Elastic constants of cellular structures

Lattice models for calculating the elastic properties of cellular structures are described; on small scales the elastic constants are isotropic, both in two and three dimensions. Stresses are transmitted by harmonic springs that connect the nodes surrounding each volume element. The force constants of the springs are determined by the local elastic stiffness, which can vary from element to element. The model was tested by comparing the elastic constants of periodic two-dimensional microstructures with analytic results. Then it was applied to calculations of the elastic constants of samples of human trabecular bone, using images of the microstructure determined by X-ray transmission microscopy.