Effect of unit cell features on mechanical properties of lattice structures at constant porosity levels: A general mixture rule based interpretation

Abstract

On the basis of general mixture rule (GMR) and micromechanics this work reports following findings. There is a possibility of wide range of unit cell features (theoretically infinite), but it is reasonable to assume that effective Young’s and shear modulus of porous lattice structures (PLSs) will lie in specified range within the limits of lower and upper Reuss-Voigt bounds. In contrast, Poisson’s ratio of PLSs has been observed to frequently violate the theoretical upper bound depending upon the unit cell features. For any given bulk porosity level of PLSs its mechanical properties (Young’s modulus, shear modulus and Poisson’s ratio) have been found to be positively correlated with scaling parameter of GMR. Change in the scaling parameter and consequent change in effective elastic properties helps to qualitatively correlate both entities with stress concentration. Significant role of unit cell features or pore design parameters (size, shape, orientation and connectivity that are represented by scaling parameter of GMR) and bulk porosity of scaffolds (PLSs) in bone tissue engineering is known. Thus, results of this work may be important for the multi-objective design of PLSs as scaffolds in Generative Design framework for Additive Manufacturing (GDfAM).