An exact solution is obtained for a new class of problems on the imposition of large deformations in nonlinear elastic micropolar bodies. The problem of determining the stress state in a compound slab having the shape of a rectangular parallelepiped, composed of pre-deformed layers and subjected to biaxial tension or compression is solved. The layers are made of isotropic incompressible nonlinear elastic micropolar materials. The layers are preliminarily deformed by straightening of circular cylindrical sectors. The solution is based on a class of universal deformations for isotropic incompressible nonlinear elastic micropolar materials. Numerical studies were carried out. The dependencies of stresses, resulting forces and moments on the parameters of initial and additional deformations are presented. Significant nonlinear effects are revealed. The influence of micropolar effects on the stress state has been studied. The solution can be used to verify software designed to numerically solve problems on the imposition of large deformations in bodies made of nonlinear elastic micropolar materials.

获得了非线性弹性微极体中施加大变形的一类新问题的精确解。解决了确定由预变形层组成并受到双轴拉伸或压缩的长方体形状的复合板中的应力状态的问题。这些层由各向同性不可压缩非线性弹性微极性材料制成。通过矫直圆柱形扇区使各层初步变形。该解决方案基于各向同性不可压缩非线性弹性微极性材料的一类通用变形。进行了数值研究。给出了应力、合力和力矩对初始变形和附加变形参数的依赖性。揭示了显着的非线性效应。研究了微极效应对应力状态的影响。该解决方案可用于验证设计用于数值解决由非线性弹性微极性材料制成的物体中施加大变形问题的软件。