As adhesively bonded layered devices scale down, micro-scale adhesive layers become common and play a key role in the overall performance of micro devices. Herein, we use the strain gradient elasticity to characterize the micro-scale adhesive layers and propose an analytical size-dependent model to predict the mechanical behaviors of adhesively bonded layered structures. The results indicate that the local interfacial tractions and the global adherend displacement both show strong size effects, especially for soft adhesives with low modulus. When the ratio of the adhesive layer thickness to its material characteristic length scale (on the order of microns), representing the scale of the layered structures, decreases to unity, the interfacial tractions increase substantially and the adherend displacement decreases significantly. Meanwhile, the adherend displacement is insensitive to the adhesive modulus. The present study reveals the stiffening behaviors of layered structures, which are attributed to the large strain gradients in the constrained micro-scale adhesive layers. The results can help us predict the deformation of adhesively bonded layered structures, and achieve high performance of micro devices by adhesive bonding.

随着粘合剂分层器件的缩小，微米级粘合剂层变得常见，并在微型器件的整体性能中发挥关键作用。在本文中，我们使用应变梯度弹性来表征微尺度的胶粘剂层，并提出了一种基于尺寸的解析模型来预测胶粘剂粘结的层状结构的力学行为。结果表明，局部界面牵引力和整体被粘物位移都表现出强烈的尺寸效应，特别是对于低模量的软胶而言。当代表层状结构的比例的粘合剂层厚度与其材料特征长度比例之比（微米级）减小至统一时，界面牵引力显着增加，并且被粘物位移显着减小。同时，被粘物的位移对粘合模量不敏感。本研究揭示了分层结构的刚性行为，这归因于受约束的微型胶粘剂层中的大应变梯度。结果可以帮助我们预测粘合层状结构的变形，并通过粘合实现微型设备的高性能。