Phase Field Modelling of Fracture Mechanics

Hello To one and All,

I am currently working on my Master's thesis in Computational Mechanics and as the Title suggests, I am working on using phase field theories to model fracture mechanics. The whole idea /concept of phase field modelling in itself has been a very complex topic for me, as it originates in superconductivity theories of which I have but a superficial understanding. I am ok with fracture mechanics terminology as I have worked on it before.

The problem I am currently facing is in understanding the theory behind computational modelling of fracture using these phase field theories. The PFT use the "order variable/order parameter" which is a scalar quantity in itself to model phase transitions, but  quite a few papers that I have come across use the terms "Conserved Order Parameters/ Non Conserved Order Parameters". Can anyone explain these terms to me please?

I am guessing itis based on the model being used, i.e. to say, if the model is based on the Balnce Laws such as the Momentum Balance and Mass Balance/Volume Balance which are basically conservation laws, in other words, if the evoliution off the parameter is given on basis of one of the conservation laws(mass balance law in e.g. Phase Field modelling of Mode I fracture by L. O. Eastgate et. al.)then it is called a "conserved order parameter". And on the other hand if the evolution for the parameter is given by a constitutive relation , then it is called a "non conserved parameter".

Is my Guess correct? Can someone please help me out with this or provide a more reasonable explanation for it?

Regards

Prajwal