution, the model provides a continuum and rigorous description of the contribution of defaults which avoids classical spectral decompositions and related inconsistencies. The model is also strongly micromechanically motivated, especially to handle the elastic moduli recovery that occurs at the closure of microcracks. The macroscopic theoretical framework proposed constitutes a general approach that leads in particular to predictions of a class of micromechanical models. The capacities of the approach are illustrated and discussed on various cases of damage configurations and opening 13closure states, with a special attention to the differences with the strain-based framework and to the influence of the damage variables order

Reliability analysis and micromechanics: A coupled approach for composite failure prediction

This work aims at associating two classical approaches for the design of composite materials: first, reliability methods that allow to account for the various uncertainties involved in the composite materials behaviour and lead to a rational estimation of their reliability level; on the other hand, micromechanics that derive macroscopic constitutive laws from micromechanical features. Such approach relies on the introduction of variabilities defined at the microscale and on the investigation of their consequences on the material macroscopic response through an homogenization scheme. Precisely, we propose here a systematic treatment of variability which involves a strong link between micro- and macroscales and provides a more exhaustive analysis of the influence of uncertainties. The paper intends to explain the main steps of such coupling and demonstrate its interests for material engineering, especially for constitutive modelling and composite materials optimization. An application case is developed throughout on the failure of unidirectional carbon fibre-reinforced composites with a comparative analysis between experimental data and simulation results

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

Basic concepts and models in continuum damage mechanics

In this paper, we present some basic elements of macroscopic modelling of damage. We then recall the general approach of continuum damage based on the thermodynamics of irreversible processes and its application to isotropic damage modelling. The study of damage induced anisotropy is treated by considering a second order tensorial damage variable. Finally, we present an original macroscopic approach through which is addressed the question of unilateral effects due to the microcracks closure

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

Identification of damaged zone in composite materials using displacement field measurements

This work presents an identification strategy of local elastic properties of orthotropic carbon-epoxy laminates for aviation industry. Based on global and local stages of study, this methodology uses the Finite Element Model Updating (FEMU) method as identification technique with simulated kinematic fields corresponding to tensile test response. The aim of this paper is to predict the spatial variation of elastic plane properties and to deduce the localization of damaged zones

A multi-level interface model for damaged masonry

The aim of the present work is to propose a new micro-mechanical model in the context of the deductive approach used to derive interface models. This model, based on a previous study introduced previously by A. Rekik and F. Lebon, is used to reproduce the damage in masonry by combining structural analysis and homogenization methods. The focal point of this method is to assume the existence of a third material, called interphase, which is a mixture of the two principal constituents of masonry, brick and mortar, and that is the interface between them. This new element presents a low thickness, a low stiffness and a given damage ratio. The mechanical problem of masonry, initially a 3D problem, is solved numerically as a 2D problem using finite element methods. The properties of the interface brick-mortar material are obtained using three essentials steps. First of all, an exact homogenisation of a laminates is used to define a first homogeneous equivalent medium named HEM-1. After, the assumption of damaged material is taken into account by using the general framework given by M. Kachanov to evaluate the global behaviour of the damaged HEM-1 defining thus a second equivalent homogeneous medium noted HEM-2. The last step consists in using an asymptotic analysis technique which is performed to model HEM-2 as an interface or a joint. The properties of this joint are deduced from those of the HEM-2 material as proposed in former papers. Particularly, through the second homogenization are taken into account the variability of microcracks oriented family and simultaneously the opening-closure effects (unilateral behaviour). Numerically this interface is modelled with connector finite elements. Numerical results are compared to experimental ones available in the literature