Browsing by Author "Cull, Stephen"

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    A solid-fluid diffusionless reacting mixture theory model for bone
    (2012-12-20) Cull, Stephen; Epstein, Marcelo
    Mixture theory provides a framework to study materials composed of an arbitrary number of constituents. In addition to describing the motion and deformation of a material, mixture theory also describes reactions between constituents. The coupling of reactions and mechanical deformations for bone will be examined using a mixture theory approach. Bone will be considered as a reactive diffusionless solid-fluid mixture. Assumed evolution equations which depend on mechanical deformations will be used to describe reactions in bone. Considering a steady state biaxial stretch case and a uniaxial stress case, assumed evolution equations will be solved numerically. Results showed an increase of solid apparent density with increased mechanical loading. The precise relation between solid apparent density and mechanics depended on the choice of remodeling constants. In addition, the steady state orientation of a transversely isotropic solid constituent was determined to depend on the initial mixture composition.
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    Theoretical Time Evolution Equations for the Microstructure of Bone
    (2016) Cull, Stephen; Epstein, Marcelo; Adeeb, Samer; Sudak, Les; Federico, Salvatore; Wan, Richard
    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.