A size-dependent model for predicting the mechanical behaviors of adhesively bonded layered structures based on strain gradient elasticity

Abstract

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.