An exact analytical solution to the problem of large deformations of a multilayer cylindrical rod under multistage deformation is obtained for incompressible isotropic nonlinear elastic materials. At each step of deformation, another layer is attached to the rod, after which twisting and tension–compression of the cylinder along with the attached layer occur. The solution is obtained on the basis of the theory of multiple superposition of large deformations using one of the universal solutions of the problem of nonlinear elasticity. Numerical results are given. Nonlinear effects and effects associated with superposition of large deformations are analyzed.

中文翻译：

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具有多个大变形叠加的层顺序连接的多层弹性圆柱体的扭转

对于不可压缩的各向同性非线性弹性材料，得到了多层圆柱杆在多级变形下大变形问题的精确解析解。在变形的每个步骤中，另一层附着在杆上，之后圆柱体与附着层一起发生扭转和拉伸-压缩。该解是在大变形的多重叠加理论的基础上，利用非线性弹性问题的通用解之一获得的。给出了数值结果。分析了与大变形叠加相关的非线性效应和效应。