Properties of operator constitutive relations in mechanics of deformable solid

IF 0.7 Q4 MECHANICS
Dimitri Georgievskii
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引用次数: 0

Abstract

The constitutive relations between stresses and strains in the mechanics of a deformable solid, including their operator connection, are considered. Some important and frequently occurring properties of tangent modulus and tangent pliability as rank four tensors are described. Depending on this, a possible classification of continuous media is proposed. Scleronomous and rheonomic media, homogeneous and inhomogeneous media (in particular, composites), media with memory, spatially nonlocal media, materials with hard or soft characteristics are distinguished. For non-linearly elastic isotropic media, the apparatus of tensor nonlinear isotropic functions of one argument is developed. Particular attention is paid to the three-term representation of power tensor series in three-dimensional space, reversibility of tensor functions, Taylor tensor series, tensor linearity (quasilinearity) and nonlinearity.
变形固体力学中算子本构关系的性质
考虑了变形固体力学中应力和应变的本构关系,包括它们的算子连接。描述了作为四阶张量的切模量和切柔韧性的一些重要和经常出现的性质。在此基础上,提出了一种可能的连续介质分类方法。硬化和流变介质,均匀和非均匀介质(特别是复合材料),具有记忆的介质,空间非局部介质,具有硬或软特性的材料被区分开来。对于非线性弹性各向同性介质,建立了一阶张量非线性各向同性函数装置。特别关注三维空间中幂张量级数的三项表示、张量函数的可逆性、泰勒张量级数、张量线性(拟线性)和非线性。
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
4
审稿时长
32 weeks
期刊介绍: Theoretical and Applied Mechanics (TAM) invites submission of original scholarly work in all fields of theoretical and applied mechanics. TAM features selected high quality research articles that represent the broad spectrum of interest in mechanics.
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