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Abstract
Inspired by the prominent adhesion capability of gecko foot-hair, micro/nano-pillar array has been fabricated and widely explored as biomimetic dry adhesives. Pillars with graded material along their length have been proved to have great advantage in simultaneously raising adhesion and reducing clusterisation, yet the design of the graded micropillars lacks theoretical and quantitative guides. In this work, we first derived the theoretical expressions of critical aspect ratio and effective elastic modulus for graded micropillars composed of rigid bases and soft tips. Then, a Cohesive Zone Model (CZM) was constructed to simulate the lateral collapse of the two-step-graded micropillars with epoxy resin and polyurethane (typical materials adopted in the reported experiments) as the base and tip materials, respectively. Combining the numerical results and the theoretical ones, we found that when the length ratio of the rigid base to the micropillar increases, the ability of the pillars to resist structural collapse enhances (i.e., the critical aspect ratio raises), while the adhesion strength reduces (i.e., the effective elastic modulus increases). Considering the tradeoff between the structural stability and the adhesion strength, we found an optimum value of ∼0.65 for the length ratio of the rigid base to the whole micropillar. Our study establishes theoretical models for the critical aspect ratio and effective elastic modulus for the graded micropillars and provides quantitative guides to the design and optimization of bioinspired dry adhesives.