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 dilitation, 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 {\it 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.
A General-Purpose, Inelastic, Rotation-Free Kirchhoff-Love Shell Formulation for Peridynamics
我们提出了一个全面的无旋转Kirchhoff-Love（KL）壳的周波（PD），能够模拟大的弹塑性变形和薄壁结构的断裂制定。为了消除对预定义的全局参数域的需要，在无网格设置中采用主成分分析来开发壳中间曲面的局部参数化。KL壳运动学被用来开发一个基于对应的PD制定。一个键稳定技术自然实现离散解的稳定性。在控制薄壳方程中只使用了中表面速度自由度。采用3D速率形式的材料模型来模拟各种材料行为。采用键关联损伤对应建模方法，在键级使用经典的失效准则，这很容易使模拟的脆性和韧性断裂。\NAT{Discretizing the model with asymptotically compatible meshfree approximation provides a scheme which converges to the classical KL shell model while providing an accurate and flexible framework for treating fracture.}一个广泛的数值例子，从弹性静力学的问题，涉及塑性，断裂和破碎，进行验证的准确性，收敛性和鲁棒性的PD薄壳制定。还值得注意的是，本方法自然地使得能够在完全非结构化的表面网格上离散化需要高阶光滑度的壳理论。
A variational framework for bond-based peridynamics with spatially varying horizons and its asynchronous time integration
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Universität Siegen（锡根大学）；California Institute of Technology（加州理工学院）；Queensland University of Technology（昆士兰科技大学）
A Finite Volume Method for Elastic Waves in Heterogeneous, Anisotropic and Fractured Media
Center for Modeling of Coupled Subsurface, Dynamics, Department of Mathematics, University of Bergen（卑尔根大学耦合地下动力学中心数学系）；NORCE Norwegian Research Centre AS（挪威研究中心有限公司）
