Dilatationally nonlinear elastic materials—II. An example illustrating stress concentration reduction
Dilatationally nonlinear elastic materials—II. An example illustrating stress concentration reduction
复制标题
扩张非线性弹性材料—II。说明减少应力集中的示例。
DOI：
10.1016/0020-7683(89)90078-4
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发表时间：
1989
影响因子：
3.6
通讯作者：
Jiang Guo
中科院分区：
文献类型：
--
作者：
R. Abeyaratne;Jiang Guo
本文是由两部分组成的研究的第二部分，使用一个特定的边值问题来说明第一部分中讨论的理论的一些特征。本文研究了内壁无牵引力、外壁具有规定径向位移δ的空心球的球对称变形。分析是在非线性弹性力学的小应变理论下进行的，假定物体是由均匀各向同性的弹性材料组成的，其剪切响应是线性的，膨胀响应是三线性的。对于一定范围的外加位移δ，问题有无穷多个解，这些解描述了涉及相边界的构型；应变场在相边界的两边都是连续的，但在相边界上有一个跳跃不连续。当δ在准静态运动中单调增加时，空腔处的环向应力首先增加，然后随着相边界从空腔壁出来时不连续地减小，然后随着相边界向外传播而缓慢增加(或对于某些特殊的动力学定律，保持不变)，最后在物体完全变形后开始以原始速率增加。
This paper, which is the second in a two-part study, uses a specific boundary-value problem to illustrate some of the features of the theory discussed in the first part. Here, the spherically symmetric deformation of a hollow sphere which has a traction-free inner wall and a prescribed radial displacement δ at its outer wall is studied. The analysis is carried out within the small-strain theory of nonlinear elasticity and the body is assumed to be composed of an elastic material which is homogeneous and isotropic, and which has a linear response in shear and a trilinear response in dilatation.For a certain range of values of the applied displacement δ, the problem has aninfinityof solutions and these describe configurations which involve a phase boundary; the strain field is continuous on either side of the phase boundary but suffers a jump discontinuity across it. A “kinetic law”, which is a supplementary constitutive law pertaining to particles located on the phase boundary and relating the driving traction on the phase boundary to its velocity, is then imposed, leading to a unique response in all quasi-static motions.As δ increases monotonically during a quasi-static motion, the hoop stress at the cavity first increases, then decreases discontinuously as the phase boundary emerges from the cavity wall, next increases slowly (or, for certain special kinetic laws, remains constant) as the phase boundary propagates outwards, and finally commences to increase at the original rate once the body has been fully transformed.