The Colloquium will focus on the development of constitutive laws for fibre-reinforced materials capable of undergoing large elastic or inelastic deformations, with particular reference to polymeric composites (glass fibre and carbon fibre composites, for example) and biological tissues (for example, arterial walls and membranous tissues), which have some features in common from the modelling point of view. Fabric and network materials will also be treated. Models with one or more families of fibres or with statistical distributions of fibres will be included, with the emphasis on anisotropic modelling. This is currently a very active and rapidly developing area of research with important technological and medical applications. Analysis of boundary-value problems for such materials, with particular attention focused on questions of stability. Treatment of instabilities of both continuous and discontinuous type: e.g. for tissues, instabilities associated with tissue thinning and growth (development of aneurysms, for example), and for polymeric composites, fibre kinking, fibre splitting, de-bonding and the development of kink bands (which requires inelastic theory).

Part of the aim is to bring together experimentalists and theoreticians — engineers, materials scientists, mechanics specialists and applied mathematicians, in particular — in order to stimulate mutual interaction and to identify key experiments that need to be performed to test the theories and also to identify what contributions theoreticians can make to the understanding of experimental results.