While atomically flat surfaces are typically restricted to flawless crystalline structures, nature overwhelmingly favours textured landscapes. From sculpting mountain ranges to skin wrinkles, multi-scale surface patterns emerge universally across physical and biological systems. Even atomically thin two-dimensional materials develop intrinsic wrinkles through thermal fluctuations. These spontaneous formations have contrasting consequences: chaotic wrinkling often undermines material performance, yet precisely engineered patterns could revolutionize functional surfaces. Ordered micro/nanoscale wrinkles indeed provide tunable properties, which are highly sought capabilities in flexible electronics, adaptive optics, and smart coatings. This duality drives global efforts to transform random creases into designed architectures. Researchers now employ innovative techniques to wrinkle materials with unprecedented control, turning a natural phenomenon into a manufacturing tool. Our review explores cutting-edge fabrication methods and their emerging applications, opening new frontiers in materials science.

1. Surface wrinkling phenomena in nature

In geology, a ‘wrinkle’ refers to the continuous wave-like bending deformation of layered rocks caused by tectonic forces. This geological structure is a classic product of rock plastic deformation and is widely distributed within crustal rock layers. Sand ripples and dunes have a different origin. They are due to a spontaneous modulation of sand flux by wind transport, akin to wave formation on the ocean.

Remarkably, surface wrinkling exhibits cross-scale universality in nature: from crustal tectonic movements to microscopic cell membranes, molecular surfaces, and even atomic arrangements, wrinkles at different scales play unique functional roles within their respective physical systems [1]. This phenomenon raises a profound question: does an absolutely flat surface truly exist in nature? Theoretically, a perfectly smooth surface is impossible. While we can define ‘flatness’ at specific scales, such as atomically smooth crystalline surfaces, closer observation reveals that even these ‘flat’ surfaces exhibit subtle undulations in their atomic arrangements.

1.1 Crustal wrinkles on Earth’s surface

Wrinkles are among the most fundamental structural forms of Earth’s crust (Figure 1). In sedimentary rocks, the initially flat bedding planes deform under tectonic motion to produce large wrinkles. In metamorphic rocks like gneiss, high pressure effects result in cleavage and foliation which can locally bend to form wrinkles. Magmatic rocks also display undulations due the surface deformation of the lava flows from which they result. Wrinkles thus exhibit a remarkable range of sizes. Some are minuscule in nature, while others are so extensive that they can rival the grandeur of mountains.

1.2 Skin wrinkles on living organisms

Wrinkles are present on the surface of all living organism skins. Take the African elephant’s trunk as an example. It ranges from 1.7 m to 2 m long, densely packed with 100,000 muscles and covered with circular skin wrinkles (Figure 2). Those enhance the skin friction and allows the trunk to bend and stretch, making it the most flexible part of elephant’s body. Although the trunk may appear soft and limp, resembling a giant leech, it is incredibly functional. It not only enables elephants to reach bananas high up in trees, but also helps them drink water.

Human bodies also exhibit remarkable biological adaptability in many parts, such as dermal folds at joint areas and fingerprints. The dermal folds at elbows, knees, and other joint areas effectively distribute mechanical stresses caused by joint movements. Hence it maintains the integrity and flexibility of the skin during extensive bending and stretching. Fingerprints are shaped by both genetic factors and physical-chemical conditions during embryonic development. Their ridge and furrow structures enhance the sensitivity of tactile receptors.

In addition to animal skins, a variety of surface wrinkling phenomena can be observed on fruits. They are primarily attributed to two key mechanisms: water evaporation and respiration, which denotes the breakdown of organic matter by its combination with oxygen. For fruits like apples that are stored over extended periods, the primary mechanism involves respiration. This process is concomitant with significant water loss, which further exacerbates the formation of surface wrinkles by a mechanism of retraction further discussed in section 2.

In contrast, the characteristic patterns on the exterior of cantaloupes arise from a unique growth dynamic. Specifically, the inner flesh expands at a faster rate than the outer skin during fruit development, leading to tensile stress that results in skin cracking. Over time, these cracks undergo a natural healing process, ultimately forming the intricate surface patterns that are visually distinct (Figure 3).

For chili peppers, the formation of complex surface features is influenced by variations in the curvature of their core-shell structure. During growth, these curvature differences induce mechanical stress, which contributes to the development of intricate wrinkle patterns.

