<FLOW> hyperbolic

Description

For this law, the hyperbolic sin function is applied to the power law of overstress, and in turn taken to a second power. The flow is written:

(398)\[\dot{\lambda} = {\tt eps0}\left[ \sinh<f/{\tt K}>^{\tt n} \right]^{\tt m}\]

with \(f\) positive. The coefficient K must be non-zero, and the coefficients n and m default to one.

The flow law is fully implemented for Runge-Kutta or the standard theta method. It cannot presently be applied to the reduced integration.

Because the \(\sinh\) can “blow up” with large values of \(f/K\) a cutoff limit on that ratio is applied. This can be user-adjusted by entering a real value for cutoff in the law’s coefficient section. The default value is 10.0 which would result in an unrealistically high strain rate for this type of model.

Syntax

The flow law accepts coefficients eps0, K, n, and m as outlined above.

Example

A simple example follows:

*flow hyperbolic
    K    22.3
    m    1.44
    eps0 .202e-8
    cutoff 8.