Elastic modeling of bone at nanostructural level

Abstract

Bone is a connective tissue which gives body its support and stability. In mechanical terms, bone is a nanocomposite material with a complex hierarchical structure which contributes to bone's excellent mechanical properties, including high stiffness, strength and fracture toughness, and light weight. At nanoscale, cross-linked collagen molecules, hydroxyapatite (HA) nanocrystals, water, and a small amount of non-collagenous proteins (NCPs) form mineralized collagen fibrils (MCF). The MCF serves as the primary building block of bone, and, thus, its physical and mechanical characterization is critical for finding structure–property relations in bone and understanding bone's overall behavior.In this paper, we review the composition and structure of the MCF and summarize the existing models proposed in literature to predict its effective elastic response. These models can be classified into the following four categories:I.Models based on strength of materials approach which are mainly variants of Voigt and Reuss bounds. Most of such models were originally proposed for characterization of composite materials; however, they are also applicable to model a MCF as a collagen–HA composite.II.Models based on micromechanics theories.III.Computational models, involving mostly a finite element method (FEM).IV.Atomistic simulations using molecular dynamics (MD).Each of these types of models has some advantages and disadvantages. The strength of materials models are simpler mathematically but they involve approximate solutions, while the micromechanics approaches usually involve simpler geometrical models which are solved more rigorously. Computational models, based mainly on the finite element method, can account more precisely for the structural features of bone including collagen–HA arrangement, collagen cross-links, and collagen–HA interphase. MD simulations, conducted at the atomic level and over very small regions, provide insights into properties of collagen molecules and fibrils, the effect of collagen cross-linking, and collagen–HA interphase, and can serve as inputs for continuum-based models.In this paper, we outline some representative models of bone at nanoscale (mineralized collagen fibril) and discuss the assumptions, limitations, and drawbacks of these models, present their comparison, and offer recommendations on the future work in this area. Such discussion will help to develop more complete models of MCF addressing physical, mechanical, and biological aspects of bone's behavior at the nanoscale. Furthermore, it will shed light on designs of collagen–HA nanocomposites with desired mechanical properties which can be used as biomaterials for orthopedic applications such as surface coatings for implant materials, as bone substitutes, and as scaffolds for bone tissue regeneration.