H. Sabar

• École Nationale d'Ingénieurs de Metz

A time-incremental Eshelby-based homogenization scheme for Maxwellian heterogeneous materials is proposed and discussed. This is based on the exact solution of the heterogeneous Eshelby ellipsoidal inclusion problem obtained in the time domain. In contrast with hereditary methods, the effective behavior and the evolution laws of the averaged stress...

The present paper deals with the micromechanical modeling of the effective thermal conductivity of composite materials containing ellipsoidal inclusions with highly conducting interfaces. At these interfaces between inclusions and the surrounding medium, the temperature field is assumed continuous while the heat flux undergoes to a discontinuity. T...

In this work, a new micromechanical model is presented to determine the effective behavior of piezoelectric composite materials with ellipsoidal reinforcements and imperfect interfaces. The integral equation is obtained by the Green's function technique applied to the electroelastic heterogeneous problem. This integral equation is further solved in...

The present paper deals with the micromechanical modeling of the effective thermal conductivity of composite materials containing ellipsoidal inclusions with interfaces thermal resistance. At these interfaces between inclusions and the surrounding medium, the heat flux is assumed continuous while the temperature field undergoes to a discontinuity....

A coated inclusion-based homogenization scheme is developed for three-phase viscoelastic composites in the Laplace-Carson domain. The interphase between inclusion and matrix is considered as a coating in a composite-like inclusion and shows altered viscoelastic behavior compared to the matrix. The strain concentration equations between the viscoela...

In this work, a new micromechanical model to determine the effective elastic behavior of composite materials with ellipsoidal reinforcements and imperfect interfaces is developed. By using the Green's functions technique, the integral equation of the linear elastic medium is reformulated in the presence of imperfect interfaces. The integral equatio...

In this work, the effective elastic properties of composite materials with multi-coated reinforcements are estimated by a new formulation of the multi-inclusion model based on Green's functions technique and integral equation which gives the local strain and stress fields through strain concentration equations in each phase of the composite-inclusi...

This contribution is focused on the analysis of the interphase in applied short glass fiber reinforced thermoplastics. The interphase in fiber-matrix composites is defined as the intersection region with modified bulk material properties. Especially for FE simulations of composites and the validation of multi-scale material modeling approaches, the...

The interphase in applied fiber-matrix composites is defined as the intersection region with modified bulk material properties. Especially for FE simulations of composites and the validation of multi-scale material modeling approaches, the information about the existing interphase becomes important. In this study, the interphase thickness in a shor...

The interphase in applied fiber-matrix composites is defined as the intersection region with modified bulk material properties. Especially for FE simulations of composites and the validation of multi-scale material modeling approaches, the information about the existing interphase becomes important. In this study, the interphase thickness in a shor...

A new time-incremental internal variables homogenization scheme for Maxwellian linear viscoelastic heterogeneous materials is proposed. This scheme is based on the exact solution of the ellipsoidal Eshelby inclusion problem obtained in the time domain. In contrast with current existing methods, the effective behavior as well as the evolution laws o...

In this work, a homogenisation method for the prediction of the effective properties of composite materials with multi-coated reinforcements is presented. Based on Green’s function techniques as well as interior and exterior-point Eshelby tensors for an ellipsoidal inclusion embedded in an infinite medium, a new micromechanical approach applied to...

In this work, a new homogenization method to estimate the effective behavior of viscoelastic heterogeneous materials with multi-coated reinforcements is presented. Unlike classical methods that are based on the Laplace transform, the present internal variables formulation operates directly in the time domain. Using the Green’s function techniques,...

In this work, a new micromechanical model for the solution of the problem of coated inclusion embedded in an infinite homogeneous medium is presented. The method is based on the Green functions technique and the concept of the interior and exterior-point Eshelby tensors for an ellipsoidal inclusion. The proposed formulation is general and can be su...

In this study, the magnetoelectroelastic behavior is investigated for magnetic–piezoelectric composites with coated reinforcements under antiplane mechanical and in-plane electromagnetic loads. The coating is considered as a layer with properties different from those of the inclusion and the matrix. The developed model is based on the solution of t...

