The article deals with the problem on setting boundary conditions for asymmetric problems in the mechanics of growing solids. Firstly, we study the conditions on the growing surface that are most important from the point of view of the theory completeness. When deriving relations on the growing surface, we use the results known from the algebra of rational invariants. Geometrically and mechanically consistent differential constraints that are valid for a very wide range of materials and metamaterials are obtained on the growing surface. Several variants of constitutive equations on the growing surface of different levels of complexity are investigated. The formulated differential constraints imply the experimental identification of several defining functions. Thus, the results obtained can serve as a general basis in applied research on the mechanics of growing solids with an asymmetric stress tensor.

中文翻译：

---

固体力学非对称理论中的微分约束

本文讨论了为增长固体力学中的非对称问题设置边界条件的问题。首先，我们从理论完整性的角度研究最重要的生长表面条件。在推导增长表面上的关系时，我们使用有理不变量的代数中已知的结果。在生长的表面上获得了几何和机械上一致的微分约束，这些约束适用于非常广泛的材料和超材料。研究了本构方程在不同复杂程度的增长表面上的几种变体。拟定的差分约束意味着对几个定义函数的实验识别。从而，