Finite element 3D modeling of mechanical behavior of mineralized collagen microfibrils

The aim of this work is to develop a 3D finite elements model to study the nanomechanical behaviour of mineralized collagen microfibrils, which consists of three phases, (i) collagen phase formed by five tropocollagen (TC) molecules linked together with cross links, (ii) a mineral phase (Hydroxyapatite) and (iii) impure mineral phase, and to investigate the important role of individual properties of every constituent. The mechanical and the geometrical properties (TC molecule diameter) of both tropocollagen and mineral were taken into consideration as well as cross-links, which was represented by spring elements with adjusted properties based on experimental data. In the present paper an equivalent homogenised model was developed to assess the whole microfibril mechanical properties (Young's modulus and Poisson's ratio) under varying mechanical properties of each phase. In this study both equivalent Young's modulus and Poisson's ratio which were expressed as functions of Young's modulus of each phase were obtained under tensile load with symmetric and periodic boundary conditions.Comment: Journal of Applied Biomaterials and Biomechanics 9, 3 (2011) xx

Editorial: Bone integrity in patients with osteoporosis: Evaluation of fracture risk and influence of pharmacological treatments and mechanical aspects

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New three-dimensional model based on finite element method of bone nanostructure: single TC molecule scale level

At the macroscopic scale, the bone mechanical behavior (fracture, elastic) depends mainly on itscomponents nature at the nanoscopic scale (collagen, mineral). Thus, an understanding of themechanical behavior of the elementary components is demanded to understand the phenomenathat can be observed at the macroscopic scale. In this article, a new numerical model based on finiteelement method is proposed in order to describe the mechanical behavior of a single Tropocollagenmolecule. Furthermore, a parametric study with different geometric properties covering themolecular composition and the rate hydration influence is presented. The proposed model has beentested under tensile loading. While focusing on the entropic response, the geometric parametervariation effect on the mechanical behavior of Tropocollagen molecule has been revealed using themodel. Using numerical and experimental testing, the obtained numerical simulation results seemto be acceptable, showing a good agreement with those found in literature

A theory for bone resorption based on the local rupture of osteocytes cells connections: A finite element study

In this work, a bone damage resorption finite element model based on the disruption of the inhibitory signal transmitted between osteocytes cells in bone due to damage accumulation is developed and discussed. A strain-based stimulus function coupled to a damage-dependent spatialfunction is proposed to represent the connection between two osteocytes embedded in the bone tissue. The signal is transmitted to the bone surface to activate bone resorption. The proposed modelis based on the idea that the osteocyte signal reduction is not related to the reduction of the stimulus sensed locally by osteocytes due to damage, but to the difficulties for the signal in travelling along a disrupted area due to microcracks that can destroy connections of the intercellular network between osteocytes and bone-lining cells. To check the potential of the proposed model to predict the damage resorption process, two bone resorption mechano-regulation rules corresponding to twomechanotransduction approaches have been implemented and tested: 1) Bone resorption based on a coupled strain-damage stimulus function without ruptured osteocyte connections (NROC); and 2) Bone resorption based on a strain stimulus function with ruptured osteocyte connections (ROC). The comparison between the results obtained by both models, shows that the proposed model based on ruptured osteocytes connections predicts realistic results in conformity with previously published findings concerning the fatigue damage repair in bone

Effect of material and structural factors on fracture behaviour of mineralised collagen microfibril using finite element simulation

Bone is a multiscale heterogeneous material and its principal function is to support the body structure and to resist mechanical loads without fracturing. Numerical modelling of biocomposites at different length scales provides an improved understanding of the mechanical behaviour of structures such as bone, and also guides the development of multiscale mechanical models. Here, a three-dimensional nano-scale model of mineralised collagen microfibril based on the finite element method was employed to investigate the effect of material and structural factors on the mechanical equivalent of fracture properties. Fracture stress and damping capacity as functions of the number of cross-links were obtained under tensile loading conditions for different densities and Young's modulus of the mineral phase. The results show that the number of cross-links and the density of mineral as well as Young's modulus of mineral have an important influence on the strength of mineralised collagen microfibrils which in turn clarify the bone fracture on a macroscale. © 2014 © 2014 Taylor & Francis

Finite element prediction of fatigue damage growth in cancellous bone

Cyclic stresses applied to bones generate fatigue damage that affects the bone stiffness and its elastic modulus. This paper proposes a finite element model for the prediction of fatigue damage accumulation and failure in cancellous bone at continuum scale. The model is based on continuum damage mechanics and incorporates crack closure effects in compression. The propagation of the cracks is completely simulated throughout the damaged area. In this case, the stiffness of the broken element is reduced by 98% to ensure no stress-carrying capacities of completely damaged elements. Once a crack is initiated, the propagation direction is simulated by the propagation of the broken elements of the mesh. The proposed model suggests that damage evolves over a real physical time variable (cycles). In order to reduce the computation time, the integration of the damage growth rate is based on the cycle blocks approach. In this approach, the real number of cycles is reduced (divided) into equivalent blocks of cycles. Damage accumulation is computed over the cycle blocks and then extrapolated over the corresponding real cycles. The results show a clear difference between local tensile and compressive stresses on damage accumulation. Incorporating stiffness reduction also produces a redistribution of the peak stresses in the damaged region, which results in a delay in damage fracture

Failure of Mineralized Collagen Microfibrils Using Finite Element Simulation Coupled to Mechanical Quasi-brittle Damage

Bone is a multiscale heterogeneous materiel of which principal function is to support the body structure and to resist mechanical loading and fractures. Bone strength does not depend only on the quantity and quality of bone which is characterized by the geometry and the shape of bones but also on the mechanical proprieties of its compounds, which have a significant influence on its deformation and failure. This work aim to use a 3D nano-scale finite element model coupled to the concept of quasi-brittle damage with the behaviour law isotropic elasticity to investigate the fracture behaviour of composite materiel collagen-mineral (mineralized collagen microfibril). Fracture stress-number of cross-links and damping capacity-number of cross-links curves were obtained under tensile loading conditions at different densities of the mineral phase. The obtained results show that number of cross-links as well as the density of mineral has an important influence on the strength of microfibrils which in turn clarify the bone fracture at macro-scale.Comment: 6; http://www.sciencedirect.com/science/article/pii/S187770581100714