Multi-scale computational homogenization of structured thin sheets

Structured and layered thin sheets are used in a variety of innovative applications, e.g. flexible displays, rollable solar cells or flexible electronics. Stacks of different materials, with often highly complex interconnects between layers, are thereby used, which are typically loaded in bending combined with intrinsic thermo-mechanical mismatches. As a result, different failure mechanisms at the level of the layered substructure occur, which constitutes a serious reliability concern. This paper deals with the two-scale homogenization of structured thin sheets, whereby a higher-order through-thickness representative volume element (RVE) is used. The methodology relies on the computational homogenization of the mechanics of microstructures, for which first-order and second-order solution strategies have been developed in the past decade. The upscaling of the deformation of structured thin sheets towards a shell-type continuum is second-order in nature. The higher-order kinematics is defined on the basis of a microstructural RVE, which represents the full thickness of the macroscopic structure and a periodic in-plane cell (e.g. a single pixel in a flexible display). The elaboration of the boundary conditions and the solution of the micro-scale boundary value problem are discussed. The obtained micro-scale stress state is homogenized towards a 3D macroscopic shell structure, for which detailed aspects will be emphasized. The coupled numerical solution strategy is briefly outlined. Finally, an example is given and the application to a number of practical problems is highlighted, where the solution provides direct information on each scale. The incorporation of failure events at the substructure level is thereby naturally at hand.