Over the past decade, the optimal design of materials and structures has been the subject of a tremendous interest for the scientific community, spanning from mathematicians to physicists, engineers, and materials scientists. Whether one is thinking about applications to physics, energy conversion, in which so-called metamaterials play a crucial role, or to other fields such as medicine and mechatronics, new construction processes (3d-printing) and new applications to other scientific fields. These numerous applications have called for the development of innovative mathematical techniques and methodologies, designed to make such novel materials and technologies amenable to a rigorous mathematical modeling.

By their very nature, these queries require two different types of mathematical efforts. The first one is in the direction of the variational formulation of mechanical processes, with a specific focus on metamaterials, in order to derive suitable, reliable mathematical descriptions. The second one concerns the shape and topology optimization of materials, so as to tailor the manifacturing of the objects at hand in such a way that some desired material properties (e.g., compliance) are enhanced.

The goal of this workshop is to bridge these two perspectives by bringing together active members of both the community of Calculus of Variations and that of Shape and Topology Optimization.