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On the treatment of boundary conditions for bond-based peridynamic models

机译：论粘合基础逆动脉模型的边界条件

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In this paper, we propose two approaches to apply boundary conditions for bond-based peridynamic models. There has been in recent years a renewed interest in the class of so-called non-local models, which include peridynamic models, for the simulation of structural mechanics problems as an alternative approach to classical local continuum models. However, a major issue, which is often disregarded when dealing with this class of models, is concerned with the manner by which boundary conditions should be prescribed. Our point of view here is that classical boundary conditions, since applied on surfaces of solid bodies, are naturally associated with local models. The paper describes two methods to incorporate classical Dirichlet and Neumann boundary conditions into bond-based peridynamics. The first method consists in artificially extending the domain with a thin boundary layer over which the displacement field is required to behave as an odd function with respect to the boundary points. The second method resorts to the idea that peridynamic models and local models should be compatible in the limit that the so-called horizon vanishes. The approach consists then in decreasing the horizon from a constant value in the interior of the domain to zero at the boundary so that one can directly apply the classical boundary conditions. We present the continuous and discrete formulations of the two methods and assess their performance on several numerical experiments dealing with the simulation of a one-dimensional bar. (c) 2020 Elsevier B.V. All rights reserved.
机译：在本文中，我们提出了两种方法来应用基于粘合的白动力学模型的边界条件。近年来近年来，对包括白动模型的所谓非本地模型的阶级的重新兴趣，用于模拟结构力学问题作为典型本地连续模型的替代方法。但是，在处理这类模型时经常被忽视的主要问题涉及边界条件应规定的方式。我们这里的观点在于古典边界条件，因为施加在固体的表面上，自然与局部模型相关。本文描述了两种方法，将古典Dirichlet和NeuMann边界条件纳入基于键的白颌动态。第一方法包括人工地扩展域，其中薄边界层在该域中需要位移场，以便相对于边界点作为奇数函数。第二种方法诉诸认为智典模型和本地模型应该兼容的想法，以至于所谓的地平线消失的极限。然后，该方法包括从域内部的恒定值降低地平线，在边界处为零，使得可以直接应用经典边界条件。我们介绍了两种方法的连续和离散制剂，并在几个数值实验中评估了处理一维棒的模拟的数值实验。 （c）2020 Elsevier B.v.保留所有权利。

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