Coupled cellular electromechanics and distributed finite elasticity

These examples use coupled electro-mechanical cellular models to generate the active fibre tension component for use in ZCTG5A, as part of the general finite elastic deformation of the tissue. The finite element strains are then used to compute the new extension ratios at each of the grid points ("cells").

The procedure used goes something like this...

1. Define the model geometry, fibres, etc;
2. Define the continuum/distributed mechanics equations, material parameters, solution method, etc;
3. Define the cellular model, material parameters, solution method, etc;
4. Time loop:
   1. Compute the cellular extension ratios from the continuum strains/geometry;
   2. Solve the cellular model for the current time step;
   3. Compute the active fibre tension component of the tension tensor at each gauss point from the grid points;
   4. Solve the continuum mechanics for the current time step.

Current problems with this technique

So far, including the fading memory equations of the HMT model leads to severe instability in the solution. This has been avoided by simply using the isometric tension generated at each of the cells - i.e., treating each of the cellular time steps as a semi steady state problem.

Examples are:

• b361. Noble 98 - HMT 2D sheet with varying fibre orientation
• b362. Noble 98 - HMT 2D sheet with infarct & SAC's

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