Homogenization of elastic grids containing rigid elements

Abstract: The inclusion of rigid elements into elastic composites may lead to superior mechanical properties for the equivalent elastic continuum, such as, for instance, extreme auxeticity. To allow full exploitation of these properties, a tool for the homogenization of two-dimensional elastic grids containing rigid elements is developed and tested on elaborate geometries, such as, for instance, Chinese lattices. The rigid elements are assumed to be either jointed with full continuity of displacement or hinged to the elastic rods. It is shown that the two different constraints induce strongly different mechanical characteristics of the equivalent elastic solid. The presented results open the way to the design of architected materials or metamaterials containing both elastic and rigid parts.