I will discuss two classes of effective, macroscopic models in elasticity: (i) 1D models applicable to thin structures, and (ii) homogenized 2D or 3D continua applicable to materials with a periodic microstructure. In both systems, the separation of scales calls for the definition of macroscopic models that slave fine-scale fluctuations to an effective, macroscopic deformation field. I will show how such models can be established in a systematic and rigorous way based on a two-scale expansion that accounts for nonlinear and higher-order (i.e. deformation gradient) effects. I will further demonstrate that the resulting models accurately predict nonlinear effects, finite size effects and localization for a set of examples. Finally, I will discuss two challenges that arise when solving these effective models: (1) missed boundary layer effects and (2) negative stiffness associated with higher-order terms.
Further Information
Dr Claire Lestringant explores new models for understanding the mechanics of thin structures under large deformations, used for example to understand morphogenesis in biological systems or for the design of multi-stable, reconfigurable space structures. She received a PhD in Mechanics from Université Pierre et Marie Curie in 2017 and worked as a post-doc in D. Kochmann’s group at ETH Zurich in Switzerland.