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research-article

Monte Carlo type Simulations of Mineralized Collagen Fibril based on Two Scale Asymptotic Homogenization

[+] Author and Article Information
Abhilash Awasthi

MS Scholar, School of Engineering, Indian Institute of Technology Mandi, Kamand − 175005, Mandi, Himachal Pradesh, India
abhiawasthi1993@gmail.com

Rajneesh Sharma

Assistant Professor, School of Engineering, Indian Institute of Technology Mandi, Kamand − 175005, Mandi, Himachal Pradesh, India
rajnish.iitmandi@gmail.com

Rajesh Ghosh

Assistant Professor, School of Engineering, Indian Institute of Technology Mandi, Kamand − 175005, Mandi, Himachal Pradesh, India
rajesh@iitmandi.ac.in

1Corresponding author.

ASME doi:10.1115/1.4042439 History: Received June 04, 2018; Revised December 30, 2018

Abstract

A multi-scale model for mineralized collagen fibril is proposed by taking into account the uncertainties associated with the geometrical properties of mineral phase and its distribution in the organic matrix. The asymptotic homogenization approach along with periodic boundary conditions has been used to derive the effective elastic moduli at two hierarchical length scales, namely: microfibril and mineralized collagen fibril. The uncertainties associated with the mineral plates have been directly included in the finite element mesh by randomly varying their sizes. A total 100 realizations for mineralized collagen fibril model with random distribution have been generated using an in-house MATLAB® code and Monte-Carlo type simulations have been performed under tension load to obtain the statistical equivalent modulus. The deformation response has been studied in both small (= 10%) and large (= 10%) strain regimes. The stress transformation mechanism has also been explored in microfibril which showed stress relaxation in the organic phase upon different stages of mineralization. The elastic moduli for microfibril under small and large strain have been obtained as 1.88 and 6.102 GPa, respectively, and have been used as input for upper scale homogenization procedure. Finally, the characteristic longitudinal moduli of the mineralized collagen fibril in the small and large strain regimes are obtained as 4.08 ± 0.062 and 12.93 ± 0.148 GPa, respectively. All the results are in good agreement to those obtained from previous experiments and molecular dynamics simulations in the literature with a significant reduction in the computational cost.

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