A hollow cylinder of incompressible material obeying Hill’s orthotropic quadratic yield criterion and its associated flow rule is contracted on a rigid cylinder inserted in its hole. Friction occurs at the contact surface between the hollow and solid cylinders. An axisymmetric boundary value problem for the flow of the material is formulated and solved, and the solution is in closed form. A numerical technique is only necessary for evaluating ordinary integrals. The solution may exhibit singular behavior in the vicinity of the friction surface. The exact asymptotic representation of the solution shows that some strain rate components and the plastic work rate approach infinity in the friction surface’s vicinity. The effect of plastic anisotropy on the solution’s behavior is discussed.

中文翻译：

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各向异性塑性的精确轴对称解

遵循Hill的正交各向异性屈服准则及其不可逆流规则的不可压缩材料空心圆柱体在插入其孔中的刚性圆柱体上收缩。摩擦发生在空心圆柱体和实心圆柱体之间的接触表面上。提出并解决了材料流动的轴对称边界值问题，并且该解决方案为封闭形式。数值技术仅对于评估普通积分是必需的。该溶液在摩擦表面附近可能表现出奇异的行为。该解的精确渐近表示表明，某些应变率分量和塑性功率在摩擦表面附近接近无穷大。讨论了塑性各向异性对溶液行为的影响。