A perturbation expansion is offered for the micromechanical prediction of the bifurcation buckling of soft viscoelastic composites with imperfections (e.g. wavy fibers). The composites of periodic microstructure are subjected to compressive loading and are undergoing large deformations. The perturbation expansion applied on the imperfect composites results in a zero and first order problems of perfect composites. In the former problem, loading exists and interfacial and periodicity conditions are imposed. In the latter one, however, loading is absent, the interfacial conditions possess complicated terms that have been already established by the zero order problem, and Bloch-Floquet boundary conditions are imposed. Both problems are solved by the high-fidelity generalized method of cells (HFGMC) micromechanical analysis. The ideal critical bifurcation stress can be readily predicted from the asymptotic values of the form of waviness growth with applied loading. This form enables also the estimation of the actual critical stress. The occurrence of the corresponding critical deformation and time is obtained by generating the stress-deformation response of the composite. The offered approach is illustrated for the prediction of bifurcation buckling of viscoelastic bi-layered and polymer matrix composites as well as porous materials. Finally, bifurcation buckling stresses of unidirectional composites in which the matrix is represented by the quasi-linear viscoelasticity theory are predicted. This quasi-linear viscoelasticity model exhibits constant damping which is observed by the actual viscoelastic behavior of biological materials.

中文翻译：

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通过有限应变 HFGMC 微力学预测软粘弹性复合材料的微屈曲


扰动展开用于对具有缺陷的软粘弹性复合材料（例如波状纤维）的分叉屈曲进行微机械预测。周期性微观结构的复合材料受到压缩载荷并发生较大变形。对不完美复合材料应用微扰展开会导致完美复合材料的零阶和一阶问题。在前一问题中，存在载荷并施加界面和周期性条件。然而，在后一种情况下，不存在载荷，界面条件具有已通过零阶问题建立的复杂项，并且施加了 Bloch-Floquet 边界条件。这两个问题都可以通过高保真广义细胞方法 (HFGMC) 微机械分析来解决。理想的临界分叉应力可以很容易地根据施加载荷时波纹增长形式的渐近值来预测。这种形式还可以估计实际临界应力。通过生成复合材料的应力-变形响应来获得相应的临界变形的发生和时间。所提供的方法用于预测粘弹性双层和聚合物基复合材料以及多孔材料的分叉屈曲。最后，预测了用准线性粘弹性理论表示基体的单向复合材料的分岔屈曲应力。这种准线性粘弹性模型表现出恒定阻尼，这是通过生物材料的实际粘弹性行为观察到的。