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8.10.4 Force-driven Problems
When the primary method of deforming the model is a force, the problem is said to be force-driven. (Opposed to a displacement-driven model where the deformation is caused by displacement boundary conditions.) Force-driven forces are inherently unstable and FEBio has limited capabilities of handling such problems [L] [L] As of FEBio 2.0, some features are available that may help with this issue, but they are still experimental.. The cause of this instability can easily be explained using a simple example. Imagine a box that is constrained in all directions except one. In the unconstrained direction, apply two equal but opposite forces on opposite faces. In order to prevent the box from flying away, the box must generate stresses which balance the applied forces exactly. Unfortunately, the numerical solution will only be approximate due to numerical round-off errors inherent in the calculation. Even the slightest deviation from balancing the forces exactly will create a net-force which in turn causes the model to fly off in the unconstrained direction (in which a rigid body mode now exists).
Usually, these problems are circumvented by adjusting the boundary conditions so that rigid body modes cannot exist. In the previous example this can be done by only modeling half of the box and enforcing a symmetry boundary condition. However, in some cases this is not possible. This is often the case in force-driven contact problems, where the contact interface is necessary to define a well-constrained model. When there is an initial separation (or even when the surfaces have no initial overlap) the initial contact force is zero, which is equivalent to having no contact enforcement, and thus the model is under-constrained. Therefore, for force-driven contact problems it is important to have some initial contact before starting the analysis.