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October 15, 2025Open Access

Phase-field modelling of cohesive fracture. Part I: $Γ$-convergence results

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Establishing $Γ$-convergence results forms the mathematical foundation for cohesive phase-field modeling.
A broad class of phase-field energies extends prior results and analytically validates existing models.
The framework generalizes the Ambrosio-Tortorelli approximation, indicating its relevance for brittleness work.
Systematic procedures and applied examples in subsequent parts will further validate the findings.

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This work establishes $Γ$-convergence results and a mathematical framework for cohesive fracture modeling, suggesting a unified approach.

Alessi et al. (2025) studied this question.

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This work establishes $Γ$-convergence results and a mathematical framework for cohesive fracture modeling, suggesting a unified approach.