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首页> 外文会议>International Conference on Trends in Computational Structural Mechanics May 20-23, 2001 Schloss Hofen, Lake Constance >ON THE LACK OF SYMMETRY IN MATERIALS
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ON THE LACK OF SYMMETRY IN MATERIALS

机译：关于材料缺乏对称性

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摘要

In this paper we examine the loss of symmetry in mechanics of material. To this end we first review the so-called Bromwich bounds of eigenvalues in linear algebra. For illustration we revisit the hierarchy of different failure diagnostics when the material properties loose symmetry. Subsequently, we examine the lack of symmetry in the stress and strain measures which appears in finite deformation analysis and in micropolar continua. For definiteness, we evaluate maximum and minimum values of the non-symmetric second order tensors, which no longer coincide with the principal eigenvalues, and we discuss the special format of the trace invariants. For geometric visualization we generalize Mohr's circle and the underlying transformation relations which account for the loss of symmetry in two dimensions. To conclude, we consider two examples of shear failure which serve as model problems to address the intricate differences of symmetric and non-symmetric stress and deformation measures.
机译：在本文中，我们研究了材料力学中对称性的损失。为此，我们首先回顾线性代数中本征值的所谓布罗姆维奇界。为了说明起见，当材料属性失去对称性时，我们将重新审视不同故障诊断的层次结构。随后，我们研究了在有限变形分析和微极连续中出现的应力和应变测量中缺乏对称性的情况。为了确定性，我们评估了非对称二阶张量的最大值和最小值，这些最大值和最小值不再与主要特征值一致，并且讨论了跟踪不变式的特殊格式。对于几何可视化，我们将莫尔圆和潜在的转换关系归纳化，从而解决了二维对称性的损失。总而言之，我们考虑剪切破坏的两个例子，它们作为模型问题来解决对称和非对称应力与变形措施的复杂差异。

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