LMA - Laboratoire de Mécanique et d’Acoustique

Theme Micro-mechanics and scale transitions

Our research focuses on methods of multiscale modeling, in a broad sense, to describe the macroscopic behaviors of heterogeneous materials and interfaces. While the emphasis is put on theoretical aspects of the methods, applications to specific materials are also routinely addressed.

Scientific objectives

The overarching goal of the group is to contribute to methods pertaining to general classes of materials and structures. The research activities concern the following aspects:

  • Theoretical: To a large extent, the focus is made on homogenization methods. Insofar as possible, exact results are sought; this is the case for example when using incremental variational principles or studying stability properties of heterogeneous media. Alternatively, approximation methods are deployed (NTFA, effective internal variables) with the associated accuracy being analyzed.
  • Computational: The group has a long-standing experience on the numerical treatment of multiscale modeling problems. These activities involve finite element platforms (in-house codes or ABAQUS) as well as a Fourier transform-based method. The latter has been developed at LMA during the 90\’92s and it is currently employed in France and abroad by a number of research groups. Methods for optimizing the composition profile of thermo-elastic functionally graded materials are also developed.
  • Experimental: The investigated materials are mostly organic matrix composites and the main questions addressed revolve around studying damage processes under monotonic or cyclic loadings of uni-axial or multi-axial (tension-torsion) nature. Local measurements can be performed during the experiments: strain field measurements using digital image correlation, damage tracking using video imaging.

Topics addressed

  • Investigation of multiscale stability issues for elastomeric composites.
  • Development of incremental variational principles for the prediction of the effective behaviors of composite media or dissipative polycrystalline materials.
  • Non-uniform transformation fields analysis (NTFA).
  • Numerical simulations based on fast discrete Fourier transforms for micro-mechanical problems.
  • Optimization of the composition profile of thermo-elastic functionally graded materials.
  • Effective thermo-elastic properties: case of infinitesimal deformations but large temperature variations.
  • Modeling of the resistance of composite structures.
  • Monitoring and diagnosis of composite structures using measurements and modeling.
  • Micro-mechanical modeling of interfaces.

Contribution to socio-economical aspects

Development of specific applications

  • Nuclear energy: behavior and aging of nuclear fuel.
  • Aerospace engineering: monitoring and diagnosis of composite structures using measurements and modeling.



  • international:
    • Univ. Pennsylvania, Los Alamos National Laboratories, California Institute of Technology, Carnegie Mellon Univ., Stony Brook Univ., Michigan State Univ. (USA)
    • Delft Univ. of Technology (Pays-Bas)
    • Fraunhofer EZRT (Allemagne)
  • national:
    • LPMTM (Univ. Paris 13), LGGE (Univ. Joseph Fourier Grenoble), PIMM (ENSAM Paris), LMS (École Polytechnique)

National labs


Industrial partners

  • EDF, Eurocopter


Louis Joëssel Frédéric LEBON machado Maria Letizia RAFFA Pierre SUQUET