This follows my questions on how energy is dissipated during the forming of leads and ridges in the Arctic ice sheet, during my postdoc time at UNM Albuquerque under Deborah Sulsy and Buck Schreyer. The answer I found at that time was vague, that friction dominates the dissipation in quasi-brittle failure. At large scale of the ice sheet, Schulson (???) briefly mentions the frictional dissipation, but a more detailed analysis by Bazant (1996) gives me a clearer answer. This triggered the curiosity and led to more questions on the effects of friction on constitutive models and their predictions and with Alexander Korsunsky, I was just able to address this issue in a simplest form with a local model. Many of my research investigations later came from this
In the context of nonlocal modelling, we performed a detailed analysis to show the importance of correctly capturing the way energy dissipates during quasi-brittle failure processes. The considered quantity to show the effects of friction is the size of the Fracture Process Zone (FPZ).
The local effects on constitutive response is seen here. A reference point is made by keeping the fracture energy constant. While the overall structural responses are almost same, the unloading paths and stress-damage relationships reflect the effects of friction.
And this is the effect of friction on the prediction of the critical wave length (as an indication of the width of the FPZ). The observed percentage of frictional dissipation (of the total budget) is 50%-75%, by Bazant (1996). Therefore it can be seen that allocating all dissipation budget to damage/fracture process will lead to over prediction of the width of the FPZ.
This figure depicts the evolution of the FPZ (of a bar under tension) during the failure process. The structural response is shown in the above figure, and we can see that they remain unchanged with respect to the amount of frictional dissipation. This shows the fixed dissipation budget, while the contribution from friction is varying. In all cases, over prediction of the FPZ size can be clearly seen.