Homogenization of Dentin Elastic Properties Based on Microstructure Characterization, Statistical Back-Analysis, and FEM Simulation

Abstract : The dentinal tissue is made of tubules surrounded by peri-tubular dentin (PTD), embedded in a matrix of inter-tubular dentin (ITD). Hashin and Rosen found exact stiffness bounds for hexagonal patterns of hollow fibers. But state of-the-art micro-macro models rely on simplified microstructure representations and lack experimental validation. The Poisson's ratios of dentin microstructure components cannot be determined by direct experimental methods. By contrast, we apply Hashin's homogenization scheme to a non-uniform PTD distribution, determined from image analysis. According to finite element simulations, a cube containing 60 tubules is a representative elementary volume. Microscopy, nanoindentation and resonant ultrasound spectroscopy data were collected from each dentin sample studied for model calibration. Despite the high variability of microstructure descriptors and mechanical properties, statistical analyses show that Hashins bounds converge and that the proposed model can be used for backcalculating the microscopic mechanical properties of dentin constituents.