The use of a virtual configuration in formulating constitutive equations for residually stressed elastic materials
The use of a virtual configuration in formulating constitutive equations for residually stressed elastic materials
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DOI：
10.1007/bf00041874
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发表时间：
1995-12-01
影响因子：
2
通讯作者：
Hoger, A
中科院分区：
文献类型：
--
作者：
Johnson, BE;Hoger, A
残余应力是物体在无载荷平衡状态下的应力。由于残余应力会显著影响部件的机械性能，因此测量这些应力并预测其对机械性能的影响是许多工程问题中的重要目标。测量残余应力的常用方法包括各种破坏性实验，其中切割物体以释放残余应力。测量产生的应变并用于近似完整主体中的原始残余应力。为了预测残余应力体的力学行为，需要一个包含残余应力影响的本构模型，本文提出了一种方法，通过该方法，从标准破坏性实验获得的数据可以被用来推导描述弹性残余应力体的力学行为的本构方程。推导是基于这样一种思想，即对于残余应力体中的每一个无穷小邻域，都存在一个相应的无应力构形。我们把这种无应力构形称为无穷小邻域的“虚”构形。推导要求无应力材料的本构方程是已知的和可逆的;它用于将残余应力与虚拟配置变形成残余应力配置相关。虽然虚拟配置的概念是核心的推导，这个配置的几何形状不需要明确地确定，它不需要通过实验来实现，为了构建本构方程的残余应力body.The一般的数学形式的残余应力弹性材料的本构方程的有效性已经推导出以前的一些情况下。这些一般形式包含许多未知的材料响应函数或材料常数，必须通过实验确定。与此相反，本文提出的方法的结果在本构方程，这是一个显式的残余应力的函数，只包括所需的材料参数来描述无应力的material.After介绍的方法推导本构方程，我们探讨了破坏性实验和推导中使用的理论之间的关系。具体来说，我们讨论了使用的理论，以改善破坏性实验的设计，并使用破坏性实验，以获得所需的数据，以构建一个特定的材料的本构方程。
Residual stress is the stress present in the unloaded equilibrium configuration of a body. Because residual stresses can significantly affect the mechanical behavior of a component, the measurement of these stresses and the prediction of their effect on mechanical behavior are important objectives in many engineering problems. Common methods for the measurement of residual stresses include various destructive experiments in which the body is cut to relieve the residual stress. The resulting strain is measured and used to approximate the original residual stress in the intact body. In order to predict the mechanical behavior of a residually stressed body, a constitutive model is required that includes the influence of the residual stress.In this paper we present a method by which the data obtained from standard destructive experiments can be used to derive constitutive equations that describe the mechanical behavior of elastic residually stressed bodies. The derivation is based on the idea that for each infinitesimal neighborhood in a residually stressed body, there exists a corresponding stress free configuration. We refer to this stress free configuration as the 'virtual' configuration of the infinitesimal neighborhood. The derivation requires that the constitutive equation for the stress free material be known and invertible; it is used to relate the residual stress to the deformation of the virtual configuration into the residually stressed configuration. Although the concept of the virtual configuration is central to the derivation, the geometry of this configuration need not be determined explicitly, and it need not be achievable experimentally, in order to construct the constitutive equation for the residually stressed body.The general mathematical forms of constitutive equations valid for residually stressed elastic materials have been derived previously for a number of cases. These general forms contain numerous unknown material-response functions or material constants that must be determined experimentally. In contrast, the method presented here results in a constitutive equation that is an explicit function of residual stress and includes only the material parameters required to describe the stress free material.After presenting the method for the derivation of constitutive equations, we explore the relationship between destructive experiments and the theory used in the derivation. Specifically, we discuss the use of the theory to improve the design of destructive experiments, and the use of destructive experiments to obtain the data required to construct the constitutive equation for a particular material.