I am trying to modify the strain equations in the membrane physics. For this, I need to add a new dependent variable that is not a function of the field u or other variables.
yes it is. Do you want it to be function of stress or strains? if dependent on stress you most likely need to add extra dofs. if it is dependent on strains you can just type it directly.
its a difficult for me to answer more since I do not know what you would like to do. if you specify more perhaps I can help you.
You could if you want change the equation directly under the equation veiw. however it is difficult to help you if you do ot give more information about your problem, e.g. a file or equation, more detailed desricption of problem etc.
You need to add a ODE/PDE physics to define a new variable. If the variable is global then ODE if it is distributed over the domain then PDE interface.