Microstructures, composites, optimization 

Materials with microstructures are everywhere, from living organisms to metals, to rocks, to serials and ice cream.  In modern engineering, composites are such materials that are widely used in countless serious applications. Their behavior, particularly the response a a smooth large scale impact, is the subject of our study. It is hopelessly difficult to compute the behavior of each piece of such materials, therefore some sort of averaged description - homogenization -  is needed.

The overall properties of materials strongly depend on their microstructure. This dependence is investigated and variational methods of structural optimization are suggested and applied to optimal  composites. Also, varying the microstructure, one finds materials with unusual and remarkable properties. Observing various bio-structures, one can learn more about the essence of optimality of "living structures". Studying ''real" composites, one needs to address the fracture of them. Percolation answer the question whether a continuos path exists in a phase in the structure or if the phase forms disconnected inclusions.

The biggest microstructrured "material" is Earth, and one wants to look into it using surface measurements. The geological structure can be recovered using methods of inverse problems. Another mysterious substance of great practical interest is the sea ice. Natural materials with microstructures (the polycrystals) arrive when the cooling mold is going through the phase transition, so the dynamics of this process is important to address. Nonlinear structures display an unusual dynamic behavior due to their inner instabilities.

Clicking on a topic sends you to detailed comments to some of the mentioned areas. More comments
will be added soon.