LMA - Laboratoire de Mécanique et d’Acoustique

Theme Contact, friction, interfaces

The aim is to better understand contact interactions (that is, occurring on the boundary) between several solids. These interactions result in a rich phenomenology: friction, adhesion, squeal, jamming. The object of the analysis is to answer issues of fundamental nature, but also to provide rapid answers to more applied issues raised by big industrial companies. The approaches are theoretical, numerical and experimental.

Scientific objectives

  • Dynamics of rigid solids systems: development of a systematic and consistent formulation of dynamics involving contact and friction. Numerical approximations of the solutions and numerical analysis of the methods. Qualitative analysis of the dynamics. Study of stability, bifurcation, flutter in nonsmooth systems.
  • Linear elasticity and friction: existence and uniqueness of solution for the quasistatic evolution problem involving contact and friction. Definition and computation of the critical friction coefficient with respect to uniqueness. Development of the mathematical theory of jamming. Numerical approximation of the solutions and numerical analysis of the methods.
  • Derivation of new interface law: extension of asymptotic analysis of thin layers to the case of elastodynamics or nonelastic constitutive laws. Asymptotic analysis of the solutions and application to interface constitutive laws.
  • Development of efficient numerical methods for frictional contact and interfaces: multigrid, local defect correction, error estimates for contact, stabilized Nitsche.

Topics addressed

  • Homogenization of masonry structures.
  • Analysis of bifurcation in the coupling between dry friction and steady quasistatic elasticity.
  • Modeling and simulation of the dynamics of an aircraft tyre during landing.
  • Systematic formulation of rigid solids systems with dry friction. Analysis of the existence and uniqueness of a solution.
  • Experimental analysis of molecular adhesion in an adhesive assembly without glue.
  • Asymptotic analysis in elastodynamics of an isotropic homogeneous thin layer between two isotropic homogeneous half-spaces.

Contribution to socio-economical aspects

Development of specific applications

  • Aerospace engineering: Numerical computation of the stress field in a deformed tyre of an aircraft tyre during landing.
  • Nuclear energy: numerical modeling of the tablet/sheath interaction.


  • academic: Université de Pékin (Chine), Université de Ferrara, Université de Rome Tor Vergata, Université de Naples, Université de Cassino (Italie), Institut de Mathématiques de Prague (République Tchèque), Université de Picardie (LAMFA)
  • industrial: Airbus, Winlight Optics, CEA, CNES


Thomas COLLAS Frédéric LEBON Thiercelin Léo