Abstract Different from an elastic film-substrate system, the buckling mode of a viscoelastic film-substrate system triggered by a local load may change over time. In this paper, the local wrinkling and the stress relaxation process of a Maxwell viscoelastic thin film-elastic substrate system subjected to a sudden homogeneous pre-stretch in a circular area is investigated. The buckling equation for this viscoelastic film-elastic substrate system is derived, and the critical wrinkling condition is given. The wrinkling mode mutation with the time is observed, and the evolution of the wrinkling pattern is presented. The influence of the film modulus and the pre-stretch radius on the mutation time is discussed in detail. The time evolution of the circumferential wrinkling wave number in viscous film-substrate system provides guidance in safety design in soft matter and viscoelastic membrane structures.

中文翻译：

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局部预拉伸引发的粘弹性薄膜-弹性基底系统的径向不稳定性：一个理论解决方案

摘要 与弹性薄膜-基材系统不同，由局部载荷触发的粘弹性薄膜-基材系统的屈曲模式可能会随时间发生变化。本文研究了麦克斯韦粘弹性薄膜-弹性基底系统在圆形区域突然均匀预拉伸后的局部起皱和应力松弛过程。推导了该粘弹性薄膜-弹性基材系统的屈曲方程，并给出了临界起皱条件。观察皱纹模式随时间的突变，并呈现皱纹模式的演变。详细讨论了薄膜模量和预拉伸半径对突变时间的影响。