On phase-field regularization in dynamic fracture with brittle and cohesive formulations

2026-07-15

AI Summary

This study addresses the unclear influence of phase-field regularization on the interaction between cracks and elastic waves in dynamic fracture, particularly the lack of systematic understanding regarding behavioral differences under various damage–displacement coupling formulations. By examining the interaction of tensile and compressive waves with phase-field cracks in a one-dimensional bar, the work analyzes the dynamic responses of three fracture models and, for the first time, extends cohesive-fracture phase-field regularization to an elastoplastic dynamic framework, deriving an analytical law for dynamic cohesive cracking. Integrating phase-field modeling, wave analysis, and two-dimensional simulations of dynamic crack branching, the research identifies key parameters governing wave–crack interactions and demonstrates the proposed model’s capability to accurately reproduce sharp-crack dynamic features and predict crack-branching behavior under varying loading intensities.

Abstract

Phase-field models of fracture are widely used for simulating crack nucleation and propagation, yet the role of the phase-field regularization in the dynamic regime is not fully understood and depends critically on how the damage variable is coupled to the displacement field. In this paper, we analyze three alternative formulations: the brittle model with stiffness degradation, its variant with stiffness+density degradation, and our recently proposed phase-field regularization of cohesive fracture, which we extend to elastodynamics. By studying the interaction of a tensile and a compressive elastic wave with a phase-field crack in a one-dimensional bar, we determine for which models and under which conditions the phase-field regularization preserves the features of the wave-crack interaction expected for a sharp crack, and we theoretically explain which variables control the behavior. For the new cohesive model extended to dynamics, we further derive an analytical dynamic cohesive opening law. Finally, we study the dynamic behavior including branching of a two-dimensional notched plate at two loading intensities.

Problem

• phase-field regularization
• dynamic fracture
• wave-crack interaction
• cohesive fracture
• brittle fracture

Innovation

• phase-field fracture
• dynamic cohesive law
• wave-crack interaction
• stiffness degradation
• elastodynamics