Orthotropic elastic constants of 2D cellular structures with variously arranged square cells: The effect of filleted wall junctions

Cellular materials are characterized by a complex interconnected structure of struts or plates and shells, which make up the cells edges and faces. Their structure can be advantageously engineered in order to tailor their properties according to the specific application. This aspect makes them particularly attractive for the manufacturing of bone prosthetics, where the elastic modulus of the implant should match that of the bone in order to avoid loosening due to the stress shielding phenomenon. In this regard, the ability to design a component with the desired mechanical response is crucial. For this reason, the present paper evaluates the stiffness of 2D cellular structures with variously arranged square cells. Specifically, two spatial arrangements are considered: the former one is a regular square cell honeycomb, while in the latter the square cells are staggered by a prescribed offset of half of the cell wall length. An analytical model based on classical beam theory is proposed to identify the effect of stretching and bending actions on the stiffness of a single cell by applying the periodic boundary conditions. The theoretical beam model is fitted on the results from a 2D Finite Elements model based on plane elements via an extensive parametric analysis. In this way, semi-analytical formulas are proposed to calculate the stiffness in large domains of the geometric parameters: wall thickness to edge length ratio in the interval [0.04,0.20] and fillet radius to edge length ratio in the interval [0,0.15].