1.3 Nanoscale wrinkles on material surfaces

Graphene, a single-atom-thick carbon sheet, forms a remarkable honeycomb lattice structure (Figure 4). Thermal fluctuations can induce spontaneous wrinkle formation. The amplitude of these surface wrinkles typically ranges between 0.7 and 30 nm, with an average height of approximately 8 nm (one nanometer, denoted ‘nm’, is a billionth of meter). While the idealized carbon-carbon (C-C) bond length is theoretically 0.142 nm, experimental measurements reveal a practical range of 0.130–0.154 nm, reflecting varying degrees of compression and tension within the lattice.

The wrinkling phenomenon on graphene surfaces can be attributed to its monolayer atomic architecture, which inherently introduces instability along the direction perpendicular to the layer surface. Interestingly, these surface wrinkles play a critical role in enabling graphene robustness and stability [2]. Indeed, by providing structural resilience against external perturbations, they allow graphene to maintain its integrity under mechanical and thermal stress.

1.4 Atomic-level wrinkles on crystal surfaces

The advent of scanning probe microscopy was a huge leap forward in surface science. It completely changed how we explore and control matter at the nanoscale, acting like a super microscope. Thanks to this novel technique, scientists can now actually ’see’ atomic details on material surfaces and even move atoms one by one (Figure 5). Atomic force microscopy relies on the force between a tiny scanning needle and the substrate. An alternative approach, called tunnelling microscopy, relies on the modulations of the electric current flowing from the needle to the substrate.

Figure 5 is a great example of what scanning tunnelling microscopy can do. It shows a ring of individual iron atoms on a copper surface, and it also reveals a fascinating circular wave pattern inside this ring. This is a standing wave electron quantum wave trapped in the iron atom ring [3], a bit like the ripples on the surface of a vibrating circular water bucket.

2. Fundamental principles and implications of surface wrinkling phenomena

2.1 Wrinkling on flat surfaces

Flat surface wrinkling mainly occurs in bilayer or multilayer systems. Wrinkles produced by a compressive stress on a thin film is show in Figure 6 [4]. Retraction of the soft surface produces a compressive stress on the upper film. When this stress reaches a critical level, it is relieved through surface wrinkling, allowing the system to achieve a new equilibrium state.

Depending on material properties and possible pre-stretched state of the substrate, various surface wrinkling morphologies can be formed, including wrinkles, folds, ridges, etc. The critical wavelength (λ) of surface wrinkles is determined by the ratio of elasticity between film and substrate and the thickness of the film: hard films on softer substrates tend to form larger wrinkle wavelengths. Similarly, the wrinkle amplitude (A) is generally proportional to the thickness of the rigid surface film and is related to the elastic modulus ratio between film and substrate.

2.2 Wrinkling on curved surfaces

Surfaces which are initially curved involve additional parameters. Typical cases include cylindrical and spherical surfaces. For cylindrical surfaces, two primary instability modes exist, as shown in Figure 7 (see ref. [4]). Axial shrinkage produces annular wrinkles with a circular cross-section while radial shrinkage produces wrinkles invariant along the cylinder axis. For spherical surfaces, the resulting wrinkle patterns are generally complex, such as hexagonal or maze-shaped configurations. Mechanical analysis shows that for both core-shell cylinders and spheres the surface wrinkling mainly depends on the core-shell elastic modulus ratio and curvature.

Thus various wrinkle morphologies can be observed on the surfaces of many spherical plants with core-shell structures, such as Korean cantaloupe, cantaloupe, pumpkin, dehydrated pollen grains, and dehydrated peas.

2.3 Drawbacks of wrinkles

Some garments, such as pleated skirts, use wrinkles to create aesthetic appeal. In most cases, however, wrinkle clothing needs to be ironed smooth before wearing (Figure 8). Similarly, materials made of a thin layer, called two-dimensional (2D) materials, are highly prone to wrinkling. Examples are provided by the silicon wafers at the heart of micro-electronic devices. Poor control of such wrinkling can severely impair the performance of optoelectronic devices. The preparation of wafer surface for computer chips indeed requires a strict control of unwanted wrinkles and undulations, at the nanometer  level. Unevenness of the wafer surface must indeed fall within the narrow focus range of the ultraviolet beam of the lithographic machines used to draw the integrated circuits.

2.4 Benefits of wrinkles

The surface wrinkles of biological tissues play an important role in filtering and absorbing nutrients (Figure 9). The stomach wall is composed of mucosa, submucosa, muscle layer, and serosa. The natural wrinkles of the gastric mucosa help the stomach expand.

The small intestine of an adult is 5-7m in length and contains many wrinkles inside, known as villi. These villi, which resemble tiny finger-like projections, significantly increase the surface area for the absorption of nutrients. The large intestine, about 1.5 m long, has circular wrinkles but lacks the villi-like projections, providing a habitat for trillions of intestinal bacteria.

