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This page prioritizes and provides specifications for feature requests associated with FEBio development.
Target Outcome
Implementation of analysis and pre- & post-processing related features in FEBio to accommodate simulations conducted using Open Knee(s)
Priority List for Implementation
- In situ strain
- Element, node, and surface set definitions
- Connector elements for joint coordinate system
- Penetration based contact
- Spring elements with wrapping
- Shell elements for cartilage
Features Related to Constitutive Modeling
In Situ Strain
Description
The zero force reference lengths (or "slack length") of the ligamentous knee structures have been shown to be important contributors to overall joint mechanics. As they are difficult to measure, ligament slack lengths are a commonly targeted parameter during optimization of specimen-specific joint level kinetic-kinematic response. Regardless of the level of refinement in the modeling approach, whether continuum or spring based, a parameter based representation facilitates these iterative studies.
Ideally, this behavior could be defined either along the ligament line of action or locally within a given element. While the local mesh coordinate frames could be used to approximate a ligament's line of action (if hexahedral elements are used), it would also be convenient to incorporate ligament wrapping, without needing to remesh to reflect this behavior (if possible).
Test Problem
The test problem will be developed using the following:
- Geometry/Mesh: a 1 by 1 by 10 mm mesh with fiber direction defined along the 10 mm length.
- Boundary Conditions: a ramp displacement profile (+/- 2.5 mm load-unload) applied to one end of the mesh along the fiber direction (see figure below). The other end is fixed.
- Material Model: a fiber based model, e.g. transversely isotropic Mooney-Rivlin.
Sensitivity: fiber direction in situ strain values ranging -0.2 to +0.2, in 0.1 increments.
- Output: force-displacement response of the loaded end of the mesh.
- For application in Open Knee(s) simulations, implementation in both implicit static and implicit dynamic analyses.
ImageLink(FEBio_insitu_test.png, width=600, alt=Experimentation Workflow)
Estimated Completion
April, 2014
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
Features Related to Pre-/Post-Processing
Set Definitions for Elements, Nodes, and Surfaces
Description
The ability to define node, element, or surface sets could add convenience to both the pre- as well as post-processing of FEBio analyses. Often, models are made up of multiple components while the output(s) of interest may be limited to a specific component, or an even smaller region of interest. In terms of pre-processing, element sets could be used to assign material properties or request specific types of output for a given region. For post-processing, instead of searching across all elements (or nodes) in a model, and cross-referencing for specific element numbers, one could simply extract the region of interest by name.
Test Problem
Estimated Completion
September, 2014
Features Related to Rigid Body Kinematics Representations
Local Coordinate Systems
Connector Elements for Joint Coordinate Systems
Description
Joint level simulations, especially in the knee, often rely on application and/or description of kinetic-kinematic response in commonly accepted joint coordinate systems (e.g. Grood and Suntay, JBME, 1983). This requires adoption of moving local coordinate systems that are assigned to a given body, e.g. the femur and tibia, to track overall rigid body motions as well as a means to "connect" two coordinate frames. In the case of Abaqus, we often use what's called "connector" elements to setup such frames. Their convenience is evident during model setup, prescription of joint level boundary conditions, as well as post-processing of the model results, where the connector outputs can be directly translated into clinically accepted descriptions of motion and/or loading.
In a Grood and Suntay convention, the following vector can be used to describe the position of an embedded tibial coordinate frame with respect to the femoral frame:
attachment:GeneralizedFrame
attachment:JointTranslations%28Fig4 )
where H = S1*e1 + S2*e2 + S3*e3 and e1, e2 and e3 are unit vectors along each of corresponding Sn magnitudes. e1 can be though of as the femoral flexion axis, while e3 is the internal-external rotation axis in the tibia and e2 is the common perpendicular between the two, i.e. the "floating axis."
In practice, all of the above can be combined to view the "connections" between two rigid bodies as a series of cylindrical joints:
If implemented in this way, the rotations, displacements and reactions about each of the cylindrical axes can be used to describe or apply the desired joint kinetics.
For reference, the yellow lines in the following represent the cylindrical connectors implemented in a joint level analysis (frames were setup to describe both tibiofemoral and patellofemoral articulations). Disaplacements, rotations, and reactions (load and moment) for each joint can be specified or extracted in this setup.
Test Problem
To accomplish this feature request, we anticipate setting up a test problem with a known input-output relationship. This test problem could act as a surrogate for joint level simulations and could be as simple as a set of linear springs between two coordinate frames.
Estimated Completion
Late 2014
Features Related to Surrogate Modeling
Penetration Based Contact
Spring Elements with Wrapping
Shell Elements for Contact Problems