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
defines the effective stiffness of .
|Xiaoyuan Tu||January 1996|