Finite deformation of materials exhibiting curvilinear aeolotropy
Finite deformation of materials exhibiting curvilinear aeolotropy
复制标题
表现出曲线各向异性的材料的有限变形
DOI：
--
复制
发表时间：
1955
期刊：
影响因子：
--
通讯作者：
J. Adkins
中科院分区：
文献类型：
--
作者：
J. Adkins
利用张量符号，提出了具有曲线各向异性的可压缩和不可压缩材料的有限弹性变形的一般理论。该理论是为完全不对称、正交异性或横向各向同性的材料制定的，相对于用于定义各向异性的曲线坐标系。在应用中，注意仅限于圆柱对称和球对称问题，从这些问题中出现了圆柱管的膨胀、延伸和扭转以及球壳的膨胀等特殊情况。此外，还考虑了直线各向异性材料的长方体的挠曲作为圆柱对称问题的极限情况。管壳或球壳弯曲的条件，以及变形长方体的曲面不受外加应力的条件，用与材料的对称性无关的一般应变-能函数的形式得到。
Using tensor notation, a general theory is developed for finite elastic deformations of compressible and incompressible materials which exhibit curvilinear aeolotropy. The theory is formulated for materials which are completely unsymmetrical, orthotropic or transversely isotropic with respect to the curvilinear co-ordinate system which is employed to define the aeolotropy. In applications, attention is confined to cylindrically symmetrical and spherically symmetrical problems, from which emerge as special cases the inflation, extension and torsion of a cylindrical tube, and the inflation of a spherical shell. In addition, the flexure of a cuboid of rectilinearly aeolotropic material is considered as a limiting case of the cylindrically symmetrical problem. The conditions for the tube or spherical shell to be everted, and for the curved faces of the deformed cuboid to be free from applied stress, are obtained in terms of a general strain-energy function in forms which are independent of symmetries in the material.