An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture
An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture
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DOI：
10.1016/j.cma.2021.113691
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发表时间：
2021-01
期刊：
影响因子：
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通讯作者：
Yue Yu;Huaiqian You;Nathaniel Trask
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文献类型：
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作者：
Yue Yu;Huaiqian You;Nathaniel Trask
基于状态的近场动力学模型的无网格离散化因其能够自然地描述一般材料的断裂而具有吸引力。然而，随着分辨率的提高，有两个因素共同阻止基于状态的近场动力学的无网格离散收敛到相应的局部解：正交误差阻碍了体力学的准确预测，并且缺乏明确的边界表示在施加牵引载荷时带来了挑战。在本文中，我们开发了线性近场动力学固体（LPS）模型的重新表述来解决这些缺点，使用改进的无网格求积、非局部膨胀的重新表述以及非局部牵引条件的一致处理来构建具有严格精度保证的模型。特别是，这些改进旨在在存在不断发展的骨折的情况下加强离散一致性，其先验未知的位置使得一致的治疗变得困难。在没有断裂的情况下，当存在相应的经典连续介质力学模型时，我们的改进提供了对相应局部解的渐近兼容收敛，消除了历史上困扰近场动力学离散化的表面效应和牵引载荷问题。当断裂发生时，我们的公式通过破坏键自动提供断裂表面的清晰表示，避免质量损失。我们提供严格的误差分析并展示许多基准的收敛性，包括制造解决方案、自由表面、非均匀牵引载荷和复合材料问题。最后，我们根据最近的钠钙玻璃动态裂纹分支实验验证了脆性断裂的模拟，证明该方案可以对实际工程问题进行准确的预测。
Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to prevent meshfree discretizations of state-based peridynamics from converging to corresponding local solutions as resolution is increased: quadrature error prevents an accurate prediction of bulk mechanics, and the lack of an explicit boundary representation presents challenges when applying traction loads. In this paper, we develop a reformulation of the linear peridynamic solid (LPS) model to address these shortcomings, using improved meshfree quadrature, a reformulation of the nonlocal dilatation, and a consistent handling of the nonlocal traction condition to construct a model with rigorous accuracy guarantees. In particular, these improvements are designed to enforce discrete consistency in the presence of evolving fractures, whosea prioriunknown location render consistent treatment difficult. In the absence of fracture, when a corresponding classical continuum mechanics model exists, our improvements provide asymptotically compatible convergence to corresponding local solutions, eliminating surface effects and issues with traction loading which have historically plagued peridynamic discretizations. When fracture occurs, our formulation automatically provides a sharp representation of the fracture surface by breaking bonds, avoiding the loss of mass. We provide rigorous error analysis and demonstrate convergence for a number of benchmarks, including manufactured solutions, free-surface, nonhomogeneous traction loading, and composite material problems. Finally, we validate simulations of brittle fracture against a recent experiment of dynamic crack branching in soda-lime glass, providing evidence that the scheme yields accurate predictions for practical engineering problems.