微极型线性理论中的零拉格朗日量及弹性理论的其他若干推广
Null Lagrangians in linear theories of micropolar type and few other generalizations of elasticity
AI总结：
该研究在微极介质、准晶等广义弹性线性理论中，利用H. Rund充分条件推导零拉格朗日量族，发现部分情形下存在非零零拉格朗日量且储存能可分解，同时明确其在类柯西对称条件下退化为零的规律。
摘要：
在涵盖均匀微极介质、准晶、压电与压磁介质的广义弹性线性理论框架下，我们探究零拉格朗日量的概念。我们采用H. Rund的充分条件来推导零拉格朗日量族。在部分情形下可得到非零的零拉格朗日量，此时储存能可分解为一个零拉格朗日量与一个余项。然而，当相关弹性张量满足可视为柯西关系类似物的特定对称条件时，零拉格朗日量将退化为零。
英文摘要：
In the context of linear theories of generalized elasticity including those for homogeneous micropolar media, quasicrystals, piezoelectric and piezomagnetic media, we explore the concept of null Lagrangians. For obtaining the family of null Lagrangians we employ the sufficient conditions of H. Rund. In some cases a non-zero null Lagrangian is found and the stored energy admits a split into a null Lagrangian and a remainder. However, the null Lagrangian vanishes whenever the relevant elasticity tensor obeys certain symmetry conditions which can be construed as an analogue of the Cauchy relations.
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