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首页> 外文期刊>Mathematics and mechanics of solids: MMS >Irreducible matrix resolution for symmetry classes of elasticity tensors
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Irreducible matrix resolution for symmetry classes of elasticity tensors

机译：用于对称性的弹性张量的不可减少的矩阵分辨率

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摘要

In linear elasticity, a fourth-order elasticity (stiffness) tensor of 21 independent components completely describes deformation properties elastic constants of a material. The main goal of the current work is to derive a compact matrix representation of the elasticity tensor that correlates with its intrinsic algebraic properties. Such representation can be useful in design of artificial materials. Owing to Voigt, the elasticity tensor is conventionally represented by a (6 x 6) symmetric matrix. In this paper, we construct two alternative matrix representations that conform with the irreducible decomposition of the elasticity tensor. The 3 x 7 matrix representation is in correspondence with the permutation transformations of indices and with the general linear transformation of the basis. An additional representation of the elasticity tensor by two scalars and three 3 x 3 matrices is suitable to describe the irreducible decomposition under the rotation transformations. We present the elasticity tensor of all crystal systems in these compact matrix forms and construct the hierarchy diagrams based on this representation.
机译：在线性弹性，21个独立组分的四阶弹性（刚度）张量完全描述了材料的变形特性弹性常数。目前工作的主要目标是导出与其内在代数性质相关的弹性张量的紧凑矩阵表示。这种代表性可用于设计人造材料。由于voigt，弹性张量通常由（6×6）对称矩阵表示。在本文中，我们构建了两个替代的矩阵表示，其符合弹性张量的不可缩短的分解。 3×7矩阵表示与索引的置换变换和基础的一般线性变换相对应。由两个标量和三个3×3矩阵的弹性张量的额外表示适用于在旋转变换下描述不可缩小的分解。我们以这些紧凑的矩阵形式呈现所有晶体系统的弹性张量，并根据该表示构建层次结构图。

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