6-4 – Nonlinear Waves in Solids
Aleksei Porubov (St. Petersburg State University), Giuseppe Saccomandi (University of Perugia), Harold Berjamin (NUI Galway)
The propagation of finite amplitude waves has fascinated scientists for long time. The subject of non-linear waves is better established and has been studied in greater depth in fluids than in solids, probably because they are much more difficult to observe in the latter than in the former. John Scott Russell was able to observe the solitary water wave traveling on the Union Canal in Edinburgh, just by jumping on his horse but, for example, seismic waves travel typically at several kilometers per second! Moreover, the amplitude of a motion in a solid is bounded by the elastic limit of the solid itself and for this reason the vast majority of scientific and technological applications in solid acoustics takes place in the context of linear wave propagation. Despite this situation nonlinear wave theories in elastic solids are beginning to attract more and more interest this is due because they score important successes in many fields of science and engineering. For example, ultrafast scanners provide a powerful tool for detecting shear wave propagation in biological soft tissues, the so called “dynamic non-linear elastic behavior” in earth materials has been observed in Geophysics investigation and many time dependent properties of meta-materials may be understood only in a nonlinear context.
The aim of the present mini symposia is to attract leading experts in nonlinear wave propagation in solids to list the theoretical advances in the field that are accompanying the development of new applications and technologies. We consider non-linear effects from different points of view. First of all we consider the possibility to approach the fully non-linear equations of motions, but we consider of interest the strong and fruitful approximation of small-amplitude motions superimposed on large strains or the approaches connected with the weakly non-linear theory of elasticity. In such a way we hope to attract a wide range of mathematical methods and modeling approaches, giving a broad overview of the topic of waves in nonlinear solids.