关于键基周波模型边界条件的处理
On the treatment of boundary conditions for bond-based peridynamic models
摘要：
在本文中，我们提出了两种方法来应用边界条件的债券为基础的周波模型。近年来，作为经典局部连续介质模型的替代方法，对包括周向模型在内的所谓非局部模型类的结构力学问题的模拟重新引起了人们的兴趣。然而，一个主要的问题，这是经常被忽视的，当处理这类模型，是有关的方式，其中边界条件应规定。我们的观点是，经典的边界条件，因为适用于表面的固体，自然与当地的模型。本文介绍了两种方法，将经典的Dirichlet和Neumann边界条件，以键为基础的周期性。第一种方法包括在人工扩展域与薄边界层的位移场需要表现为一个奇函数的边界点。第二种方法诉诸于这样的想法，即在所谓的地平线消失的限制下，周波模型和局部模型应该是兼容的。该方法包括然后在减少的地平线从一个恒定的值在内部的域为零的边界，以便可以直接应用经典的边界条件。我们提出了连续和离散配方的两种方法，并评估其性能的几个数值实验处理模拟的一维酒吧。
英文摘要：
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.
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