Dans ce travail, nous proposons une approche micromécanique de détermination des champs de déformation dans les différentes phases des matériaux contenant des inclusions sphériques enrobées noyées dans une matrice soumise à une déformation uniforme E imposée à l'infini. Basée sur les fonctions potentielles exprimant le tenseur d'Eshelby aussi bien...

In this work, a micromechanical model for the estimate of the magneto-electro-elastic behavior of the magnetic-piezoelectric composites with coated reinforcements is proposed. The coating is considered as a thin layer with properties different from those of the inclusion and the matrix. The micromechanical approach based on the Green’s functions te...

Study of effective behavior of heterogeneous materials, starting from the properties of the microstructure, represents a critical step in the design and modeling of new materials. Within this framework, the aim of this work is to introduce a general internal variables approach for scale transition problem in linear viscoelastic case. A new integral...

Predicting the overall behavior of heterogeneous materials, from their local properties at the scale of heterogeneities, represents a critical step in the design and modeling of new materials. Within this framework, an internal variables approach for scale transition problem in elastic–viscoplastic case is introduced. The proposed micromechanical m...

In this work, a micromechanical model for the estimate of the electroelastic behavior of the piezoelectric composites with coated reinforcements is proposed. The piezoelectric coating is considered as a thin layer with active electroelastic properties different from those of the inclusion and the matrix. The micromechanical approach based on the Gr...

Ce travail concerne la modélisation micromécanique du comportement des matériaux hétérogènes élastoviscoplastiques, en vue d'une application au cas des polymères recyclés et des alliages de polymères. Face à la lourdeur des approches de type héréditaire, on privilégie les approches à variables internes pour leur simplicité numérique. Dans ce cadre,...

The subject of this paper is identification of the physical mechanisms of spalling at low impact velocities for Ti–6Al–4V alloy and determination of the macroscopic stress of spalling via meso-macro approach. Spalling is a specific mode of fracture which depends on the loading history. The aspects of the initial microstructure and its evolution dur...

Pearlitic steel cords may reach a tensile strength up to 4 GPa [1]. This property is related to the process of cold drawing which reduces the size of the lamellar substructure, in proportion to the wire diameter (Embury's similitude principle [2]) and induces the formation of nanocrystalline and morphological textures.Using a multiscale transition...

In this paper we give a brief presentation of the approaches we have recently developed on the oxidation of metals. Firstly, we present an analytical model based on non-equilibrium thermodynamics to describe the reaction kinetics present during the oxidation of a metal. Secondly, we present the molecular dynamics results obtained with a code specia...

This work concerns dislocation microstructure analysis in order to assess stored elastic energy using Fourier coefficients of diffraction lines. These coefficients are related to the lattice distortion heterogeneity evaluated using a micromechanical approach. The lattice distortion formulation is based on dislocation density and Green's function te...

The goal of this work was to introduce a novel thermodynamic approach for the oxidation of metals, which has been developed by considering the methods of non-equilibrium thermodynamics. Our proposition allows the linking between some elementary mechanisms (e.g., diffusion, mechanics) for determining the evolution of the oxidation process of the sys...

In real heterogeneous materials, the simultaneous presence of instantaneous mechanisms (elasticity) and time dependent ones (non linear visco-plasticity) leads to a complex space-time coupling between the mechanical fields, difficult to represent in a simple and efficient way. In this work, a new micro-macro model is proposed, starting from the int...

The determination of the effective behavior of heterogeneous materials from the properties of the components and the microstructure constitutes a major task in the design of new materials and the modeling of their mechanical behavior. In real heterogeneous materials, the simultaneous presence of instantaneous mechanisms (elasticity) and time depend...

Viscoelastic (and elastoviscoplastic) heterogeneous materials are characterized by a strong space/time connection, which results in complex intergranular interactions whose effect has to be accounted for by the scale transition. Internal variable approaches require a complete mechanical formulation of the problem, since mechanical fields are coupl...

Actually, micromechanical approaches give only few references related to glide mechanisms in a lamella and especially load transfer mechanism between lamellae in pearlites. At large strains the concept of interphase barrier has to be introduced and considered as the determinant mechanism of hardening compared with the classical bulk work hardening....

Nanoscaled lamellar structures involve complex deformation behaviour at finite strain due to the preserve of a large number of interfaces. The aim of the work is to develop a micromechanical approach based on interfacial operators in the context of statistical continuum mechanics. Using Hill's formalism, constitutive equations at mesoscale (1 μm) a...

