An embedded element based 2D finite element model for the strength prediction of mineralized collagen fibril using Monte-Carlo type of simulations

A computationally efficient statistical model for the prediction of the strength of mineralized collagen fibril (a basic building block of bone) is presented by taking into account the uncertainties associated with the geometrical and material parameters of collagen and mineral phases. The mineral plates have been considered as one-dimensional bar elements embedded in the two-dimensional plane stress collagen matrix. The mineral phase is considered as linear elastic and a hyperelastic material model is adopted for the collagen phase. Further, the crack initiation and propagation in the collagen phase have been modeled using a damage plasticity approach. Different realizations of the arrangement of mineral plates have been generated to account for the associated geometrical uncertainties using an in-house MATLAB® code. Monte-Carlo type simulations have been performed on the different realizations of mineralized collagen fibril to predict its characteristic stress-strain response under tensile load. The characteristic strength of 3.64 GPa is obtained for mineralized collagen fibril using Weibull’s analysis which is found to be in agreement with the molecular dynamics simulation data and numerical studies reported in the past. A parameter sensitivity analysis concluded that mineral modulus has a significant effect on the overall tangent modulus of mineralized collagen fibril in large strain regime.