### Introduction

There are different ways to impose constraints or connections between parameters in MCalibration. In the window below, the parameters `mu`

and `tauBase`

are unknown and will be search for during a calibration. There is no connection between the two parameters.

### Parameter Constraint Option 1

Note that if two parameters in the Optimize column have the same (non-zero) value then those two parameters will be forced to have the same value. That value will be searched for during an optimization. This is my preferred method to impose a constraint between two parameters. It is very easy to use, and usually good enough.

### Parameter Constraint Option 2

One way to impose a constraint on the value of a parameter is to set its lower and upper bound based on the value of other parameters. In this example, the parameter `tauBase`

has a lower bound that is 1.9 times `mu`

, and an upper bound that is 2.1 times `mu`

. Both parameters are independent, but the `tauBase`

parameter has to be within the bounds specified by `mu`

. Note that this constraint option does not always work so well, and is my least favorite of the 4 options summarized here.

### Parameter Constrains Option 3

Another way to impose a connection between different parameters is to use the Fitness dialog (button with the text “Fit”). In this way you can add a fitness penalty factor based on the value of the current material parameter set. In a sense this is similar to a Lagrange multiplier. In the example below, MCalibration will try to find parameters such that `(tauBase-2*mu)`

becomes close to zero, in orther words, `tauBase`

gets a value that is 2.0 times `mu`

. The pre-factor 10, in the example, specifies how important this constraint is.

### Parameter Constraint Option 4

A fourth and final way to impose constraints between parameters is to write them in the material model dialog as part of a material model template. In the example below, the PolyUMod BB model template has been modified so that instead of defining the parameter `%tauBase%`

, it uses the equation `$2.2*mu$`

. This will completely eliminate the `tauBase`

parameter since it is instead fully defined by the other parameters.

Once you accept the modified material model, the main window of MCalibration looks as follows:

In this case the parameter `tauBase`

is not part of the table of parameters. It is instead directly defined by the template we just edited.w