On the effective behavior of nonlinear inelastic composites: II A second-order procedure

International audienceA new method for determining the overall behavior of composite materials comprising nonlinear viscoelastic and elasto-viscoplastic constituents is presented. Part I of this work showed that upon use of an implicit time-discretization scheme, the evolution equations describing the constitutive behavior of the phases can be reduced to the minimization of an incremental energy function. This minimization problem is rigorously equivalent to a nonlinear thermoelastic problem with a transformation strain which is a nonuniform field (not even uniform within the phases). In part I of this paper the nonlinearity was handled using a variational (or secant) technique. In this second part of the study, a proper modification of the second-order procedure of Ponte Castañeda is proposed and leads to replacing, at each time-step, the actual nonlinear viscoelastic composite by a linear viscoelastic one. The linearized problem is even further simplified by using an “effective internal variable” in each individual phase. The resulting predictions are in good agreement with exact results and improve on the predictions of the secant model proposed in part I of this paper

Incremental variational principles with application to the homogenization of nonlinear dissipative composites

International audienceThis study is devoted to the overall response of nonlinear composites composed of phases which have a partly reversible and partly irreversible behavior, typically elasto-viscoplastic constituents. Upon use of an implicit time-discretization scheme, the evolution equations describing the constitutive behavior of the phases are reduced to the minimization of an incremental energy function. This minimization problem is rigorously equivalent to a nonlinear thermoelastic problem with a nonuniform transformation field. Two different techniques for approximating the nonuniform eigenstrains by piecewise uniform eigenstrains and for linearizing the nonlinear thermoelastic problem will be presented

On the effective behavior of nonlinear inelastic composites: I. Incremental variational principles.

International audienceA new method for determining the overall behavior of composite materials comprised of nonlinear inelastic constituents is presented. Upon use of an implicit time-discretization scheme, the evolution equations describing the constitutive behavior of the phases can be reduced to the minimization of an incremental energy function. This minimization problem is rigorously equivalent to a nonlinear thermoelastic problem with a transformation strain which is a nonuniform field (not even uniform within the phases). In this first part of the study the variational technique of Ponte Castaneda is used to approximate the nonuniform eigenstrains by piecewise uniform eigenstrains and to linearize the nonlinear thermoelastic problem. The resulting problem is amenable to simpler calculations and analytical results for appropriate microstructures can be obtained. The accuracy of the proposed scheme is assessed by comparison of the method with exact results

Variational estimates for the effective response and field statistics in thermoelastic composites with intra-phase property fluctuations

International audienceIn this work, variational estimates are provided for the macroscopic response, as well as for the first and second moments of the stress and strain fields, in thermoelastic composites with non-uniform distributions of the thermal stress and elastic moduli in the constituent phases. These estimates are obtained in terms of a 'comparison composite' with uniform phase properties depending on the first and second moments of a certain combination of the given intra-phase thermal stresses and modulus field distributions. Under certain hypotheses, these estimates can be shown to lead to upper and lower bounds for the free energy of the composite, which reduce to standard results when the intra-phase fluctuations vanish. An illustrative application is given for rigidly reinforced composites with a non-uniform distribution of the thermal stress in the matrix phase

Rupture de structures stratifiées avec concentrations de contraintes : apport du Volume Caractéristique de Rupture = Failure of laminated structures with stress concentrations : use of the Fracture Characteristic Volume

National audienceDans ce travail, nous présentons une approche pragmatique pour décrire la rupture de structures stratifiées en présence de gradient de contrainte. Si dans le cas de stratifiés soumis à un champ de déformation homogène, les critères de rupture classiques fonctionnent bien, ce n'est pas le cas pour les structures présentant des gradients de contraintes. Des méthodes de type ‘Average Stress' ou ‘Point Stress' permettent de décrire la rupture de structures avec concentrations de contraintes. Notre approche repose sur un Volume Caractéristique de Rupture (VCR) plus cohérent avec la zone rompue et plus adapté aux simulations numériques

