Dear Sophie,

I find your question really interesting, I hope my answer here will help you clarify a bit your doubts.

1. Yes, FFM is a two-parameter fracture criterion. In fact, Dölling & co-authors refer to the foundational paper of Leguillon (Article Strength or Toughness? A Criterion for Crack Onset at A Notch

2. Yes, fracture processes are not modeled. Why? Because it's hard to do it. In terms of energy balance, the fracture problem involves external energy transferred macroscopically to the specimen that is dissipated by microscopic mechanisms at or very close to the crack tip. Thus, it is an inherently multi-scale problem. But we want to model it while staying in the realm of continuum (macroscopic) mechanics. Models like the cohesive zone model (cohesive elements) or phase field fracture mechanics try to model these dissipation mechanisms through internal variables and/or material properties, which have proven to be quite difficult to measure. In FFM, we simply assume that we can model the end result of these processes (i.e. macroscopic fracture) with a two-parameter macroscopic criterion. So, can you say something about these microscopic dissipative processes? Not really, as we are not modeling them. We assume that we can predict the end result by neglecting their exact physics and using a "correct" macroscopic criterion.

3. So, why the "Finite" in FFM? Well, it is so-called in comparison with what came before, i.e. Linear Elastic Fracture Mechanics (LEFM). Now, it is the latter name that is deceiving. The name LEFM is more historical than mathematical. Historically, first came elasticity, and upon the results of the theory of elasticity people like Irwin, Griffith, Westergaard built the foundations of what became Fracture Mechanics (FM). It was thus called LEFM. But if you look at the mathematical formulation of the fracture criteria proposed, it should be more properly called Infinitesimal Fracture Mechanics (IFM?). Why? Because the properties governing fracture (Stress Intensity Factors, Energy Release Rate, mode ratio, etc...) are evaluated in the limit r-->0 with r the radial distance from the crack tip, i.e. infinitesimally. In contrast, FFM starts from the assumption that fracture propagation is characterized by a finite length scale. Thus the properties governing fracture should not be evaluated infinitesimally, but at a finite "characteristic" distance from the crack tip. Thus the "finite" in FFM. How do you determine this characteristic distance? This is actually the problem in FFM, as the characteristic length is the main link between macroscopic criterion and microscopic dissipative processes. Usually, some calibration with experiments is needed to find a fitting value.

I hope it helps.

Best,

Luca