Course Topics:
- Introduction.
- Definitions of a continuum – biological
examples.
- Vectors and matricides, index notations; a
concept of tensors
- Basic types of ordinary and partial
differential equations; biological problems in which differential
equations are involved.
- The idea of force and stress in a solid.
- Equations
of equilibrium; balance of momentum; stress boundary conditions.
- Finding principal stresses and axes; Mohr's circle
for plane stress.
- The idea of deformation, displacement
gradient and strain in a solid.
- Principal strains.
- Constitutive equations; Hookean
elastic solid.
- Velocity and rate of deformation; constitutive
equation for Newtonian fluid.
- Gauss's
Theorem; derivation of field equations in fluid.
- Material
description of the motions of a continuum; conservation of
mass; transport equation; equations
of continuity and
motion.
- The Navier-Stokes equation;
boundary conditions at solid-fluid or fluid-fluid interface.
- Solving
Navier-Stokes equation for steady flow; Couette and Poiseuille
flow.
- Dynamic similarity and Reynolds number.
- Solving Navier-Stokes
equation for unsteady flow; pulsating flow.
- Concepts
of boundary layer.
- Mechanical properties of real solids
and fluids.
- Linear viscoelastic
bodies and theories.
- Non-Newtonian fluid; blood flow.
(2 hour)
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