Rupture en fatigue de structures composites stratifiés

National audienceUn modèle basé sur la mécanique continue de l'endommagement et un critère de rupture non local ont été développés pour étudier le comportement à rupture de structures stratifiées. Dans ce travail, le modèle développé précédemment dans le cas de chargements statiques a été étendu à la fatigue. Le modèle d'endommagement décrit les effets de la dégradation du composite dans des directions transversales et de cisaillement ainsi que les déformations anélastiques dans la direction de cisaillement. Le critère non local permet de décrire la rupture dans la direction des fibres en présence de concentrations de contrainte. Le modèle et le critère non local ont été étendus à la fatigue et implémentés dans Abaqus. Enfin, des exemples sont présentés dans le cas de stratifiés tissés déséquilibrés verre/époxy et de plaques trouées sous chargements cycliques de tension-tension

Analysis of inhomogeneous materials at large strains using fast Fourier transform

invited lecture at the IUTAM Symposium - Stuttgart 2001International audienceThis paper focuses on a numerical method which has been recently developed to analyze the response of highly inhomogeneous materials, often with complex microstructure. This numerical method is based on Fast Fourier Transforms and allows to make direct use of digital images of the ”real” microstructure in the numerical simulation. The case of elastic nonhomogeneous phases is reduced to an integral equation (Lippman- Schwinger equation) which is solved iteratively. A nice feature of the method is that it involves a multiplication in Fourier space, a multiplication in real space, a FFT and an inverse FFT. The two first operations can be easily parallelized. It has been extended to various nonlinear behaviours (elastoplasticity, phase transformations, 3d analysis of texture evolution in polycrystals). Our work has been mainly concentrated on providing reference results to assess the accuracy of theoretical estimates for nonlinear compos- ites with simple behaviours (ideally plastic or power-law materials)

Model reduction by mean-field homogenization in viscoelastic composites. II. Application to rigidly reinforced solids

The mean-field homogenization scheme proposed by Lahellec & Suquet (2007 Int. J. Solids Struct. 44, 507–529 (doi:10.1016/j.ijsolstr.2006.04.038)) and revisited in a companion paper (Idiart et al. 2020 Proc. R. Soc. A 20200407 (doi:10.1098/rspa.2020.0407)) is applied to random mixtures of a viscoelastic solid phase and a rigid phase. Two classes of mixtures with different microstructural arrangements are considered. In the first class the rigid phase is dispersed within the continuous viscoelastic phase in such a way that the elastic moduli of the mixture are given exactly by the Hashin–Shtrikman formalism. In the second class, both phases are intertwined in such a way that the elastic moduli of the mixture are given exactly by the Self-Consistent formalism. Results are reported for specimens subject to various complex deformation programmes. The scheme is found to improve on earlier approximations of common use and even recover exact results under several circumstances. However, it can also generate highly inaccurate predictions as a result of the loss of convexity of the free-energy density. An auspicious procedure to partially circumvent this issue is advanced.Centro Tecnológico Aeroespacia

Modélisation et expertise de la rupture de structures composites

La mécanique de l’endommagement continu peut décrire les endommagements diffus induits par de petites fissures parallèles à la direction des fibres. Nous proposons ici un modèle pour décrire la rupture dans le sens des fibres en statique et fatigue. Ce modèle repose sur une diminution de la résistance sens fibre pour des niveaux d’endommagement transverse élevés. Ce type de modélisation peut être intégré dans un code de calcul EF et utilisé pour l’expertise de structures composites rompues

ESTIMATING THERMOMECHANICAL RESIDUAL STRESSES IN FDM 3D PRINTED COMPOSITE PARTS

peer reviewedWe implemented a two-step methodology to estimate the residual stresses induced by the FDM manufacturing process in 3D printed composite parts. The first step consisted in an analytical thermo-viscoelastic homogenization procedure to derive the effective behavior of the filament. The second step consisted in a coupled thermomechanical structural analysis of the part. The homogenization procedure was assessed by comparing its predictions to full-field FFT-based computations. The structural analysis was assessed by comparing its predictions to experimental results