Theoretical Time Evolution Equations for the Microstructure of Bone
Abstract
The response of the microstructure of bone to mechanical loads will be described using a continuum theory. Understanding the response of the microstructure of bone to mechanical loading will be important, as the microstructure will be assumed to influence the mechanical properties of bone. As a result of the assumed coupling between the microstructure and mechanical properties of bone, external mechanical loads will influence the mechanical properties of bone. The influence of mechanical loads on the mechanical properties in the proposed bone model will provide insights into how specific mechanical properties will be obtained through external mechanical loading.
Constitutive equations will be used to describe the response of bone to changes in temperature, mechanical deformations, and the microstructure of bone. Time evolution equations which describe the changing microstructure of bone will be proposed, that are consistent with the Second Law of Thermodynamics. Due to the assumed constitutive equations, the time evolution equations depend on the temperature, mechanical deformations, and the microstructure of bone. The time evolution equations were solved numerically for a uniaxial case study with fixed porosity. Results showed that the stiffness of bone would tend to increase along the direction of loading. The stiffness of bone would tend to decrease along the direction perpendicular to the applied load.
The microstructural changes in bone will also be related to mass transfers in bone. A thermodynamic driving force for mass transfer in bone will be proposed for a solid-fluid mixture, that is consistent with the Second Law of Thermodynamics. A continuous distribution of material interfaces will be assumed to separate the solid and fluid phases of bone. The proposed driving forces for mass transfer depend on the hydrostatic stress of each phase, the Helmholtz free energy of each phase, and the chemical energy of each phase.
Description
Keywords
Applied Sciences, Applied Mechanics, Engineering, Engineering--Mechanical
Citation
Cull, S. (2016). Theoretical Time Evolution Equations for the Microstructure of Bone (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/28262