考虑惯性效应的动态断裂相场模型

IF 5.6 2区工程技术 Q1 ENGINEERING, MECHANICAL

Theoretical and Applied Fracture Mechanics Pub Date : 2025-10-13 DOI:10.1016/j.tafmec.2025.105283

Yuanfeng Yu , Chi Hou , Timon Rabczuk , Meiying Zhao

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引用次数: 0

摘要

惯性效应在动荷载作用下结构的断裂过程中起着重要的作用。裂纹尖端处的惯性力常常影响裂纹的形态。为了有效地描述动态断裂问题，本文建立了考虑相场惯性的相场模型。首先，通过对位移场和相场进行类比，找到两个场变量中某些参数的相似性，给出了由材料参数确定的相场惯性参数表达式，建立了包含相场惯性能量在总能量泛函中的相场模型。其次，在拉格朗日动力学方程的基础上，得到了动力条件下的力学平衡方程和相场演化方程；然后，采用有限元离散化策略和交错法实现模型。最后，通过数值算例对模型进行了验证。详细分析了相场惯性对裂纹形态和能量特性的影响，并与实验和参考数值结果进行了比较。结果表明，相场惯性效应影响了系统中应变能、断裂耗散能和动能的分布，自然地捕捉了终端裂纹速度的减小，防止了不良裂纹模式的出现。这进一步完善了动态断裂的相场理论框架。

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A phase field model considering inertial effect in dynamic fracture

Inertial effect plays a significant role in the fracture process of structures under dynamic loading. The inertial force at the crack tip often influences the crack pattern. To effectively describe dynamic fracture problem, a phase field model that accounts for phase field inertia is developed in this paper. First, a phase field inertial parameter expression determined by the material parameters is given by analogizing the displacement field and the phase field, finding the similarity of some parameters in the two field variables, and establishing a phase field model that includes the inertial energy of the phase field in the total energy functional. Secondly, the mechanical equilibrium equations and phase field evolution equations under dynamic conditions are obtained based on the Lagrangian kinetic equations. Then, the model is implemented using the finite element discretization strategy and staggered approach. Finally, the presented model is validated through several numerical examples. The impact of phase field inertia on crack patterns and energy characteristics is analyzed in detail and compared with experiment and reference numerical results. It is demonstrated that the phase field inertial effect affects the distribution of strain energy, fracture dissipated energy and kinetic energy in the system, naturally capturing the decrease in terminal crack velocity and preventing undesirable crack patterns. This further improves the phase field theoretical framework for dynamic fracture.

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来源期刊

Theoretical and Applied Fracture Mechanics 工程技术-工程：机械

CiteScore

8.40

自引率

18.90%

发文量

435

审稿时长

37 days

期刊介绍： Theoretical and Applied Fracture Mechanics'' aims & scopes have been re-designed to cover both the theoretical, applied, and numerical aspects associated with those cracking related phenomena taking place, at a micro-, meso-, and macroscopic level, in materials/components/structures of any kind. The journal aims to cover the cracking/mechanical behaviour of materials/components/structures in those situations involving both time-independent and time-dependent system of external forces/moments (such as, for instance, quasi-static, impulsive, impact, blasting, creep, contact, and fatigue loading). Since, under the above circumstances, the mechanical behaviour of cracked materials/components/structures is also affected by the environmental conditions, the journal would consider also those theoretical/experimental research works investigating the effect of external variables such as, for instance, the effect of corrosive environments as well as of high/low-temperature.