Abstract:
In this thesis, the importance of structural viscoelasticity in the mechanical response of deformable
porous media with incompressible constituents under sudden changes in the external
applied quasi-static loads using mathematical analysis has been investigated. Here, the applied
load is characterized by a step pulse or a trapezoidal pulse. Mathematical models of nondivergence
free deformable porous media are often used to characterize the behaviour of biological
tissues such as cartilages, engineered tissue scaffolds, and bones which are viscoelastic and
incompressible in nature, and viscoelasticity may change with age, disease or by design. The
problem is formulated as a mixed boundary value problem of the theory of poro-viscoelasticity,
in which an explicit solution has been obtained using separation of variables technique coupled
with Fourier series analysis in one-dimension. Further, dimensional analysis is utilized to identify
dimensionless parameters that can aid the design of structural properties so as to ensure that
the fluid velocity past the porous medium remains bounded below a given threshold to prevent
potential damage. The study shows that the fluid mechanics within the medium can abruptly be
altered if the applied load encounters a sudden change in time and structural viscoelasticity is
too small. The analysis is used to explain the confined compression experiment clarifying the
cause of micro-structural damages in biological tissues associated with loss of tissue viscoelastic
property, which leads to the cause of diseases like Glaucoma.
xiv