Based on projection operators, an integral formulation is proposed for elastoviscoplastic heterogeneous materials. The problem requires a complete mechanical formulation, including the static equilibrium property concerning the known field σ, in addition to the classical field equations concerning the unknown fields ɛ˙ and σ˙. The formulation leads...

Thermoelastic martensitic transformation can be controlled by external stress and/or temperature to produce the thermoelastic shape memory effect. The thermomechanical behavior of shape memory alloys has been modeled in the framework of continuum mechanics and micromechanics. Martensitic phase transformation in ductile materials, like iron-base all...

Based on the determination of the Helmholtz free energy and the dissipation of an elastoplastic solid containing moving surfaces of plastic strain discontinuity, we develop a micromechanical approach to study the formation of dislocation cell structure and their effects on the mechanical behavior of metals. The results are applied to an evolutive t...

The method of Bollmann has been used to determine the role of epitaxy in the formation of the mechanical stress field near the metal/oxide interface during the high temperature oxidation of zirconium. The strains due to epitaxy combine with those due to both oxygen diffusion in metal and thermal expansion of the metal/oxide composite in a model bas...

The aim of the presented model is to evaluate the mechanical stresses at the metal/oxide interface of an oxidized zirconium sample using a micromechanical formalism. This model takes into account three parameters which generate strains in the material : oxygen diffusion in the metal, thermal expansion and interfacial epitaxy. Oxygen diffusion and e...

The effect of a thin coating on the local fields and on the effective properties of composites is studied in this paper. The micromechanical approach is based on Green function techniques as well as on the interfacial operators and generalized to a non-homothetic topology. By using the classical self-consistent scheme we obtain the effective elasti...

The linear thermoelastic behavior of composites with coated inclusions is studied. The coating is considered as a thin layer with different thermomechanical properties from those of the inclusion and the matrix. The interactions between the reinforcements are deduced from a self-consistent scheme. The residual thermal stresses deduced from this mod...

Classical plasticity (dislocation motion) coupled to solid-solid phase transformation (lattice changes) is the primary cause of the special behaviour of TRIP (TRansformation Induced Plasticity) steels. Internal stresses associated with the phase change induces in fact a large additional plastic flow inside austenite and martensite. We propose a kin...

The transformation induced plasticity in steels is studied using a tangent micromechanical modelling. The modelization is based on a physical kinematic description of the transformation itself using the local Bain strain rate of martensite variants and their volume fractions. The local behavior of each phase being supposed to be known, a classical...

The effect of a thin coating on the local fields and on the effective properties of composites is studied in this paper. The micromechanical approach is based on the Green function techniques as well as on the interfacial operators and generalized to a nonhomothetic topology. Using the classical self-consistent scheme we obtain the effective elasti...

Classical plasticity (dislocation motion) coupled to deformation due to lattice changes (phase transformation) occurs in several materials where interfaces are moving under external forces (TRIP (TRansformation Induced Plasticity) steels, even shape memory alloys). In the case of steels (transformation induced plasticity) the internal stress associ...

A micromechanical model using simultaneously Green's function techniques and interfacial operators is proposed in order to solve the elastic inhomogeneous inclusion problem. For a composite material made of a non dilute concentration of coated inclusions and a homogeneous matrix, the interactions between the reinforcements are solved by a self-cons...

A micromechanical model using Green functions techniques and interfaces operators is proposed in order to solve the elastically inhomogeneous coated inclusion problem. For a composite material made of a non dilute concentration of coated inclusions and an homogeneous matrix, the interaction between the reinforcements are solved by a self consistent...

The field equations in statics of polycrystalline materials constitued, for example, of martensitic and austenitic grains are described by use of Green’s functions taking into account inelastic and elastic heterogeneities. Now, question arises when looking at the evolution of inelasticity (phase transformation, ...) induced by external loading. The...

Phase transformations, recrystallisation, displacements of dislocation walls in a polycrystal or some others metallurgic phenomena show a common point due to interfaces sweeping with velocities differing from that of the constitutive particles like atoms. According to these observations, we extend the solution of inelastically strained inclusion pr...