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material constitutive laws using CellML

In CMISS there is currently a method implemented and validated for specifying material constitutive laws using CellML. This allows for the specification of spatially varying material parameters within constitutive laws and the spatial distribution of the actual material laws. This implementation is probably still too tightly coupled to grid points and activation modelling.

Also in CMISS (at least Andre's version) there is a well established method for inclusion of active tension from cellular models into the full stress tensor (see a description of active tension in CMISS). This is definately tied to grid points and activation modelling - not nescessarily a bad thing in terms of electromechanics models but possibly over the top for simple active tension models.

We want to start investigating the combination of these two methods such that active tension and material constitutive laws are given in one CellML model - i.e., you want to pass in the deformation gradient tensor and get back the 2nd Piola-Kirchhoff stress tensor (or the Cauchy or some other kind of stress tensor?)

At an initial guess, this would not seem too hard to accomplish given the code already in CMISS and Andre's version of CMISS - more an issue of Andre having the time to merge his code back into global CMISS and adding the extra bits required to achive this goal.

Issues that would need consideration:

  • Extra overhead in electromechanics models of evaluating passive material equations during the solution of electrical activation.
  • Use of sheet and normal strain components in cellular models of passive and active mechanics.
  • others?

Would seem a good idea for Andre to look at this generalised solution rather than committing his code in a active mechanics only focussed solution.