In this paper, we carry out linear stability analysis of a coupled solid–fluid system in a plane Couette flow past an initially stressed neo-Hookean solid at creeping flow limit (Re=0) and arbitrary Reynolds number (Re), as well as for different solid thicknesses. In biological and engineering systems, we often encounter flows past initially stressed deformable solids. For these cases, initial strain or initial stress appears as an additional symmetry representing tensor in the constitutive relation. Consequently, initial stress induces anisotropy (transverse isotropy in the present case) and affects material properties. We employ a hyperelastic model for the initially stressed deformable solid to study the effects of both uni-axial and equi-biaxial initial stresses on flow instability. This study also presents a case where anisotropy in the solid interferes with the stability of the solid–fluid coupled system. In contrast with the previous formulations with two or three state Eulerian–Lagrangian formulations, the present formulation requires four configurations for the initially stressed solid, viz. stress-free, initially stressed, deformed, and the perturbed state. This formulation applies to any fluid–solid coupled problems where the solid contains initial/residual stress. Our results show that initial tensile stress stabilizes the flow, while compressive initial stress destabilizes the same. Fortuitously, this observation of coupled fluid–solid stability is in agreement with the stability of solid column-like structures, where compressive axial stress leads to buckling. We report similar results for uni-axial and equi-biaxial initial stress, for different wave modes at creeping flow limit and their extensions at higher $Re$, and various solid thicknesses. Two modes of instability, viz., short-wave and finite-wave modes present in the creeping-flow limit are significantly affected by tensile/compressive initial stress for both uni-axial and equi-biaxial cases. For uni-axial tensile initial stress, the finite-wave mode does not extend to high $Re$. Instead of them, we observe multiple upstream modes to become unstable for higher $Re$, which show the wall mode scaling as O($R{e}^{-1/3}$). These upstream modes are not observed for stress-free solid. This behavior is triggered by the additional coupling terms between initial stress and perturbed variable in the governing equations of initially stressed solids. However, for the equi-biaxial case, the finite-wave mode does extend to higher $Re$ to show wall mode scaling. This mode further stabilizes/destabilizes depending on the tensile/compressive nature of the initial stress present in the solid.

在本文中，我们在蠕变流极限 ( Re = 0) 和任意雷诺数 ( Re)，以及不同的固体厚度。在生物和工程系统中，我们经常遇到流过最初受力变形的固体。对于这些情况，初始应变或初始应力表现为表示本构关系中张量的附加对称性。因此，初始应力会引起各向异性（在本例中为横向各向同性）并影响材料特性。我们对初始应力变形实体采用超弹性模型来研究单轴和等双轴初始应力对流动不稳定性的影响。该研究还提出了固体中的各向异性干扰固-流耦合系统稳定性的情况。与之前的两态或三态欧拉-拉格朗日公式相比，目前的公式需要四种初始应力实体的配置，即。无应力、初始应力、变形和扰动状态。该公式适用于固体包含初始/残余应力的任何流固耦合问题。我们的结果表明，初始张应力使流动稳定，而初始压应力使流动不稳定。幸运的是，这种对流固耦合稳定性的观察与固体柱状结构的稳定性一致，其中压缩轴向应力导致屈曲。我们报告了单轴和等双轴初始应力的类似结果，对于蠕变流动极限下的不同波模式及其在更高的扩展 该公式适用于固体包含初始/残余应力的任何流固耦合问题。我们的结果表明，初始张应力使流动稳定，而初始压应力使流动不稳定。幸运的是，这种对流固耦合稳定性的观察与固体柱状结构的稳定性一致，其中压缩轴向应力导致屈曲。我们报告了单轴和等双轴初始应力的类似结果，对于蠕变流动极限下的不同波模式及其在更高的扩展 该公式适用于固体包含初始/残余应力的任何流固耦合问题。我们的结果表明，初始张应力使流动稳定，而初始压应力使流动不稳定。幸运的是，这种对流固耦合稳定性的观察与固体柱状结构的稳定性一致，其中压缩轴向应力导致屈曲。我们报告了单轴和等双轴初始应力的类似结果，对于蠕变流动极限下的不同波模式及其在更高的扩展 这种对流固耦合稳定性的观察与固体柱状结构的稳定性一致，其中压缩轴向应力导致屈曲。我们报告了单轴和等双轴初始应力的类似结果，对于蠕变流动极限下的不同波模式及其在更高的扩展 这种对流固耦合稳定性的观察与固体柱状结构的稳定性一致，其中压缩轴向应力导致屈曲。我们报告了单轴和等双轴初始应力的类似结果，对于蠕变流动极限下的不同波模式及其在更高的扩展$\mathrm{电阻}\mathrm{电子}$，以及各种固体厚度。对于单轴和等双轴情况，蠕变极限中存在的两种不稳定模式，即短波和有限波模式受到拉伸/压缩初始应力的显着影响。对于单轴拉伸初始应力，有限波模式不会扩展到高$\mathrm{电阻}\mathrm{电子}$. 而不是它们，我们观察到多个上游模式变得不稳定$\mathrm{电阻}\mathrm{电子}$, 显示墙模式缩放为 O($\mathrm{电阻}{\mathrm{电子}}^{-1/3}$）。对于无应力固体，未观察到这些上游模式。这种行为是由初始应力实体控制方程中初始应力和扰动变量之间的附加耦合项触发的。然而，对于等双轴情况，有限波模式确实扩展到更高$\mathrm{电阻}\mathrm{电子}$显示墙模式缩放。这种模式进一步稳定/不稳定取决于固体中存在的初始应力的拉伸/压缩性质。