This paper investigates the elastic instability behavior in soft periodic laminates subjected to finite strains, with a focus on both macroscopic and microscopic instabilities. Considering the deformation-induced phase stiffening, the Gent model with a high bulk-to-shear modulus ratio describes the behavior of incompressible phases. This non-Gaussian statistics-based model captures the non-linear constitutive results from the limited extensibility of polymeric molecular chains. This paper derives an analytical prediction for the onset of macroscopic (or longwave) instability and microscopic instability as functions of material parameters. Moreover, a numerical Bloch-Floquet analysis is imposed on identifying the instability behavior under compression. We consider a wide range of phase combinations and find that the relatively rapid stiffening of the matrix compared to the stiff layer increases the stability of laminates by decreasing the critical stretch ratio. Essentially, properly manipulating the stiffening parameters can produce an absolutely stable region without observed instability. This paper also systematically illustrates the changes in instability and the transition between macro and micro instability in fully Gent laminates, which show higher stability than fully neo-Hookean laminates with larger critical stretch ratios. The critical characteristics of instabilities, such as critical stretch ratios and critical wavenumbers, can be controlled by the choice of stiffening parameters and other material properties, enlarging the tuning of soft laminates for desired buckling patterns in practical applications.

中文翻译：

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具有硬化行为的软层压板的弹性不稳定性

本文研究了有限应变下软周期层合板的弹性不稳定性行为，重点关注宏观和微观不稳定性。考虑到变形引起的相硬化，具有高体积剪切模量比的 Gent 模型描述了不可压缩相的行为。这种基于非高斯统计的模型捕获了聚合物分子链有限延伸性的非线性本构结果。本文对作为材料参数函数的宏观（或长波）不稳定性和微观不稳定性的发生进行了分析预测。此外，还采用数值 Bloch-Floquet 分析来识别压缩下的不稳定行为。我们考虑了广泛的相组合，发现与刚性层相比，基体相对快速的硬化通过降低临界拉伸比来提高层压板的稳定性。本质上，正确操纵硬化参数可以产生绝对稳定的区域，而不会观察到不稳定。本文还系统地阐述了全 Gent 层合板的不稳定性变化以及宏观和微观不稳定性之间的转变，其比具有更大临界拉伸比的全 Neo-Hookean 层合板表现出更高的稳定性。不稳定性的关键特性，例如临界拉伸比和临界波数，可以通过选择硬化参数和其他材料特性来控制，从而扩大软层压板在实际应用中所需屈曲模式的调节。