For 2D materials, mechanical strain can strongly disturb the electron propagation in the material. This enables the effective adjustment of their optical, electrical, and mechanical properties. Wrinkling structures thus lead to new physical and chemical properties that are completely different from those in the natural state. Therefore, constructing 2D materials into different wrinkling structures can achieve the adjustment of their physical properties. This will promote their application in the fields of smart surfaces, wearable devices, and health monitoring. It provides new opportunities to explore functions emerging from such heterogeneous deformation.

3. Methods for constructing surface wrinkle patterns

3.1 Stretch-release method using an elastic plane

In accordance with the principle of  ‘following the way of nature’, called ‘biomimetics’, scientists have proposed a series of micro-construction methods based on surface wrinkling, providing a universal approach for their structuring.  Wrinkling is initiated by external stimuli, such as stretching, heating, light exposure, solvent wetting, etc. The resulting  stress imbalance is then released by the spontaneous deformation of  the surface associated with wrinkling.

In this respect, the pre-stretch and release method on planar surfaces is the most commonly used approach (Figure 10, see ref. [4]). An elastic polymer substrate is firstly pre-stretched to a certain length. Then a thin film is deposited on the pre-stretched elastic substrate to obtain skin layers with different elastic modulus. After that, the stress is released to obtain a plane wrinkle pattern. When the material is stretched in a single direction and then contracted in that direction, a sinusoidal plane wave pattern is produced. If stretching occurs in two directions and stress is released sequentially, a ‘zigzag’ pattern is formed. When both directions are stretched and stress is released simultaneously in different ways, a more complex labyrinthine pattern is obtained.

3.2 Stretch-release method using an elastic fibre

Circular wrinkles of cylindrical surfaces can be constructed using pre-stretched elastic fibres. In this method, highly elastic elasomere fibres are pre-stretched, then wrapped with carbon nanotube sheets. An electrically conductive sheath thus covers the polymere core.   When the stress is released, the sheath wrinkles, forming concentric wrinkles of short period (Figure 11). Complex elastic structures can be obtained by wrapping such nanotubes on a rubber core itself stretched in the direction transverse to the fibres. This provides a hierarchically buckled structure with crossed orientations [5], providing a very flexible conducting sheet (see section 4.4) .  Some polymeric fibres, such as polyacrylonitrile fibres, can also form similar wrinkling under thermal treatment.

3.3 Inflation-deflation method using an elastic balloon

The use of inflatable balloons is a more convenient and feasible method, which does not require the use of fixtures to pre-stretch the substrate (Figure 12). The balloons can be chosen with different shapes, for instance spherical or cylindrical. After the balloon is inflated, a coating such as graphene oxide is applied to the surface of the balloon. Then it is dried at room temperature to form a uniform thin film. The balloon shrinks if air is deflated, producing a compressive stress on the coating. When this stress exceeds a critical value, highly folded graphene oxide wrinkles will be formed. The wrinkles caused by the deflation increase light absorption, significantly deepening the colour.

Due to the synchronous shrinkage of the three dimensions during the deflation process, the resulting morphology can gradually transit from a hexagonal shape to a highly interwoven maze pattern depending on the shrinking rate.

3.4 Dynamic induction method using an environmental stimulus

In addition to the pre-stretching and releasing method mentioned above, wrinkles can also be generated by heating, light exposure, solvent wetting, and other stimuli. Furthermore, the periodic multi-scale wrinkling patterns with stimulus responsiveness and dynamic adjustment can autonomously regulate the properties of materials in situ as needed. These features have broad application perspectives in fields such as self-cleaning, adhesion, anti-interference, camouflage, and tissue engineering.

Therefore, researchers have attempted to introduce dynamic physical interactions or chemical reactions into classical bilayer wrinkling systems for regulating wrinkle structures, enabling the construction of smart surface materials. For example, dynamic wrinkle structures can be constructed using thermally reversible Diels-Alder reactions (Figure 13), photo-reversible dimerization, and solvent wetting [6].

4. Typical applications of surface wrinkle patterns

4.1 Application in droplet manipulation

A solid surface tends to repel water if its surface energy is low and its roughness is high. The introduction of wrinkle structures usually increases this hydrophobicity, compared to the planar structures. However, if a hierarchically wrinkle structure is constructed using an intrinsically hydrophilic materials such as graphene oxide, it allows droplets to be suspended on the surface, as it occurs on rose petals and various types of leaves (read Between protection and defence: the plant cuticle ).

