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9.4 Guidelines for Dynamic Analyses

A dynamic analysis differs from a quasi-static analysis in that the mass inertia of the model is taken into account. This adds an explicit time-dependency to the model (through the nodal velocities and accelerations) and therefore the solver needs to integrate the equations of motion in time. There are several integration schemes available in FEBio.

Implicit Dynamics Solver

The implicit solid solver implements the generalized alpha integration rule, which can be controlled via several parameters. Although the default settings will usually suffice, there might be instances where the parameters should be modified. (For example, see False Transient Analysis).

The main parameter that controls the time integration of the solid solver is the rhoi parameter. The following rules apply:

  1. \(\rho_{\infty}=-1\), All other integration parameters are set to one.

  2. \(0\leqq\rho_{\infty}\leqq1\), Newmark integration parameters are set to defaults, based on the value of \(\rho_{\infty}\).

  3. Any other value for \(\rho_{\infty}\), default/user-specified values for Newmark integration parameters are not modified.

False Transient Analysis

Quasi-static models may sometimes exhibit instabilities that may prevent the default Newton-based solver from converging. In such situations, a dynamic analysis can be tried instead, with the anticipation that the inertia of the model provides sufficient stability to solve the model successfully. Since in these situations, only the long-term quasi-static solution is sought, it is important to damp the oscillations introduced by the dynamics of the system. Such damping can be accomplished several ways.

The generalized-alpha time integration scheme of the implicit solver uses several parameters that control the overall energy-conservation of the model. By choosing these parameters such that the system looses energy over time, artificial damping can be introduced.

The rhoi control parameter controls the amount of artificial damping. This parameters takes a value between 0 (more numerical damping) and 1 (least numerical damping). Thus, by setting this value to 0, the most numerical damping can be introduced.

The rhoi control parameter sets the actual alpha, beta, gamma parameters of the generalized-alpha rule. Instead of using rhoi, users can set these actual parameters directly. To introduce the most numerical damping, set the values as follows.

<rhoi>-2</rhoi>             
<gamma>1.5</gamma>
<beta>1</beta>

Note that rhoi needs to be set to -2 so that FEBio uses the actual alpha, beta, gamma parameters.