Characterization of the symmetry class of an elasticity tensor using polynomial covariants
Characterization of the symmetry class of an elasticity tensor using polynomial covariants
复制标题
使用多项式协变表征弹性张量的对称类
DOI：
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发表时间：
2018
影响因子：
2.6
通讯作者：
B. Desmorat
中科院分区：
文献类型：
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作者：
M. Olive;B. Kolev;R. Desmorat;B. Desmorat
我们制定有效的必要和充分条件，以确定对称类的弹性张量，四阶张量，这是弹性理论的基石和玩具模型的线性本构关系在物理学。新颖之处在于，这些条件是使用多项式协变写的。作为一个推论，我们推断，对称类仿射代数集，这似乎是新的结果。同时，我们也得到了四阶调和张量的协变代数的70个生成元的最小集合，并在全对称张量上引入了一个新的广义叉积。最后，使用这些张量协变，我们产生了一个新的最小集的294个发电机的不变代数的弹性张量。
We formulate effective necessary and sufficient conditions to identify the symmetry class of an elasticity tensor, a fourth-order tensor which is the cornerstone of the theory of elasticity and a toy model for linear constitutive laws in physics. The novelty is that these conditions are written using polynomial covariants. As a corollary, we deduce that the symmetry classes are affine algebraic sets, a result which seems to be new. Meanwhile, we have been lead to produce a minimal set of 70 generators for the covariant algebra of a fourth-order harmonic tensor and introduce an original generalized cross-product on totally symmetric tensors. Finally, using these tensorial covariants, we produce a new minimal set of 294 generators for the invariant algebra of the elasticity tensor.