This property called ‘lotus effect’, or  ‘rose petal effect’, can be used for droplet manipulation (Figure 14) [7]. This can be applied for instance to digital microfluidics (controlling chemical reactions on micro-electronic chips). Such droplet manipulation could be also applied to freshwater collection or heat transfer.

4.2 Application in adaptive camouflage

Camouflage is commonly found in nature, engineering, and military applications. Dynamic surface wrinkles enable materials to control the wavelength of reflection, providing an adaptive camouflage potential. For example, an adaptive camouflage bilayer system can be composed of anthracene copolymer (PAN) and pigment containing polydimethylsiloxane (p-PDMS) (Figure 15) [8]. In this system, the photothermal effect can induce thermal expansion of p-PDMS to eliminate wrinkles. The dynamic surface wrinkles driven by multi-wavelength light can adjust the scattering of light, as well as visibility of interference colours in PAN thin films. As a result, the sample colour can switch between a distinguishing state and a camouflage state. This adaptive visible camouflage strategy is simple to configure and easy to operate.

4.3 Application in health and medical monitoring

Resistive sensors can measure shape changes by monitoring electrical resistance and are widely used in wearable devices for health monitoring applications. In a wrinkle-based resistive sensor, the wrinkles create numerous contact points that can be viewed as countless switch-like devices. When an external stress is applied, the wrinkles expand or shrink with the elongation of the elastic substrate, causing the contact points to either break or make contact, leading to changes in resistance. This type of sensor is capable of detecting not only large-scale movements such as those of limbs, but also subtle deformations due to breathing and pulse (Figure 16).

4.4 Application in flexible electronic devices

Stretchable electrodes have attracted significant attention due to their potential applications in various wearable and soft electronic devices. Their structures can rely on wrinkles, grids, serpents, cracks, etc. The wrinkle structure is relatively simple and controllable, hence it is one of the most commonly used. The sheath-core type wrinkling fibre structures presented in section 3.2 (see ref. [5]) is particularly promising. The variation in electrical  resistance is less than 5% under a tensile stress variation by a factor 10. Additionally, the wrinkle structure enhances the resistance to friction and has great potential in the field of flexible electrodes for triboelectric nanogenerator (TENG) (Figure 17). Triboelectricity denotes the production of current by friction, which can provide power to sensors in an autonomous way.

4.5 Application in electromagnetic wave shielding or absorption

Carbon nanotube wrinkle layers on a rubber substrate exhibit excellent electromagnetic shielding properties, particularly with a stretch-enhanced effect (Figure 18) [9]. When the stretching direction is parallel to the direction of the electric field, the electromagnetic shielding effect can be further improved.

In addition to shielding, polymeric spheres with carbon nanotube wrinkles can also be used for microwave absorbing [10]. Compared with the smooth spheres, the core-shell structured wrinkling spheres are indeed capable of improving microwave absorbing performance. This is the electromagnetic equivalent of the roughness used in acoustic absorption. For good absorption efficiency, the roughness size must be close to the wavelength. This corresponds to the so-called  ‘impedance matching’.

5. Messages to remember

• Wrinkles refer to a series of wavy bending deformations of layered rocks. They are the result of the plastic deformation caused by tectonic movements.
• The surface wrinkles can be controlled in an orderly manner. Disordered and uncontrollable wrinkles might negatively affect material properties, whereas ordered and controllable wrinkles can provide adjustable physical and chemical properties.
• External stimuli, such as stretching, heating, light exposure, and solvent wetting, cause stress imbalance within the bilayer system, thereby leading to the formation of wrinkles. Those can be dynamically controlled for various applications.
• Depending on substrate, wrinkling can be divided into planar wrinkling and curved wrinkling, both of which are related to the elastic modulus ratio between film and substrate.
• 2D materials inherently exhibit wrinkles, which is the inevitable result of thermal fluctuations. Effective adjustment of their optical, electrical, and mechanical properties can be done through mechanical deformation.
• Ordered and controllable wrinkling patterns have important potential applications: droplet manipulation, adaptive camouflage, health and medical monitoring, flexible electronic devices, electromagnetic shielding and absorption.

I sincerely thank all individuals and organizations that have made efforts and contributions for this. Special thanks to Professor Wang Xiaodong and the relevant staff of the University of Chinese Academy of Sciences for their invaluable guidance, high-quality images, and text materials, which greatly enhanced the richness and professionalism of this article. Great thanks to my graduate students for their participation and outstanding contributions in the early stages of this work.

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Notes & references

Cover image. Persimmons before and after dehydration—dehydration develops surface wrinkles. [Source : right, photo Fumikas Sagisavas, CC0, via Wikimedia Commons]

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