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Wrinkle
Wrinkle
Wrinkle
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Wrinkles on the face and hands are a typical sign of aging

A wrinkle, also known as a rhytid, is a fold, ridge or crease in an otherwise smooth surface, such as on skin or fabric. Skin wrinkles typically appear as a result of ageing processes such as glycation,[1] habitual sleeping positions,[2] loss of body mass, sun damage,[3] or temporarily, as the result of prolonged immersion in water. Age wrinkling in the skin is promoted by habitual facial expressions, aging, sun damage, smoking, poor hydration, and various other factors.[4] In humans, it can also be prevented to some degree by avoiding excessive solar exposure and through diet (in particular through consumption of carotenoids, tocopherols and flavonoids, vitamins (A, C, D and E), essential omega-3-fatty acids, certain proteins and lactobacilli).[5]

Skin

[edit]
Main article: Skin fold

Causes for aging wrinkles

[edit]
A woman of European origin with facial wrinkles

Development of facial wrinkles is a kind of fibrosis of the skin. Misrepair-accumulation aging theory suggests that wrinkles develop from incorrect repairs of injured elastic fibers and collagen fibers.[6][7][8] Repeated extensions and compressions of the skin cause repeated injuries of extracellular fibers in derma. During the repairing process, some of the broken elastic fibers and collagen fibers are not regenerated and restored but replaced by altered fibers. When an elastic fiber is broken in an extended state, it may be replaced by a "long" collagen fiber. Accumulation of "long" collagen fibers makes part of the skin looser and stiffer, and as a consequence, a big fold of skin appears. When a "long" collagen is broken in a compressed state, it may be replaced by a "short" collagen fiber. The "shorter" collagen fibers will restrict the extension of "longer" fibers, and make the "long" fibers in a folding state permanently. A small fold, namely a permanent wrinkle, then appears.

Sleep wrinkles

[edit]

Sleep wrinkles are created and reinforced when the face is compressed against a pillow or bed surface in side or stomach sleeping positions during sleep.[9] They appear in predictable locations due to the underlying superficial musculoaponeurotic system (SMAS), and are usually distinct from wrinkles of facial expression.[10] As with wrinkles of facial expression, sleep wrinkles can deepen and become permanent over time, unless the habitual sleeping positions which cause the wrinkles are altered.[11]

Water-immersion wrinkling

[edit]
A wrinkled finger after a warm bath

The wrinkles that occur in skin over prolonged exposure to water are sometimes referred to as pruney fingers or water aging. This is a temporary skin condition where the skin on the palms of the hand or feet becomes wrinkly. This wrinkling response may have imparted an evolutionary benefit by providing improved traction in wet conditions,[12] and a better grasp of wet objects.[13] These results were called into question by a 2014 study that failed to reproduce any improvement of handling wet objects with wrinkled fingertips.[14] However, a 2020 study of gripping efficiency found that wrinkles decreased the force required to grip wet objects by 20%, supporting the traction hypothesis.[15]

Prior to a 1935 study, the common explanation was based on water absorption in the keratin-laden epithelial skin when immersed in water,[16] causing the skin to expand and resulting in a larger surface area, forcing it to wrinkle. Usually the tips of the fingers and toes are the first to wrinkle because of a thicker layer of keratin and an absence of hairs which secrete the protective oil called sebum.

Adult sole showing water immersion wrinkling

In the 1935 study, however, Lewis and Pickering were studying patients with palsy of the median nerve when they discovered that skin wrinkling did not occur in the areas of the patients' skin normally innervated by the damaged nerve. This suggested that the nervous system plays an essential role in wrinkling, so the phenomenon could not be entirely explained simply by water absorption. Recent research shows that wrinkling is related to vasoconstriction.[17][18] Water probably initiates the wrinkling process by altering the balance of electrolytes in the skin as it diffuses into the hands and soles via their many sweat ducts. This could alter the stability of the membranes of the many neurons that synapse on the many blood vessels underneath skin, causing them to fire more rapidly. Increased neuronal firing causes blood vessels to constrict, decreasing the amount of fluid underneath the skin. This decrease in fluid would cause a decrease in tension, causing the skin to become wrinkly.[19]

This insight resulted in bedside tests for nerve damage and vasoconstriction. Wrinkling is often scored with immersion of the hands for 30 minutes in water or EMLA cream with measurements steps of 5 minutes, and counting the number of visible wrinkles in time. Not all healthy persons have finger wrinkling after immersion, so it would be safe to say that sympathetic function is preserved if finger wrinkling after immersion in water is observed, but if the fingers emerge smooth it cannot be assumed that there is a lesion to the autonomic supply or to the peripheral nerves of the hand.[20]

