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首页> 外文期刊>Engineering Fracture Mechanics >Minimum energy multiple crack propagation. Part-II: Discrete solution with XFEM
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Minimum energy multiple crack propagation. Part-II: Discrete solution with XFEM

机译：最小能量多重裂纹传播。 第2部分：与XFEM的离散解决方案

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摘要

The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and fracture energies, which stems directly from the Griffith's theory of cracks, is applied to the problem of arbitrary crack growth in 2D. The proposed formulation enables minimisation of the total energy of the mechanical system with respect to the crack extension directions and crack extension lengths to solve for the evolution of the mechanical system over time. The three parts focus, in turn, on (I) the theory of multiple crack growth including competing cracks, (II) the discrete solution by the extended finite element method using the minimum-energy formulation, and (III) the aspects of computer implementation within the Matlab programming language. The Part-II of our three-part paper examines three discrete solution methods for solving fracture mechanics problems based on the principle of minimum total energy. The suitability of each solution approach is determined by the stability property of the fracture configuration at hand. The first method is based on external load-control. It is suitable for stable crack growth and stable fracture configurations. The second method is based on fracture area-control (or length-control in 2D). This method is applicable to stable or unstable fracture growth but the fracture front must be stable. The third solution method is based on a gradient-descent. Although the method is aimed at solving general crack growth problems, its weak point is that the converged solution cannot be guaranteed to be optimal in the particular case of competing crack growth and an unstable fracture front configuration. Nonetheless, the main focus is on the implementation and application of the gradient-descent solution approach within the framework of the extended finite element method. Concerning the aforementioned case of competing crack growth, an alternative solution strategy is pursued to supplement the gradient-descent approach. The proposed method, however, is only a proof of concept since its robustness is assessed by solving fabricated benchmark problems. The open-source Matlab code, documentation and example cases are included as supplementary material. (C) 2017 Published by Elsevier Ltd.
机译：三部分纸涉及在准静态条件下线性弹性固体中的能量最小的多裂纹传播。最小总能量的原理，即潜在和断裂能量的总和，源于格里菲斯的裂缝理论，适用于2D任意裂纹增长的问题。所提出的配方使得能够最小化机械系统的总能量相对于裂缝延伸方向和裂缝延伸长度，以便随着时间的推移解决机械系统的演化。这三个零件焦点又在（i）上（i）多裂纹增长理论，包括竞争裂缝，（ii）通过最小能量配方的扩展有限元方法的离散解决方案，以及（iii）计算机实现的各个方面在Matlab编程语言中。我们的三部分纸张的第II部分研究了三种离散解决方法，用于基于最小总能量原理解决骨折力学问题。每个溶液方法的适用性由手头断裂配置的稳定性性决定。第一种方法基于外部负载控制。它适用于稳定的裂纹生长和稳定的骨折配置。第二种方法基于断裂区域控制（或在2D中的长度控制）。该方法适用于稳定或不稳定的骨折生长，但骨折前沿必须稳定。第三种解决方案方法基于梯度下降。虽然该方法旨在解决一般裂纹生长问题，但其弱点是在竞争裂纹增长的特定情况和不稳定的断裂前构造的特定情况下，不能保证收敛的解决方案。尽管如此，主要重点是在扩展有限元方法的框架内实现和应用梯度 - 下降解决方案方法。关于上述竞争裂缝增长的情况，追求替代解决方案策略来补充梯度 - 血统方法。然而，所提出的方法只是概念证据，因为通过解决制造的基准问题来评估其鲁棒性。开源MATLAB代码，文档和示例情况包括为补充材料。 （c）2017年由elestvier有限公司出版

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  • 来源
    《Engineering Fracture Mechanics》 |2018年第2018期|共32页
  • 作者

    Sutula Danas; Kerfriden Pierre; van Dam Tonie; Bordas Stephane P. A.;

  • 作者单位

    Univ Luxembourg Inst Computat Engn 6 Ave Fonte L-4362 Esch Sur Alzette Luxembourg;

    Cardiff Univ Sch Engn Queens Bldg Cardiff CF24 3AA S Glam Wales;

    Univ Luxembourg Inst Computat Engn 6 Ave Fonte L-4362 Esch Sur Alzette Luxembourg;

    Univ Luxembourg Inst Computat Engn 6 Ave Fonte L-4362 Esch Sur Alzette Luxembourg;

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  • 正文语种 eng
  • 中图分类 工程力学;
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