Mechanical Modeling of Material Behavior - Continuum Mechanics of Anisotropic Materials - page 17

Fig. 1.10 The application of the Terzaghi model to articular cartilage. On the bottom left the
applied stress history is illustrated. A constant stress ( s o ) is applied to a sample of articular
cartilage at an instant of time and held constant thereafter. The creep response of the
sample under this loading is illustrated on the bottom right . At the top are drawings of the sample
illustrating the tissue response. From these illustrations one can see that the creep is accompanied
by exudation of the fluid from the sample and that the rate of exudation decreases over time from
point A to B to C. At equilibrium the flow ceases and the load is borne entirely by the solid matrix
(point C) and the water carries none of the load (due to the fact that any pressure in the water would
cause it to flow out of the matrix) (From Nordin and Frankel (1989))

Fig. 1.9c the spring supporting the piston initially takes none of the load because it
cannot deflect. It cannot deflect because the piston cannot move due to the fact that
the cylinder chamber is filled with a relatively incompressible liquid (water).
However, once the water has a chance to exit the cylinder through the orifice in
the piston, then it is possible for the piston to begin to move downward under the
action of the applied compressive loading. This process of consolidation or settle-
ment proceeds until the spring has deflected an amount sufficient to create a force
equal to the applied loading. The relation between the force F applied to the piston
of this model and the resulting displacement x of the piston is given by the same
constitutive equation that characterizes the Voigt model if the dashpot viscosity

in

the Voigt model is replaced by ( A 2 / A o )( L / ). The application of this model to

articular cartilage is illustrated in Fig. 1.10 . This figure illustrates the response of
a sample of articular cartilage when a force applied to the sample is changed from
0 to a finite value at an instant of time and held constant thereafter. Like the Voigt

k