The underlying mechanisms of stability, metastability, or instability of the Cassie-Baxter and Wenzel wetting modes and their transitions on superhydrophobic surfaces decorated with periodic micropillars are quantitatively studied in this article. Hydraulic pressure, which may be generated by the water-air interfacial tension of water droplets or external factors such as raining impact, is shown to be a key to understanding these mechanisms. A detailed transition process driven by increasing hydraulic pressure is numerically simulated. The maximum sustainable or critical pressure of the Cassie-Baxter wetting state on a pillarlike microstructural surface is formulated for the first time in a simple, unified, and precise form. This analytic result reveals the fact that reducing the microstructural scales (e.g., the pillars' diameters and spacing) is probably the most efficient measure needed to enlarge the critical pressure significantly. We also introduce a dimensionless parameter, the pillar slenderness ratio, to characterize the stability of either the Cassie-Baxter or the Wenzel wetting state and show that the energy barrier for transitioning from the Cassie-Baxter to the Wenzel wetting mode is proportional to both the slenderness ratio and the area fraction. Thus, the Cassie-Baxter wetting mode may collapse under a hydraulic pressure lower than the critical one if the slenderness ratio is improperly small. This quantitative study explains fairly well some experimental observations of contact angles that can be modeled by neither Wenzel nor Cassie-Baxter contact angles and eventually leads to our proposals for a mixed (or coexisting) wetting mode.

To understand why lotus leaf surfaces have a two-scale structure, we explore in this paper two stability mechanisms. One is the stability of the Cassie-Baxter wetting mode that generates the superhydrophobicity. A recent quantitative study (Zheng et al., Langmuir 2005, 21, 12207) showed that the larger the slenderness ratio of the surface structures was, the more stable the Cassie-Baxter wetting mode would be. On the other hand, it is well-known that more slender surface structures can only sustain lower critical water pressures for structure buckling, or Euler instability, while in the natural environments, the water pressure impacting on the lotus surface can reach a fairly high value (105 Pa in a heavy rain). Our analysis reveals that the two-scale structure of the lotus leaf surfaces is necessary for keeping both the structure and the superhydrophobicity stable. Furthermore, we find that the water-air interfacial tension makes the slender surface structure more instable and the two-scale structure a necessity.

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Designing metamaterials with programmable features has emerged as a promising pathway for reusable energy absorption. While the current designs of reusable energy absorbers mainly exploit mechanical instability of flexible beams, here is created a new kind of metamaterial for reusable and programmable energy absorption by integrating rigid granular materials and compliant stretchable components. In each unit cell of the metamaterial, the stretchable components connect the granular particles to maintain the integrity and control the deformation pattern of the material. When the metamaterial is subjected to an external load, the input energy is partially trapped as elastic energy in the stretchable components, and partially dissipated by friction between the granular particles, forming hysteresis between the loading and unloading force-displacement curves. Through tuning the structural design of the metamaterial, the pretension and stiffness of the stretchable components, and the size of and friction between the particles, a vast design space is achieved to program the mechanical behavior of the metamaterial, such as the load-displacement curve, the multistability, and the amount of energy dissipation. Experimental impact tests on a thin glass panel confirm energy-absorbing capability of the proposed metamaterial. This design strategy opens a new avenue for creating reusable energy-absorbing metamaterials.The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adfm.201901258. and a long working distance. Most commercial energy-absorbing products adopt plastic deformation or fragmentation of foams, [3] metals, [4] and ceramics, [5] to gain the desired hysteresis behavior, and introduce artificial defects, such as prefolding of origami, [6][7][8] to control the deformation mode. In the products with plastic deformation or fragmentation, dislocations and bond breakage occur at the molecule level, and a large amount of energy can be absorbed. However, they are only for one-time usage, since the materials are permanently damaged.In order to overcome the shortcoming of one-time usage, reusable energyabsorbing materials have been proposed by developing damage-tolerant micro [9] or nano lattices, [5] architectured composite materials, [10,11] and mechanical metamaterials. [12][13][14][15] Mechanical metamaterials are materials with microstructures, which give rise to unique mechanical properties that are otherwise hard to achieve. [12][13][14] By designing the microstructures, researchers have developed energy-absorbing metamaterials mainly through exploiting mechanical instability of the deformable microstructures. [16][17][18][19][20] A well-utilized strategy to achieve reusability is making use of bistability of curved beams and tilted straight beams under buckling, [21][22][23] since during the working process, deformation of these constituent structures is elastic. Although the energyabsorbing capability of these metamaterials is currently not comparable to those...

This paper proposes a singularity-free beam element with Euler-Bernoulli assumption, i.e., the cross section remains rigid and perpendicular to the tangent of the centerline during deformation. Each node of this two-nodal beam element has eight nodal coordinates, including three global positions and one normal strain to describe the rigid translation and flexible deformation of the centerline, respectively, four Euler parameters or quaternion to represent the attitude of cross section. Adopting quaternion instead of Eulerian angles as nodal variables avoids the traditionally encountered singularity problem. The rigid cross section assumption is automatically satisfied. To guarantee the perpendicularity of cross section to the deformed neutral axes, the position and orientation coordinates are coupled interpolated by a special method developed here. The proposed beam element allows arbitrary spatial rigid motion, and large bending, extension, and torsion deformation. The resulting governing equations include normalization constraint equations for each quaternion of the beam nodes, and can be directly solved by the available differential algebraic equation (DAE) solvers. Finally, several numerical examples are presented to verify the large deformation, natural frequencies and dynamic behavior of the proposed beam element.