A refined formulation is presented for linearized problems on internal multiscale spatial buckling modes of a fiber or fiber bundle — the structural elements of fibrous composites — that is in a subcritical (unperturbed) state under the action of shear and tensile (compressive) stresses in the transverse direction. Such an initial stress state is formed in fibers and fiber bundles in tension and compression tests of plane test specimens of angle-ply composites reinforced with straight fibers. To formulate the problem, equations are constructed by reducting a consistent variant of geometrically nonlinear equations of elasticity theory to one-dimensional equations of the theory of straight rods taking into account their interaction with the surrounding matrix. These equations are based on using the refined Timoshenko shear model in the perturbed state of composite with account of tension-compression strains in the transverse direction for a rigid fiber (fiber bundle) represented in the form of a rod with a rectangular cross section and the model of a transversely soft layer with a fixed outer boundary of the periodicity cell of composite for four binder elements introduced into consideration. It is shown that, in loading test specimens with a [±45]2s structure, a continuous rearrangement of the composite structure is possible in both compression and tension. This occurs owing to the realization and continuous changes of internal buckling modes with continuous variations of the parameter of wave formation. This fact, in particular, can explain the phenomenon of decreasing of the averaged shear modulus of a fibrous composite with growing shear strains and the formation of a reversible nonlinearly elastic component of its total strain.

中文翻译：

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具有[±45]2s堆叠序列的复合材料纤维（纤维束）在试样拉伸和压缩下的空间屈曲模式

针对纤维或纤维束（纤维复合材料的结构元素）的内部多尺度空间屈曲模式的线性化问题提出了一种改进的公式，该模型在剪切和拉伸（压缩）应力的作用下处于亚临界（未扰动）状态。横向。在用直纤维增强的角层复合材料的平面试样的拉伸和压缩试验中，在纤维和纤维束中形成这种初始应力状态。为了表述这个问题，方程是通过将弹性理论的几何非线性方程的一致变体简化为直杆理论的一维方程来构建的，同时考虑到它们与周围矩阵的相互作用。这些方程基于在复合材料的扰动状态下使用改进的 Timoshenko 剪切模型，并考虑到刚性纤维（纤维束）在横向上的拉压应变，该刚性纤维（纤维束）以具有矩形横截面的棒的形式表示，并且考虑了四种粘合剂元素的复合材料周期性单元的固定外边界的横向软层模型。结果表明，在具有[±45]2s结构的加载试样中，复合结构在压缩和拉伸方面的连续重排是可能的。这是由于内部屈曲模式的实现和连续变化以及波浪形成参数的连续变化而发生的。这个事实，特别是