Concept for derivation of homogenized models for piezo metal modules

One research objective of the Transregional Collaborative Research Centre 39 PT-PIESA "Production Technologies for light metal and fiber reinforced composite based components with integrated PIEzoceramic Sensors and Actuators" (by promotion of the German Research Foundation (DFG)) is the direct integration of piezo-fibers in sheet metal such as aluminium sheets. For numerical simulations of the behaviour of such piezo-metal-modules as active part of a machine or device, a discretization in the scale of the piezo-fibers is not possible. Therefore it is necessary to use homogenized material parameters. In this talk several concepts, based on the finite element method, for homogenization of material parameters of such piezo-metal-modules will be discussed. The concept of a unit cell uses constant loading condition at the boundaries of the unit cell. For the piezo-metall-modules this has to be modified, because piezo-fiber and sheet thickness are in the same order of magnitude, that is to say the unit cell is not small compared to the homogenized material part ("active sheet"). Therefore a loading gradient at the boundary of the unit cell has to be considered. And the homogenized "active sheet" has to adhere the possibility to generate bending. Another concept to include active sheets" in an overall simulation which will be discussed in this talk is the usage of so-called superelements. With this method any kind and form of boundary conditions can be used, but discretisation at overall label is bounded to the dimension of the representative volume.