Exact solution of one problem of imposition of large deformations in a compound slab with pre-deformed layers of incompressible nonlinear elastic micropolar material

IF 1.9 4区工程技术 Q3 MECHANICS Continuum Mechanics and Thermodynamics Pub Date : 2024-03-16 DOI:10.1007/s00161-024-01294-4

V. A. Levin, K. M. Zingerman, A. E. Belkin

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Abstract

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.

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在带有不可压缩非线性弹性微波材料预变形层的复合板坯中施加大变形的一个问题的精确解法

对一类新的关于在非线性弹性微极体中施加大变形的问题给出了精确的解决方案。解决了如何确定由预变形层组成并受到双轴拉伸或压缩的矩形平行四边形复合板坯的应力状态问题。这些层由各向同性的不可压缩非线性弹性微波材料制成。这些层是通过拉直圆形圆柱扇形初步变形的。求解基于各向同性不可压缩非线性弹性微波材料的一类通用变形。进行了数值研究。介绍了应力、所产生的力和力矩对初始变形和附加变形参数的依赖关系。揭示了显著的非线性效应。研究了微波效应对应力状态的影响。求解结果可用于验证设计用于数值解决由非线性弹性微波材料构成的体的大变形问题的软件。

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来源期刊

Continuum Mechanics and Thermodynamics 物理-力学

CiteScore

5.30

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena. Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.