In this project, we aim to create mathematical tools to help us describe, understand, and control how different stable phases are distributed within composite materials.
Understanding composite materials
Composite materials have complex internal structures that affect their overall macroscopic physical properties. For example, adding tiny pieces of a hard material to a soft material can make the soft material stronger. When a material has different stable phases, it is not only the geometry of the microstructure that matters, but also the distribution of phases inside the microstructure. To design materials with specific desired properties, it's crucial to understand how these two factors interact.
Towards models for material design
The goal of this project is to develop precise mathematical methods to describe, understand, and manage the distribution of stable phases within composite materials. Our results will pave the way towards a rigorous multi-scale analysis of these phenomena. This will provide a solid foundation for creating accurate models needed for computer simulations. These simulations will not only capture experimental observations but also help design materials with specific behaviors for advanced applications.
