Large Strain Challenges in Materials Science

The project aims at advancing the mathematical modeling of nonlinear mechanical phenomena described by large strain deformations in three different directions. First, we will investigate effective simplified models for problems in materials science whose energetic formulations simultaneously involve both energy terms defined on the original stress-free configuration and energy contributions arising in the deformed state. Our analysis will affect fields that are currently at the research forefront in materials science, such as modeling of active materials. Second, we will focus on the interaction between fracture and delamination effects and large strain deformations in a special class of materials exhibiting a sharp difference (high contrast) in the behavior of their components. This will advance the understanding of microstructure formation, as well as the analysis of fine properties of special functions with bounded deformation, and the study of crack propagation models in materials. Eventually, the project will shed new light on the modeling of injectivity constraints.