Nucleation of fracture: The first-octant evidence against classical variational phase-field models

TL;DR

This paper demonstrates that classical variational phase-field models are fundamentally incapable of accurately predicting fracture nucleation in elastic brittle materials under tension-dominated conditions, challenging their applicability.

Contribution

It provides explicit formulae and results showing the limitations of classical phase-field models in first-octant tension-dominated fracture nucleation scenarios.

Findings

Classical phase-field models cannot predict fracture nucleation in tension-dominated cases.

Explicit formulae illustrate the models' inability to capture nucleation phenomena.

Results highlight the need for alternative modeling approaches.

Abstract

As a companion work to [1], this Note presents a series of simple formulae and explicit results that illustrate and highlight why classical variational phase-field models cannot possibly predict fracture nucleation in elastic brittle materials. The focus is on ``tension-dominated'' problems where all principal stresses are non-negative, that is, problems taking place entirely within the first octant in the space of principal stresses.