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220.127.116.11 Ellipsoidal Fiber Distribution Uncoupled
The material type for an ellipsoidal continuous fiber distribution in an uncoupled formulation is “EFD uncoupled”. Since fibers can only sustain tension, this material is not stable on its own. It must be combined with a stable uncoupled material that acts as a ground matrix, using a “uncoupled solid mixture” container as described in Section 18.104.22.168↓. The following material parameters need to be defined:
The stress for this material is given by [38, 7, 4]: is the square of the fiber stretch , is the unit vector along the fiber direction (in the reference configuration), which in spherical angles is directed along , , and is the unit step function that enforces the tension-only contribution. The fiber stress is determined from a fiber strain energy function in the usual manner, where in this material, The materials parameters and are determined from: The orientation of the material axis can be defined as explained in detail in Section 4.1.1↑.
<material id="1" type="uncoupled solid mixture"> <mat_axis type="local">0,0,0</mat_axis> <k>1000</k> <solid type="Mooney-Rivlin"> <c1>1</c1> <c2>0</c2> </solid> <solid type="EFD uncoupled"> <ksi>10, 12, 15</ksi> <beta>2.5, 3, 3</beta> </solid> </material>