Each spring-damper pair forms a uniaxial Voigt viscoelastic unit
(Fig. ) that simulates, in a simple way, the
viscoelasticity of biological tissue [Terzopoulos and Fleischer1988]. A Voigt
viscoelastic unit comprises an elastic element (a Hookean spring with
nonzero rest length) in parallel with a viscous element (a
dashpot). Let denote the Voigt viscoelastic unit connecting
node *i* to node *j*. It has elasticity constant , viscosity
constant and rest length (the rest length of
the muscle units may change over time in order to activate motion, see
Section ). The deformation of the elastic
component is , where
and .

According to Hooke's law, the elastic force that the spring component
of exerts on node *i* is

The same spring also exerts the force on node *j*.

The linear viscous component of is a dashpot (see
Fig. (b)). It exerts a viscous force on node *i* which is proportional to :

where and
defines the difference between the velocities of node *i* and *j*. The
same component exerts the force on node *j*.

Given the above derivations of the elastic and viscous
component forces, the total force exerted by the viscoelastic unit
on node *i* is

where

defines the *effective stiffness* of .

Xiaoyuan Tu | January 1996 |