Phase-field modelling of cohesive fracture. Part II: Reconstruction of the cohesive law

TL;DR

This paper develops a systematic method to construct phase-field models that accurately replicate prescribed cohesive laws, enhancing the flexibility and precision of cohesive fracture simulations within a unified theoretical framework.

Contribution

It introduces a flexible procedure for deriving phase-field models from cohesive laws, expanding the modeling toolkit for cohesive fracture analysis.

Findings

Multiple phase-field models can reproduce the same cohesive law.

The methodology allows tailoring models to specific cohesive responses.

Theoretical results are validated through worked examples.

Abstract

This is the second paper of a three-part work the main aim of which is to provide a unified consistent framework for the phase-field modelling of cohesive fracture. Building on the theoretical foundations of the first paper, where {$\Gamma$-convergence} results have been derived, this second paper presents a systematic procedure for constructing phase-field models that reproduce prescribed cohesive laws. By either selecting the degradation function and determining the damage potential or vice versa, we enable the derivation of multiple phase-field models that exhibit the same cohesive fracture behavior but differ in their localized phase-field evolution. This methodology provides a flexible and rigorous strategy for tailoring phase-field models to specific cohesive responses, as shown by the several examples worked out. The mechanical responses associated with these examples, highlighting their features and validating the theoretical results, are investigated in the third paper from a more engineering-oriented and applied perspective.