Lattice structures in ‘pore shape-stiffness’ framework: A ‘porosity-moment of inertia’ based interpretation

Abstract

• A novel ‘Porosity-Moment of inertia’ based interpretation. • Helpful to analyze the effect of change in pore shape on the effective stiffness of considered lattice structures at constant porosity levels. • To minimize stress-shielding in scaffolds: A desirable development from the perspective of design of lattices. Existing mathematical models (scaling laws) that correlate stiffness of lattices with their porosity and shape of pores, only suggest the monotonic decrease of stiffness with increase in porosity levels for the given shape of pore. Such mathematical models are of limited use to analyze the effect of change in shape of the pore(s) on the stiffness of lattice at constant porosity levels. To address the highlighted research gap, this work utilizes the archaic concept of classical mechanics (moment of inertia) to propose a normalized parametric tensor for the unified-quantification of the shape of pore(s) in lattices. Micromechanics based results successfully demonstrate the application of suggested framework to improve the understanding, interpretation, and predictability of effect of change in shape of the pore(s) on the stiffness of lattice structures.