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Title: Mixture Theory Modeling of Multiphasic Deformation
Authors: Ali, Usman
Keywords: Physical Sciences
Issue Date: 2022
Publisher: Capital University of Science & Technology, Islamabad.
Abstract: In this dissertation, the bio-mechanical response of a fiber reinforced solid matrix (soft tissue) has been formulated. A constant magnetic field effects has been incor porated in the binary mixture of fluid and porous solid. The governing dynamics involved in the multiphasic deformation was based upon the loading imposed at the rigid bony interface. The fluid flow through the cartilage network depends upon the rate of applied compression as well as strain-dependent permeability of the soft tissues. The components of the mixture were assumed intrinsically incom pressible; however, in the derivation of governing dynamics, visco-elastic behavior of the solid and an interstitial fluid were developed. The continuum mixture the ory approach is employed in modeling solid deformation and local fluid pressure. In deriving the governing dynamics, strain-dependent permeability has been in corporated in the governing equations of binary mixture. The governing nonlinear coupled system of partial differential equations was developed for the solid de formation and fluid pressure, in the presence of Lorentz forces. In the case of permeability dependent flow, a numerical solution is computed, whereas, an exact solution is provided for constant permeability case. Graphical results highlight the influence of various physical parameters both on the solid displacement and fluid pressure. In the second problem, the mechanical response of a radially constrained elastic porous shell during the passage of charged fluid has been formulated . The motion of fluid as well as solid deformation were based upon the rate of applied compres sion at the inner radius of the shell. A nonlinear diffusion equation applicable to plana and radial geometries was developed for the porosity along with informal integral boundary conditions on both the extremities. An equation for solid de formation is derived in the form of an integral equation. The governing system of equations is solved numerically for the transient case, whereas, an exact solution is provided for the steady-state problem. In the case of linear permeability, an excellent agreement is noticed between both the solutions. The comparison of the fluid flow through the planar, cylindrical, and spherical shell is used in exploring xi the process of fluid flow affected by the geometrical constraint. Graphical results highlight the influence of different physical parameters on the porosity and solid displacement. Moreover, a detailed analysis of the fluid flow through a thick and thin wall elastic porous shell is also presented. Finally, for the same geometry as was in the second problem, the mathematical model describing visco-elastic behavior of an elastic porous shell during passage of non-Newtonian fluids was developed. In formulating the flow behavior, power law model was used in the constitutive equations of the mixture theory. The dominant mechanism of the fluid flow was considered outwardly directed when loading imposed at the inner radius of the shell. The outer boundary of the shell is considered as rigid mesh which offers negligible resistance for the passage of fluids. The general system of equations is derived for the porosity and solid deformation both for planar and radial geometries. The governing system of equations is solved analytically for steady-state case, whereas, numerical solution is computed for the transient problem. The significance of power-law index on the porosity and solid displacement is presented graphically.
Gov't Doc #: 25278
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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