Theoretical optimization of micropillar arrays for structurally stable bioinspired dry adhesives

Inspired by the excellent adhesion performances of setae structure from organisms, micro/nano-pillar array has become one of the paradigms for adhesive surfaces. The micropillar arrays are composed of the resin pillars for adhesion and the substrate with different elastic modulus for supporting. The stress singularity at the bi-material corner between the pillars and the substrate can induce the failure of the micropillar-substrate corner and further hinder the fabrication and application of micropillar arrays, yet the design for the stability of the micropillar array lacks systematical and quantitative guides. In this work, we develop a semi-analytical method to provide the full expressions for the stress distribution within the bi-material corner combining analytical derivations and numerical calculations. The predictions for the stress within the singularity field can be obtained based on the full expressions of the stress. The good agreement between the predictions and the FEM results demonstrates the high reliability of our method. By adopting the strain energy density factor approach, the stability of the pillar-substrate corner is assessed by predicting the failure at the corner. For the elastic mismatch between the pillar and substrate given in this paper, the stability can be improved by increasing the ratio of the shear modulus of the substrate to that of the micropillar. Our study provides accurate predictions for the stress distribution at the bi-material corner and can guide the optimization of material combinations of the pillars and the substrate for more stable bioinspired dry adhesives.