Identification of the spongy bone mechanical behavior under compression loads:: numerical simulation versus experimental results

In the fields of crashworthiness, ballistic protections, and other medical applications, the accurate material constitutive law of spongy bone is needed to carry out valid finite element analyses. The direct identification of bone mechanical behavior law is not easy since it is a complex network of intersecting osseous spans (trabeculae), where the space in and around the trabeculae contains bone marrow and fluids. We propose in this work to overtake the bone geometrical dispersion by applying an inverse scheme identification method, based on the global mechanical response, correlated with the exact geometry. First step study was made on spongy bone cylindrical samples cut in beef ribs. Compression tests on these samples showed a large dispersion and suggested that the fluid effect can be neglected during the quasi-linear part of the mechanical response. The micro-architecture of each sample was acquired thanks to microcomputed tomography technique (ACT). After applying a threshold, we used the ACT data to build a micro-FE model of the spongy bone. This model is introduced in FE code in order to simulate quasi-static compression of the sample. An elastic plastic constitutive law is assigned to the spongy bone. An optimization procedure is then applied in order to identify the spongy bone's behavior. The optimization function is based on the global. response (force versus displacement) of the sample. This procedure was repeated for different samples in order to obtain average spongy bone behavior.