Abstract—

The general representation of a symmetric isotropic tensor-function of the second rank in three-dimensional space, depending on two tensor arguments of the second rank, is investigated. This representation includes eight scalar material functions of ten invariants of dependent tensors, including four joint invariants. The tensor function is interpreted as the constitutive relation of an isotropic nonlinear material, which expresses the relationship between deformations and stresses and stress rates. A certain type of stress state is selected, corresponding to a combination of axial tension of the rod by a constant force and (θz) -torsion by a time-periodic moment. It is shown that with a proper selection of the above-mentioned eight material functions as functions of the stress state invariants, it is possible to describe a much stronger change in axial deformations under joint tension and cyclic torsion than under separate tension without torsion. Such an “orthogonal effect” of the stress-strain state is close in form to the ratchetting and vibration creep known in experimental mechanics.

中文翻译：

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两个参数的非线性张量函数和应力应变状态的“正交效应”

摘要-

研究了二维空间中第二列的对称各向同性张量函数的一般表示，具体取决于第二列的两个张量参数。此表示包括十个从属张量不变量的八个标量材料函数，其中包括四个关节不变量。张量函数被解释为各向同性非线性材料的本构关系，它表示变形与应力和应力率之间的关系。选择某种类型的应力状态，对应于由恒定力产生的杆的轴向张力与由时间周期力矩产生的（θz）扭转的组合。结果表明，与上述8层材料的功能的适当选择作为应力状态不变的功能，与没有扭转的单独拉力相比，在关节拉力和周期性扭转下轴向变形的变化要大得多。应力-应变状态的这种“正交效应”在形式上接近实验力学中已知的棘轮和振动蠕变。