Deformation and failure in cellular materials

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Abstract
An isotropic, three-dimensional, lattice-spring model is proposed to describe deformation and failure in heterogeneous materials. Young's moduli of samples of trabecular bone have been calculated, using images of the microstructure obtained from x-ray microtomography. An analysis of the stress distribution indicates that trabecular bone will most likely fail due to local tensile stresses, even when the macroscopic load is compressive. In the samples studied, there does not seem to be a homogenization length scale beyond which the material can be described by an effective medium theory.