论文标题
平面磁力机械加载的多项式不变完整性基础
Reduced polynomial invariant integrity basis for in-plane magneto-mechanical loading
论文作者
论文摘要
对经过多物理载荷的材料的行为的描述需要制定构造定律，通常使用不变的数量，这些定律通常根据所考虑的物理和材料对称性来衍生。另一方面，大多数晶体材料都可以通过其晶体质地和强晶体对称性（所谓的纤维）的相关优选方向来描述。此外，在工业上生产的材料中，许多是以薄片或薄层的形式制造的。本文具有对磁机械耦合的研究，这是压力$σ$和磁化的函数。我们考虑一种具有立方对称性的材料，其质地可以由三种纤维之一描述为$θ$，$θ$，$γ$或$ a $''，并且可以将压力和大量化为量化的量很薄。我们提出了一种能够在最小完整性基础的30立方体不变的I K之间得出线性关系，描述了磁弹性问题，当它们仅限于平面载荷条件和不同的光纤方向时。该算法/程序输出是{100}面向面向的$θ$纤维的Cardinal 7的不变性列表，{110}面向{110}的$α$'纤维的Cardinal 15和{111}的{111}}面向{111}面向的$γ$γ$γ$γ$γ$γ$ fiber。这种降低（与初始基数30相比）可以有助于制定低参数宏观磁力机械模型。
The description of the behavior of a material subjected to multi-physics loadings requires the formulation of constitutive laws that usually derive from Gibbs free energies, using invariant quantities depending on the considered physics and material symmetries. On the other hand, most of crystalline materials can be described by their crystalline texture and the associated preferred directions of strong crystalline symmetry (the so-called fibers). Moreover, among the materials produced industrially, many are manufactured in the form of sheets or of thin layers. This article has for object the study of the magneto-mechanical coupling which is a function of the stress $σ$ and the magnetization M. We consider a material with cubic symmetry whose texture can be described by one of three fibers denoted as $θ$, $γ$ or $α$ ' , and which is thin enough so that both the stress and the magnetization can be considered as in-plane quantities. We propose an algorithm able to derive linear relations between the 30 cubic invariants I k of a minimal integrity basis describing a magneto-elastic problem, when they are restricted to in-plane loading conditions and for different fiber orientations. The algorithm/program output is a reduced list of invariants of cardinal 7 for the {100}-oriented $θ$ fiber, of cardinal 15 for the {110}-oriented $α$ ' fiber and of cardinal 8 for the {111}-oriented $γ$ fiber. This reduction (compared to initial cardinal 30) can be of great help for the formulation of low-parameter macroscopic magneto-mechanical models.
