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Optimal design of multi-component fractured media

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DNM - The mathematical design of new materials

Multi-component materials are fundamental in many applications: the different mechanical, physical, and chemical properties of each component can be exploited to design a composite with tailored properties. The presence of sharp interfaces between different component leaves room for the formation of microcracks and therefore the generation of a multiscale geometry of the material. In this seminar, we will discuss an optimal design problem for two-component fractured media for which a macroscopic strain is prescribed. The presence of fractures motivates setting the problem in the framework of structured deformations. In this context, we start from an energy functional accounting for bulk and surface contributions coming from both constituents of the material and we derive an integral representation for the relaxed energy functional. The  relaxed energy densities, obtained via a blow-up method, are determined by a delicate interplay between the optimization of sharp interfaces and the diffusion of microcracks. This model has the far-reaching perspective to incorporate elements of plasticity in optimal design of composite media.
These results have been obtained jointly with José Matias and Elvira Zappale.

This talk is part of the Isaac Newton Institute Seminar Series series.

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