Design piezo-electromechanical systems for boundary-prescriptions in strain gradient elasticity

Many micro-structural effects in mechanical systems can be modeled by means of continuum theories [1]. A natural way to build a suitable theoretical model, when strongly localized deformation features are observed, is to complement the displacement field with some additional kinematical descriptors, which leads to the so-called micromorphic models. Another possibility is to consider higher order gradient theories, in which the deformation energy depends on second and/or higher gradients of the displacement. In this presentation a two-dimensional solid consisting of a linear elastic isotropic and homogeneous material is considered and the strain energy is expressed as a function of the strain and of the gradient of strain. Analytical solutions for classical problems such as the heavy sheet, the bending and the flexure problem are provided. The idea is very simple: the solutions of the corresponding problem of first gradient classical case are imposed and the corresponding forces, bi-forces and wedge-forces are found out. On the basis of such solutions, a method is outlined which is able to identify the six constitutive parameters. In other words, ideal (or gedanken) experiments are designed to allow to write equations that have as unknowns the six constants and as known terms the values of the experimental measurements of appropriately selected quantities. The aim of this work is to present a strategy to design piezo-electromechanical systems that are able to apply the necessary boundary conditions that are necessary to obtain the found analytical solution.