论文标题
微极性类型的线性理论和弹性概括的无效理论
Null Lagrangians in linear theories of micropolar type and few other generalizations of elasticity
论文作者
论文摘要
在普遍弹性的线性理论的背景下，包括均质微极介质，准晶体，压电和压电媒体的均质弹性，我们探索了无效的lagrangians的概念。为了获得无效的Lagrangians家族，我们采用了H. Rund的足够条件。在某些情况下，发现了非零的零拉格朗日语，并且存储的能源承认分为零的拉格朗日和剩余时间。但是，每当相关弹性张量遵守某些对称条件时，无效的拉格朗日就会消失，这些条件可以解释为cauchy关系的类似物。
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.
