Large Strain Challenges in Materials Science

The project aims at joining the complementary expertise of two research groups, based in Vienna and in Prague, in order to build an international team, and to advance 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 (Lagrangian), and energy contributions arising in the deformed state (Eulerian). Our analysis will affect fields of investigation that are currently at the research forefront in materials science, such as the 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 metamaterials, that is those 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 metamaterials. Eventually, the project is expected to shed a new light on the modeling of injectivity constraints and frictionless contact, by proposing an approximation of the seminal Ciarlet-Necas condition via nonlocal terms, that is both apt for being numerically implemented, and functional to prevent the occurrence of Lavrentiev phenomena. This will have an impact on the modeling of impenetrability in inelastic phenomena occurring at large strains, as well as on the numerical simulation of non-simple and gradient-polyconvex materials. The PIs of the proposal are Elisa Davoli (University of Vienna) and Martin Kružk (Institute of Information Theory and Automation, Czech Academy of Sciences).

The project has joined the complementary expertise of two research groups, based in Vienna and in Prague, in order to build an international team, and to advance the mathematical modeling of nonlinear mechanical phenomena described by large strain deformations in three different directions. First, we have investigated effective simplified models for problems in materials science whose energetic formulations simultaneously involve both energy terms defined on the original stress-free configuration (Lagrangian), and energy contributions arising in the deformed state (Eulerian). Our analysis will affect fields of investigation that are currently at the research forefront in materials science, such as the modeling of active materials. Second, we have focused on the interaction between inelastic effects and large strain deformations in a special class of metamaterials, that is those 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 plasticity and damage in metamaterials. Eventually, the project has shed a new light on the modeling of injectivity constraints and frictionless contact, by proposing an analysis of the seminal Ciarlet-Nečas condition in brittle materials and establishing its connection with linearized contact conditions. The PIs of the proposal have been Elisa Davoli (TU Wien) and Martin Kružk (Institute of Information Theory and Automation, Czech Academy of Sciences).