Stress softening, strain localization and permanent set in the circumferential shear of an incompressible elastomeric cylinder
Stress softening, strain localization and permanent set in the circumferential shear of an incompressible elastomeric cylinder
复制标题
不可压缩弹性体圆柱体周向剪切中的应力软化、应变局部化和永久变形
DOI：
10.1093/imamat/59.3.309
复制
发表时间：
1997
影响因子：
1.2
通讯作者：
K. Rajagopal
中科院分区：
文献类型：
--
作者：
H. E. Huntley;A. S. WlNEMAN;K. Rajagopal
弹性材料的本构理论是近年来发展起来的，根据该理论，应力是在不同变形水平下由不同的微机制产生的。当变形较小时，应力由通常的橡胶弹性理论给出。随着变形的增加，一些大分子微观结构的连接点断裂。然后，连接点重新形成，形成新的微观结构。随着变形的增加，本构方程允许原结点的连续断裂和新结点的形成。大分子断裂导致应力降低。新的微观结构的形成导致永久凝固的释放外载荷。本工作考虑由这种材料组成的空心圆柱体，也假设其不可压缩且各向同性。圆柱体内表面刚性固定，由于外表面施加均匀轴向力矩而发生轴对称变形。形成了具有原始微观结构的材料外区和经过大分子断裂的材料内区，由一个圆柱形界面隔开，其半径随着外表面的旋转而增大。确定了剪力变形分布、弯矩-旋转响应和释放弯矩时的永久设定值。研究发现，与纯弹性响应相比，微结构断裂可导致圆柱体内表面附近更高水平的剪切变形。还可以看出，在圆柱体内边界的薄层材料中可以产生高剪切变形的残余状态。
A constitutive theory for elastomeric materials has recently been developed according to which stress is generated by different micromechanisms at different levels of deformation. When the deformation is small, the stress is given by the usual theory of rubber elasticity. As the deformation increases, some junctions of the macromolecular microstructure rupture. Junctions then re-form to generate a new microstructure. The constitutive equation allows for continuous scission of the original junctions and formation of new ones as deformation increases. The macromolecular scission causes stress reduction. The formation of new microstructures results in permanent set on release of external load. The present work considers a hollow circular cylinder composed of such a material, also assumed to be incompressible and isotropic. The cylinder is fixed rigidly at its inner surface and undergoes axisymmetric deformation due to a uniform axial moment applied at the outer surface. There develops an outer zone of material with the original microstructure and an inner zone of material having undergone macromolecular scission, separated by a cylindrical interface, the radius of which increases with the rotation of the outer surface. The shear deformation distribution, moment-rotation response and permanent set on release of moment are determined. It is found that microstructural scission can lead to higher levels of shear deformation near the inner surface of the cylinder than in the case of purely elastic response. It is also seen that a residual state of high shear deformation can arise in a thin layer of material at the inner boundary of the cylinder.