Dispersion of elastic waves in Second Gradient Continuum : A geometric approach

Propagation of elastic wave within linear elastic continuum is classically governed by the famous Navier equation when the matter is assumed homogeneous. In the case where the density varies smoothly, the model still applies with only slight adaptations.

In this talk, we define the Second Gradient Continuum (SGC) as a continuum with the presence of defects field or sharp gradients of material properties, assumed to be continuously distributed within the matter. Some necessary mathematical conditions will be reminded to ensure covariance of the model. Then we present by means of simple examples the influence of these defects and sharp gradients on the elastic wave dispersion after « generalizing » the Navier equation. Extension of the method to other physical waves will be esquissed.
 
Bio:
Lalaonirina Rakotomanana obtained his PhD at the Mechanics Department of the EPFL in 1986. Following his phD, he was a member of the Orthopedics Biomechanics Group of the Biomedical Engineering Laboratory (EPFL), Privat Docent and Maître d’Enseignement et Recherche at the Medical School (University of Lausanne). He moved then to the Mathematics Department of the University of Rennes 1 (France).  His research topics focus on the development of mathematical models for dynamics of structures and materials, for thermomechanics of tissues and for wave propagation within non homogeneous matter.