A method is proposed for calculating the near-surface effect in piecewise homogeneous bodies under large deformations based on a combined use of one-level applied and two-level carcass theories. The applied theory is used for a macromechanical continuation of the solution of the problem, but the carcass theory is used in the final part of the loading path or directly at the final loading of the body. The implementation of the problem by the carcass theory for the body as a whole ends with solution of extreme problems using a highly gradient scheme for assemblies of structural blocks near boundary surfaces of the body. The rotation-caused development of configurations of cylinders reinforced with ring fibers is studied using this method and the model of a piecewise homogeneous medium. The results obtained by the carcass theory and the model of a piecewise homogeneous medium differed only slightly, confirming the high accuracy of the analysis using the two-level approach. A higher stability of the numerical implementation of the carcass theory, in comparison with the model of a piecewise homogeneous medium, was revealed when the macromechanical continuation was carried out within the framework of this theory itself. An even higher stability of the approach was reached by implementation of the macromechanical continuation of the applied theory. Performing calculations only for nodal blocks of the medium at the micromechanical level of the carcass theory, together with application of the applied theory for the macromechanical continuation, led to an extremely high efficiency of the two-level approach. In contrast to the piecewise homogeneous medium model, this approach made it possible to study the behavior of piecewise homogeneous cylinders considering the near-surface effect up to the configurationdetermined ultimate rotation speed.

中文翻译：

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基于两水平法的大变形分段均质体近表面效应计算方法

结合一级应用理论和二级胴体理论，提出了一种大变形下分段均质体近地表效应的计算方法。应用理论用于解决问题的宏观力学延续，但胴体理论用于加载路径的最后部分或直接用于车身的最终加载。用胴体理论对整个车身的问题的实施以使用高梯度方案解决极端问题而告终，该方案用于在车身边界表面附近组装结构块。使用这种方法和分段均质介质模型研究了由旋转引起的环形纤维增强圆柱体构型的发展。通过胴体理论和分段均匀介质模型获得的结果仅略有不同，证实了使用两级方法进行分析的高精度。与分段均匀介质模型相比，当在该理论本身的框架内进行宏观力学延续时，揭示了胴体理论的数值实现具有更高的稳定性。通过应用理论的宏观力学延续实现了该方法的更高稳定性。在胎体理论的微观力学水平上仅对介质的节点块进行计算，结合应用理论在宏观力学延续中的应用，导致了两级方法的极高效率。