In this study, Single-Walled and Multi-Walled Carbon Nanotubes in their perfect forms were investigated by the Finite Element Method. Details on the modeling of the structure are provided in this paper, including the appropriate elements, the element properties that should be defined based on the atomic structure of Carbon Nanotubes and the corresponding chemical bonds. Non-covalent van der Waals interactions between two neighbor atoms as well as the required approximations for the modeling of the structures with this kind of interaction are also presented. Specific attention was dedicated to the necessity of using some time- and energy-consuming steps in the simulation process. First, the effect of simulating only a single ring of the whole structure is studied to find out if it would represent the same mechanical behavior as the long structure. Results show that by applying an appropriate set of boundary conditions, the stiffness of the shortened structure is practically equal to the long perfect structure. Furthermore, Multi-Walled Carbon Nanotube structures with and without defining the van der Waals force are studied. Based on the observations, applying the van der Waals force does not significantly influence the obtained Young's modulus of the structure in the case of a uniaxial tensile test.
Human bones can be categorised into one of two types--the compact cortical and the porous cancellous. Whilst the cortical is a solid structure macroscopically, the structure of cancellous bone is highly complex with plate-like and strut-like structures of various sizes and shapes depending on the anatomical site. Reconstructing the actual structure of cancellous bone for defect filling is highly unfeasible. However, the complex structure can be simplified into an idealised structure with similar properties. In this study, two idealised architectures were developed based on morphological indices of cancellous bone: the tetrakaidecahedral and the prismatic. The two architectures were further subdivided into two types of microstructure, the first consists of struts only and the second consists of a combination of plates and struts. The microstructures were transformed into finite element models and displacement boundary condition was applied to all four idealised cancellous models with periodic boundary conditions. Eight unit cells extracted from the actual cancellous bone obtained from micro-computed tomography were also analysed with the same boundary conditions. Young's modulus values were calculated and comparison was made between the idealised and real cancellous structures. Results showed that all models with a combination of plates and struts have higher rigidity compared to the one with struts only. Values of Young's modulus from eight unit cells of cancellous bone varied from 42 to 479 MPa with an average of 234 MPa. The prismatic architecture with plates and rods closely resemble the average stiffness of a unit cell of cancellous bone.
The wrist is the most complex joint for virtual three-dimensional simulations, and the complexity is even more pronounced when dealing with skeletal disorders of the joint such, as rheumatoid arthritis (RA). In order to analyse the biomechanical difference between healthy and diseased joints, three-dimensional models of these two wrist conditions were developed from computed tomography images. These images consist of eight carpal bones, five metacarpal bones, the distal radius and ulna. The cartilages were developed based on the shape of the available articulations and ligaments were simulated via mechanical links. The RA model was developed accurately by simulating all ten common criteria of the disease related to the wrist. Results from the finite element (FE) analyses showed that the RA model produced three times higher contact pressure at the articulations compared to the healthy model. Normal physiological load transfer also changed from predominantly through the radial side to an increased load transfer approximately 5% towards the ulnar. Based on an extensive literature search, this is the first ever reported work that simulates the pathological conditions of the rheumatoid arthritis of the wrist joint.