Where next for applied mathematics and mechanics in heterogeneous media applications?
Speaker: William Parnell, School of Mathematics, University of Manchester
Title: Where next for applied mathematics and mechanics in heterogeneous media applications?
Abstract: Heterogeneous media are ubiquitous in the world around us. They occur naturally in the form of geological and biological materials for example, and we are now able to produce an incredible array of synthetic media that exploit inhomogeneity over many length scales in order to give rise to material properties that even a couple of decades ago would have been considered unimaginable.
Despite the immense computational resource now available, theoretical applied mathematics and mechanics have continued to play an invaluable role in the field of heterogeneous media in the 21st century.
In this talk I will describe and review a number of problems associated with inhomogeneous media that I have worked on over the last few years, that have exploited applied mathematical techniques both modern and classical. These will include (as time permits) models of complex lightweight nonlinear composite materials in both static and dynamic regimes, tunable and so-called invariant phononic crystals, acoustic metamaterial designs for sound attenuation applications, multiple scattering in multi-phase media and finally nonlinear anisotropic viscoelastic models of soft tissue such as tendon and ligament that are inspired by information garnered from their microstructure. Some of the work is motivated by direct industrial and healthcare applications whereas other aspects are extremely blue sky in their nature.