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Viscoelastic Units

Each spring-damper pair forms a uniaxial Voigt viscoelastic unit (Fig. gif) 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 tex2html_wrap_inline2344 denote the Voigt viscoelastic unit connecting node i to node j. It has elasticity constant tex2html_wrap_inline2350 , viscosity constant tex2html_wrap_inline2352 and rest length tex2html_wrap_inline2354 (the rest length of the muscle units may change over time in order to activate motion, see Section gif). The deformation of the elastic component is tex2html_wrap_inline2356 , where tex2html_wrap_inline2358 and tex2html_wrap_inline2360 .

  figure399

According to Hooke's law, the elastic force that the spring component of tex2html_wrap_inline2344 exerts on node i is

displaymath2338

The same spring also exerts the force tex2html_wrap_inline2374 on node j.

The linear viscous component of tex2html_wrap_inline2344 is a dashpot (see Fig. gif(b)). It exerts a viscous force tex2html_wrap_inline2380 on node i which is proportional to tex2html_wrap_inline2384 :

displaymath2339

where tex2html_wrap_inline2386 and tex2html_wrap_inline2388 defines the difference between the velocities of node i and j. The same component exerts the force tex2html_wrap_inline2394 on node j.

Given the above derivations of the elastic and viscous component forces, the total force exerted by the viscoelastic unit tex2html_wrap_inline2344 on node i is

displaymath2340

where

  equation455

defines the effective stiffness of tex2html_wrap_inline2344 .


next up previous contents
Next: Newtonian equations of motion Up: Mechanics Previous: Mechanics
Xiaoyuan TuJanuary 1996