Waves in Nonlinear Pre-Stressed Materials

September 4, 2006 — September 8, 2006


  • Giuseppe Saccomandi (Università d. Studi di Perugia, Perugia, Italy)
  • Michel Destrade (CNRS, UMR 7607, Paris Cedex 05, France)

Pre-stressed bodies are ubiquitous in technical applications and in several fields of science. For instance in biomechanics, the behaviour in service of many soft biological tissues (such as arterial walls or veins) can be explained under the condition that they are modelled as pre-stressed viscoelastic materials. In civil engineering, bridge bearings or seismic shock absorbers under a building are clear examples of devices operating in conditions of pre-stress. Other examples can be found in the automotive industry, in seismology, in oil prospecting, in non-destructive ultrasonic evaluation, in high frequency signal processing for electronic devices, fibers optics, etc.
The study of wave motion is a natural and revealing approach of the properties of a pre-stressed body. Indeed, acoustic waves may be used to evaluate the material parameters of a given elastic body or, if these are known, to evaluate the state of induced anisotropy or of residual stress. They may also be used to detect structural defaults. Another major interest is the study of standing waves, with applications to stability and bifurcation analyses.
Hence, the understanding of the mathematics and of the mechanics of dynamical problems in pre-stressed elastic and viscoelastic materials is of paramount importance to many applications. Nevertheless, a complete and efficient training in this subject is still lacking.
The aim of this course is to provide a unique state-of-the-art multidisciplinary overview on the subject of waves in pre-stressed materials through the interaction of several topics, ranging from the mathematical modelling of incremental material response (elastic and inelastic), to the analysis of the governing differential equations and boundary-value problems, and to computational methods for the solution to these problems, with particular reference to industrial, geophysical, and biomechanical applications.
The School proposes a complete view on the title subject, including:
– The basic and fundamental theoretical issues (mechanical modelling, exact solutions, asymptotic methods, numerical treatment);
– A unified introduction to wave propagation (small on large and large on large);
– A look toward classical (such as geophysics and the mechanics of rubber-like solids) and emergent (such as biomechanics) applications.
The course is self-contained and aimed at graduate students commencing their studies in this area, and at postdoctoral researchers in applied mathematics, engineering, and materials science. It will also provide an overview of the subject for specialists in related areas who wish to gain a more detailed knowledge of the subject for use in their own research. Because the topics covered are relevant for industrial applications, it will also be a valuable experience for researchers from industry.

See also