Inspired by the gecko's climbing ability, adhesion between an elastic nanofilm with finite length and a rough substrate with sinusoidal roughness is studied in the present paper, considering the effects of substrate roughness and film thickness. It demonstrates that the normal adhesion force of the nanofilm on a rough substrate depends significantly on the geometrical parameters of the substrate. When the film length is larger than the wavelength of the sinusoidal roughness of the substrate, the normal adhesion force decreases with increasing surface roughness, while the normal adhesion force initially decreases then increases if the wavelength of roughness is larger than the film length. This finding is qualitatively consistent with a previously interesting experimental observation in which the adhesion force of the gecko spatula is found to reduce significantly at an intermediate roughness. Furthermore, it is inferred that the gecko may achieve an optimal spatula thickness not only to follow rough surfaces, but also to saturate the adhesion force. The results in this paper may be helpful for understanding how geckos overcome the influence of natural surface roughness and possess such adhesion to support their weights.

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When the thickness of metallic cantilever beams reduces to the order of micron, a strong size effect of mechanical behavior has been found. In order to explain the size effect in a micro-cantilever beam, the couple-stress theory (Fleck and Hutchinson, J Mech Phys Solids 41:1825-1857, 1993) and the C-W strain gradient theory (Chen and Wang, Acta Mater 48:3997-4005, 2000) are used with the help of the BernoulliEuler beam model. The cantilever beam is considered as the linear elastic and rigid-plastic one, respectively. Analytical results of the cantilever beam deflection under strain gradient effects by applying these two kinds of theories are obtained, from which we find an explicit relationship between the intrinsic lengths introduced in the two kinds of theories. The theoretical results are further used to analyze the experimental observations, and predictions by both theories are further compared. The results in the present paper should be useful for the design of micro-cantilever beams in MEMS and NEMS.

In this article, optimization of shear adhesion strength between an elastic cylindrical fiber and a rigid substrate under torque is studied. We find that when the radius of the fiber is less than a critical value, the bondingbreaking along the contact interface occurs uniformly, rather than by mode III crack propagation. Comparison between adhesion models under torque and tension shows that nanometer scale of fibers may have evolved to achieve optimization of not only the normal adhesive strength but also the shear adhesive strength in tolerance of possible contact flaws.

Summary. We recently proposed a strain gradient theory to account for the size dependence of plastic deformation at micron and submicron length scales. The strain gradient theory includes the effects of both rotation gradient and stretch gradient such that the rotation gradient influences the material character through the interaction between the Cauchy stresses and the couple stresses; the stretch gradient measures explicitly enter the constitutive relations through the instantaneous tangent modulus. Indentation tests at scales on the order of one micron have shown that measured hardness increases significantly with decreasing indent size. In the present paper, the strain gradient theory is used to model materials undergoing small-scale indentations. A strong effect of including strain gradients in the constitutive description is found with hardness increasing by a factor of two or more over the relevant range behavior. Comparisons with the experimental data for polycrystalline copper and single crystal copper indeed show an approximately linear dependence of the square of the hardness, H 2 , on the inverse of the indentation depth, 1=h, i.e., H 2 / 1=h, which provides an important self-consistent check of the strain gradient theory proposed by the authors earlier.

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