北京大学力学与工程科学学院

力学系学术报告

报告人  李少凡

University of California, Berkeley

时间：2026年7月27日（周一）上午10:00-11:00

地点：新奥工学大楼4047会议室

报告内容摘要：

Conventional phase-field modeling of fracture has an elegant variational structure, but it uses the degraded strain energy density (SED) at the crack tip as a material force to drive crack growth, which differs markedly from established engineering fracture mechanics. To avoid non-physical evolution in the crack phase-field, various SED splitting schemes have been proposed or adopted, leading to the development of "anisotropic"-SED-based formulations that may capture realistic crack nucleation and propagation under mixed-mode loading. In this work, we propose a stressintensity-factor-driven (SIF-driven) phase field method as an alternative to achieve the same goal. To retain the spirit of variational fracture mechanics, the proposed method still follows the variational principle but uses a novel free-energy form that also converges to the Mumford-Shah functional as the length scale approaches zero. Using the crack phase-field distribution as a marker of the material's configurational change and leveraging the phase-field crack tip landscape and its gradient, we employ a nonlocal Griffith energy, expressed in terms of the stress intensity factor, as the material force driving crack growth. The nonlocal SIF-powered fracture energy release rate near the crack tip is computed within the framework of linear elastic fracture mechanics (LEFM) for hyperplastic materials. This non-local energy release rate is then incorporated into a variational phase-field modeling framework as the driving force for material configurational changes, i.e., crack phase-field evolution.

The proposed formulation is validated through multiple numerical examples, demonstrating its capability to capture mode I, mode II, and mixed-mode fracture behaviors without mesh dependency. The key contributions of this work include: (1) accurate representation of the cracktip stress asymptotic field, (2) precise prediction of crack growth and material failure without the need for additional splitting techniques, (3) introducing a physics-based stress-intensity-factorgoverned crack driving force to replace the SED-based approach, thereby effectively bridging the gap between phase-field formulation for fracture and well-established LEFM theory, and (4) providing a numerically efficient and straightforward implementation that closely resembles that of conventional phase field methods. This work establishes a robust connection between the phase field method and full-fledged fracture mechanics, providing a practical, physics-consistent tool for cleavage fracture analysis in engineering applications.

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