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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.
You are very welcome to join the seminar on teams here: teams.microsoft.com/l/meetup-join/19%3ameeting_MWU2MzJiNjgtYzM2Mi00ZWNkLWFiMjktOGQwOTc0MGRkZDll%40thread.v2/0?context=%7b%22Tid%22%3a%22cc95de1b-97f5-4f93-b4ba-fe68b852cf91%22%2c%22Oid%22%3a%22e6ced614-5673-458c-832d-5d4ada66f593%22%7d
