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, whose a priori unknown 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.

基于状态的动力学模型的无网格离散化具有吸引力，因为它们具有自然描述一般材料断裂的能力。但是，有两个因素共同作用，即随着分辨率的提高，防止基于状态的动力学的无网格离散化收敛到相应的局部解：正交误差妨碍了对块体力学的准确预测，而缺乏明确的边界表示法则在施加牵引载荷时提出了挑战。在本文中，我们使用改进的无网格正交积分，非局部扩张的重构以及对非局部牵引条件的一致处理，开发了线性绕动实体（LPS）模型以解决这些缺点，从而构建了具有精确度的模型保证。特别是，先验位置不明使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体力学模型时，我们的改进为相应的局部解提供了渐近兼容的收敛，从而消除了表面效应和牵引载荷问题，这些问题历来困扰着绕动离散化。当发生断裂时，我们的配方会通过断开键自动提供断裂表面的清晰图像，从而避免质量损失。我们提供严格的误差分析，并证明了许多基准测试的收敛性，其中包括制造解决方案，自由表面，非均匀牵引载荷以及复合材料问题。最后，我们通过对钠钙玻璃中动态裂纹分支的最新实验验证了脆性断裂的模拟，