A multiscale homogenization procedure using the fabric tensor concept

Bone is a heterogeneous material in which structural levels can be identified, from the microscale to macroscale. Multiscale models enable to model the material using homogenization techniques. In this work, an innovative homogenization technique for trabecular bone tissue is proposed. The technique combines the fabric tensor concept and a bone phenomenological material law, linking the apparent density with the trabecular bone mechanical properties. The proposed methodology efficiently homogenizes the trabecular bone highly heterogeneous medium, allowing to define its homogenized microscale mechanical properties and to reduce the analysis computational cost (when compared with classical homogenization techniques). In order to verify the efficiency of the technique several examples were solved using a confined square patch of trabecular bone under compression. In the end, the results obtained with a classic homogenization technique and the proposed methodology were compared.