Knee Implant, Dynamic Contact:

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Study the effects of knee extension and flexion on an artificial cartilage.

3D CAD model setup with variable-elastic, material model for the femur and tibia, hyper-elastic material model for the artificial cartilage, it included sliding and rolling, contact friction and actuator elements.

Nodal strains, stresses, and displacements.

Another knee analysis with unique challenges.

First, the bone material had to be accurately modeled. Bone has a variable modulus, from very elastic on the outside, to almost spongy on the inside. It is impossible to manually assign discrete modulus numbers to the nodes of a fine mesh and yet account for the gradient continuum without artificially introducing what will result in unreal and unwanted stress concentrations in the bone. So, a method had to be devised whereby a continuously variable modulus could be applied to the bone. This was solved by first performing a Steady State heat transfer analysis on the bone, where the outside surface of the bone was given an arbitrary temperature value of 1 (one) and an inner surface with a value of 0 (zero). The resulting thermal contours are shown in the 3rd and 4th figures below, where the 2nd figure shows part of the Femur sectioned for better viewing, the green material comprising the softer, interior demarcation. The hypothetical temperature was then used to define a temperature dependent elastic modulus using an appropriate curve applied to Algor's ThermoCurve material model. Now the variable elasticity of the bone could be realistically represented.

The second problem regarded actually articulating the knee joint to simulate not only motion, but loading, from a sitting to standing position, among other scenarios. The last figure below shows the concept. Since the connective tissue surrounding the knee joint can not be discretely modeled, an alternative was devised whereby the Femur was allowed to "float" vertically on a fixed Tibia. The location of the Femur with respect to the Tibia was controlled by a displacement actuator driven by a data curve. Another actuator controlled the extent of knee flexion (bending). These operated cooperatively. Also, a Moment and Force were applied to the end of the Femur stub such that the resultant force at the knee joint cartilage was always under compression. Again, the Moment and Force were driven by data curves and "timed" with the actuators. The resulting simulation accurately modeled the compressive and frictional forces acting between the Femur, Tibia, and the artificial cartilage system (cartilage is not shown to protect the client's proprietary interests).