Include(Specifications/FebioFeatures, "Specifications", 2, from="== In Situ Strain ==", to="=== Progress ===")

Progress

An algorithm for enforcing a user-defined fiber stretch has been implemented in FEBio2. The implementation is based on the paper by Weiss et. al [1] and uses an iterative method for enforcing the prescribed in-situ fiber stretch while maintaining stress equilibrium. The current implementation only works with transversely isotropic Mooney-Rivlin materials but can easily be expanded to other constitutive models. The examples below show the current capabilities.

Example 1: A constant in-situ fiber stretch of 50% was enforced on a cubical block. The example shows that a constant fiber strain can be achieved while maintaining stress equilibrium.

ImageLink(insitu_block1.png, width=400)

Example 2: A constant in-situ fiber stretch of 3% is prescribed on a cylindrical geometry with the fibers oriented circumferentially (left panel). The first principal stress is shown in the middle panel. A radial cut is introduced which relieves the stresses and introducing the opening angle.

ImageLink(insitu_cylinder1.png, width=600)

[1] Weiss J.A., Gardiner J.C., Ellis B.J., Lujan T.J., Phatak N.S., Three-dimensional finite element modeling of ligaments: Technical aspects, Medical Engineering & Physics 27 (2005) 845-861

Test problem implementation in FEBio

The implementation of the in-situ stretch was tested with the proposed test problem. The geometry was created in PreView and the analysis was done as a two-step analysis. In the first step, the in-situ strain is enforced using the algorithm described above. In the next step a saw-tooth prescribed displacement was applied on the free end of the beam. The model uses a trans-iso Mooney-Rivlin material and the stress-displacement is shown below for different levels of in-situ stretch.

attachment:test_results.png

-- ["aerdemir"] DateTime(2013-12-20T09:35:05Z) It seems like the material model is not tension only. If it is, I would suspect to see zero force/stress based on in situ strain level. Also, for the in situ strain case of 0.1 (if nominal) zero length of the object will be around 9.09 mm. For -1 mm displacement from reference length (10 mm), I would suspect the force/stress be less then zero as the nominal strain will be approximately -0.01. According to the plot above, the force/stress drops to zero at a displacement of ~ -1.75 mm. Any insight on this will be helpful.

-- ["belgiansteve"] DateTime(2014-02-23T18:52:07Z) I've found a problem with the initial test runs. The in-situ strain was being enforced during the entire analysis instead of during the first step. This fix changed the results significantly. I've also confirmed that for the case 0 in the figure the result is now identical to the regular trans-iso MR material in FEBio (which was not the case either in the previous runs).

Another test problem

A repeat of test 1 but with different material parameters. The parameters are: c1 = 4.36, c2=0, c3=2.4, c4=30.6, c5=323, k=100, lambda=1.055.

attachment:stress-displacement3.png