To achieve better adhesion, micropillar arrayed surfaces inspired by the gecko adhesion system have gained significant attention. However, debate continues on whether micropillar arrayed surfaces actually enhance interfacial adhesion compared to smooth surfaces. To clearly understand the factors influencing the adhesion force of micropillar arrayed surfaces and provide a criterion for achieving enhanced adhesion of such the surfaces, a theoretical model of a micropillar arrayed surface containing an elastic backing layer is established. Under a vertically uniform displacement load, the micropillars will detach from the rigid substrate. The adhesion behavior of each micropillar and the variation pattern of the entire adhesion force influenced by the geometry of the micropillars, materials of the micropillars and backing layer during the detaching process are analyzed. A load sharing efficiency is defined, and is found to increase with an increase in the micropillar aspect ratio, Young's modulus ratio of the backing layer to the micropillars, and separation distance between neighboring micropillars, but decrease with an increase in sample size. The entire adhesion force of a micropillar arrayed surface can be quantified, which is larger than that of a smooth surface if the micropillar aspect ratio, Young's modulus ratio of the backing layer to the micropillars and separation distance between neighboring micropillars are appropriate. Detailed diagrams are respectively provided for the load sharing efficiency of all the micropillars and the comparison of the adhesion forces between micropillar arrayed and smooth surfaces with different geometric and material parameters, from which the design strategies of approaching equal load sharing regime and stronger adhesion force of the micropillar arrayed surface than that of the smooth one can be clearly found. The obtained results can not only deepen the understanding of the adhesion behavior of fibrillar surfaces but also provide theoretical guidance for achieving robust adhesion of the micropillar arrayed surfaces.

中文翻译：

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仿生微柱阵列表面增强粘附力的理论模型

为了获得更好的粘附力，受壁虎粘附系统启发的微柱阵列表面受到了广泛关注。然而，与光滑表面相比，微柱阵列表面是否确实增强了界面粘附力的争论仍在继续。为了清楚地了解影响微柱阵列表面粘附力的因素并提供增强此类表面粘附力的标准，建立了包含弹性背衬层的微柱阵列表面的理论模型。在垂直均匀位移载荷下，微柱将从刚性基底上脱离。分析了分离过程中每个微柱的粘附行为以及整个粘附力受微柱几何形状、微柱材料和背衬层影响的变化模式。定义了负载共享效率，并且发现负载共享效率随着微柱纵横比、背衬层与微柱的杨氏模量比以及相邻微柱之间的间隔距离的增加而增加，但随着样本大小的增加而减少。如果微柱长宽比、背衬层与微柱的杨氏模量比以及相邻微柱之间的间距合适，则微柱阵列表面的整体粘附力可以量化，该粘附力大于光滑表面的粘附力。分别提供了所有微柱的负载分配效率的详细图表以及不同几何和材料参数的微柱阵列和光滑表面之间的粘附力的比较，从中得出接近相等的负载分配状态和更强的粘附力的设计策略可以清楚地看到微柱阵列表面比光滑表面的微柱阵列表面。所获得的结果不仅可以加深对纤维表面粘附行为的理解，而且可以为实现微柱阵列表面的牢固粘附提供理论指导。