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Accueil du site > Equipes de recherche > Matériaux et Structures Architecturés (MSA) > Modélisation et changements d’échelle > Multiscale modeling

Multiscale modeling

Our team has long experience in model reduction techniques and multiscale modelling applied to structures. We develop models by means of variational approaches (Hellinger-Reissner formulation for instance), perturbative techniques (e.g. Asymptotic expansions), micromorphic approaches (Cosserat medium or higher order media from P. Germain). These models enable us to capture several microstructural effects such as : boundary layers, cracks, strain localization etc., where classical approaches fail.

Research Topics :

  • Composite laminated plates : Laminated plates are made of fiber reinforced composite layers stacked together. They are extremely difficult to model because of their strong anisotropy both in terms of stiffness but also of strength. Thus several families of models enable us to capture edge effects and stress singularities. We develop two main types of models : layerwize models and equivalent single layer models :
    • Layerwize models give a very detailed picture of the actual stress inside laminated plates. Edge effects are well captured and crack propagation criteria are suggested (Diaz Diaz, Caron & Ehrlacher 2007). MSA has also implemented a finite element version of these models including material non-linearities (e.g. plastic interfaces, see also : "renforcement" ).
    • We also extended rigorously to laminated and periodic plates the well-known Reissner-Mindlin model for thick plates(Lebee & Sab 2010). This model, which we call Bending-Gradient, was derived from asymptotic expansions and provides a very accurate and efficient estimation of transverse shear effects in thick plates. Hence we revisited in detail cellular sandwich panels theory (Lebee & Sab 2012) and we are currently applying it to numerous civil engineering applications such as orthotropic deck of cross laminated timbers.
  • Long term behavior of composites : Glass Fiber Reinforced Polymers (GFRP) show a complex long-term behavior that involves creep and progressive strength loss that has to be taken into account in structural applications with permanent loadings. A micromechanical model that considers the role of the viscous matrix and the progressive breakage of the fibers has been recently developed ( PhD thesis of N. Kotelnikova-Weiler defended in 2012 and PhD thesis of E. Dib started in 2013). This model enables the identification of the crucial micro-mechanisms that are related to macroscopic damage and creep and, by up-scaling, it allows the formulation of macroscopic models in the frame of continuum mechanics. The theoretical models in combination with creep experiments under controlled temperature performed in the laboratory help to improve our state of knowledge regarding the durability of pultruded composited structures, which are mainly used in construction (Nedjar 2011, Nedjar, Kotelnikova-Weiler & Ioannis Stefanou 2013,Kotelnikova-Weiler, Caron & Baverel 2013). MSA participates actively towards the establishment of the new Eurocode for composites.
  • Masonry structures : Masonry is a heterogeneous, composite material formed by regularly distributed bricks and mortar. Three scales may be distinguished in a masonry structure, i.e. the micro-scale, the meso-scale and the macro-scale, which should be taken into account in modeling (Cecchi & Sab 2002, Sab 2009, Stefanou, Sulem & Vardoulakis 2008, 2010). Micromechanical approaches (DEM, FEM) and approaches based on continuum mechanics (homogenization, model reduction, generalized continua) are used in order to model the non-linear behavior of masonry under dynamic excitations (PhD thesis of M.Godio started in 2012). Besides modern masonry structures, a considerable part of the European cultural heritage is made of masonry, which is situated in seismically active areas. The understanding of the dynamic behavior of these systems and the estimation of the seismic risk is very important for the preservation of our cultural heritage and the safety of tourists (Psycharis, Fragiadakis & Stefanou 2013).
  • Large deformations : We have a long term partnership with Arcelor-Mittal for developping a real time modelization of steel hot rolling by means of closed-form solutions including large deformations. Currently we focus on improving the contact modelling between the rolls and the workpiece including thermal effects (Patrault, Ehrlacher & Legrand 2012).
    Finally, multilayered organic elastomers were investigated in large deformations in order to model shoe soles (optimization of damping : Hung Ly, Alaoui, Erlicher & Baly 2010)
  • Multiscale approaches are also studied for modeling phase transformation in materials such as shape memory alloys.

Figures :
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Contraintes entre les couches et aux bords d’un composite troué (MPFEAP).
Interface stresses near a free edge in a crossply (MPFEAP).



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Distorsion de peaux d’un panneau sandwich à âme pliée sous l’effet de l’effort tranchant.
Out-of-plane skin distortion in folded core sandwich panel induced by shear forces.



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Contraintes de cisaillement dans un adhésif elastoplastique dans un assemblage collé en double recouvrement. Comparaison MPFEAP et 3D ABAQUS.
Shear stress history in the adhesive of a double lap shear test during load-unload cycles. MPFEAP and 3D ABAQUS results.



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Déformation plastique en cisaillement (glissement) : avant le chargement (à gauche) et après un cycle de chargement/déchargement.
Plastic sliding in an adhesive submitted to shear stress, before loading (left), after one cycle of loading/unloading (right) : plastic deformation is highlighted .



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Modélisation de la rupture des fibres dans un composite unidirectionnel sans prendre en compte (photo à gauche) et en prenant en compte la viscosité de la matrice (fluage, photo à droite).
Fiber breakage modeling of unidirectional composite with (creep, right) and without (left) taking into account the viscous behavior of the matrix.



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Bâti des essais de fluage en flexion quatre points sous température contrôlée.
Four-point bending creep test of pultruded beams under under controlled temperature.



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Rupture des briques (en rouge) dans un mur de maçonnerie soumis en cisaillement simple.
Block failure (in red) of a masonry wall under simple shear.



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Probabilité de ruine d’une colonne classique en fonction de la magnitude du séisme et de la distance de l’épicentre. La probabilité de ruine est très faible même pour des séismes forts.
Collapse probability of a classical column in function of the magnitude of an earthquake and the distance from the epicenter. The probability of collapse is low even for quite strong earthquakes (vidéo).



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Laminage aciers, évaluation des champs de contraintes de contact.
Steel rolling and evaluation of induced contact stresses.



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Représentation 3D des fractions volumiques dans un alliage à mémoire de forme (cas d’un matériau à 4 phases).
Three-dimensional representation of volumetric fractions in shape memory alloys (4-phase material).

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