Advanced mathematical formulations, computational and hybrid schemes for modelling of strongly inhomogeneous multi-component and multi-layered structures, are within the focus of the program. The course is bringing together a broad multidisciplinary expertise inspired by numerous engineering applications, including, in particular, manufacturing and design of photovoltaic panels, laminated glass, and also lightweight vehicles, soft robots, energy harvesting devices, and bio-composites.

The recent progress in material science, combined with growing demands of environmentally friendly technologies, stimulate increasingly strong interest in composite materials with high-contrast properties, as well as strongly inhomogeneous layered structures. The presence of strong contrast in material parameters, say, up to 10-5 in layer stiffness of photovoltaic panels, necessitates development of novel approaches to mathematical models governing their mechanical behaviour.

The course combines a number of theoretical approaches to studying high-contrast multi-component and multi-layered structures, including formulations based on physical assumptions, as well as asymptotic procedures. The course is also aimed at enriching the listeners with new developments in metamaterial synthesis, novel homogenisation techniques for periodic media, wave propagation in soft phononic crystals, and fatigue and fracture in soft materials.

In particular, the phenomenon of specific low natural frequencies arising as a consequence of strong inhomogeneity is discussed, along with a delicate treatment of boundary conditions, following from the appropriately adapted Saint-Venant’s principle for a thin laminate. Also, an overview of the homogenization methods of continuous or discrete periodic media is provided, addressing successively various scenarios, e.g. strain-gradient formulations of fibre-reinforced media, non-conventional behaviour of reticulated structures etc., demonstrating that generalized continua may arise from modelling of high-contrast media. In addition, a class of meta-materials associated with pantographic micro-structures, that could bear large deformations while remaining in the elastic regime, is discussed. A related topic of large deformations, buckling and post-buckling deformations and their effects on wave propagation in soft phononic crystals and metamaterials is covered. Another related subject is concerned with analysis of modelling failure in soft materials, relying on the concept of bounding strain-energy by means of energy limiters.

The lectures are chosen to appeal to researchers, graduate students and postdoctoral fellows, specializing in Mechanical, Aerospace and Civil Engineering, as well as Applied Mathematics and Physics, with the focus on recent developments in the area of high-contrast elastic solids that have not been yet included in traditional university graduate courses. Both theoreticians and experimentalists are expected to gain useful knowledge from attending the course.