Other animals with wrinkles

[edit]

Examples of wrinkles can be found in various animal species that grow loose, excess skin, particularly when they are young. Several breeds of dog, such as the Pug and the Shar Pei, have been bred to exaggerate this trait. In dogs bred for fighting, this is the result of selection for loose skin, which confers a protective advantage.[21]

Techniques for reducing the appearance of aging wrinkles

[edit]
A man receiving a botox injection

Current evidence suggests that tretinoin decreases cohesiveness of follicular epithelial cells, although the exact mode of action is unknown. Additionally, tretinoin stimulates mitotic activity and increased turnover of follicular epithelial cells.[22] Tretinoin is better known by the brand name Retin-A.

Topical glycosaminoglycans supplements can help to provide temporary restoration of enzyme balance to slow or prevent matrix breakdown and consequent onset of wrinkle formation. Glycosaminoglycans (GAGs) are produced by the body to maintain structural integrity in tissues and to maintain fluid balance. Hyaluronic acid is a type of GAG that promotes collagen synthesis, repair, and hydration. GAGs serve as a natural moisturizer and lubricant between epidermal cells to inhibit the production of matrix metalloproteinases (MMPs).

Dermal fillers are injectable products frequently used to correct wrinkles, and other depressions in the skin. They are often a kind of soft tissue designed to enable injection into the skin for purposes of improving the appearance. The most common products are based on hyaluronic acid and calcium hydroxylapatite.

Botulinum toxin is a neurotoxin protein produced by the bacterium Clostridium botulinum. Botox is a specific form of botulinum toxin manufactured by Allergan for both therapeutic and cosmetic use. Besides its cosmetic application, Botox is used in the treatment of other conditions including migraine headache and cervical dystonia (spasmodic torticollis) (a neuromuscular disorder involving the head and neck).[23]

Dysport, manufactured by Ipsen, received FDA approval and is now used to treat cervical dystonia as well as glabellar lines in adults. In 2010, another form of botulinum toxin, one free of complexing proteins, became available to Americans. Xeomin received FDA approval for medical indications in 2010 and cosmetic indications in 2011.

Botulinum toxin treats wrinkles by immobilizing the muscles which cause wrinkles. It is not appropriate for the treatment of all wrinkles; it is indicated for the treatment of glabellar lines (between the eyebrows) in adults. Any other usage is not approved by the FDA and is considered off-label use.

Laser resurfacing is FDA-cleared skin resurfacing procedure in which lasers are used to improve the condition of the skin.[citation needed] Two types of lasers are used to reduce the appearance of fine lines and wrinkles on the face; laser ablation, which removes thin layers of skin, and nonablative lasers that stimulate collagen production. Nonablative lasers are less effective than ablative ones but they are less invasive and recovery time is short. After the procedure people experience temporary redness, itching and swelling.

See also

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References

[edit]
[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Wrinkle

View on Grokipedia
from Grokipedia
A wrinkle is a fold, ridge, or crease in an otherwise smooth surface, such as or fabric. Wrinkles can arise in biological contexts, including the of humans and animals or surfaces, as well as in non-biological materials like textiles, where they result from mechanical stress, contraction, or environmental factors. The physics of wrinkling involves surface instabilities and , studied in various fields. Detailed discussions of wrinkles in , other organisms, and materials follow in subsequent sections.

Wrinkles in Human Skin

Types of Wrinkles

Wrinkles are creases, folds, or ridges in the skin that form due to the loss of elasticity and collagen, which are essential proteins supporting skin structure. This natural process is primarily driven by aging, though environmental factors can accelerate it. Wrinkles are broadly classified into static wrinkles and dynamic wrinkles based on their visibility and formation. Static wrinkles are permanent lines visible even at rest, resulting from long-term such as UV exposure that degrades over time. Common examples include forehead lines and deepened crow's feet that persist without facial movement. In contrast, dynamic wrinkles appear only during facial expressions due to repeated muscle contractions pulling on the skin. These include lines between the eyebrows and smile lines around the mouth, which may evolve into static wrinkles with prolonged repetition. Further categorization considers depth and appearance, such as fine lines and deep wrinkles or furrows. Fine lines are shallow surface creases, often the earliest signs of aging or resulting from skin dehydration that temporarily reduces plumpness. They are typically less than 1 mm in width and depth and may appear around the eyes or before progressing. Deep wrinkles or furrows, however, are pronounced grooves exceeding 1 mm in depth, stemming from significant breakdown and often visible as persistent folds. These commonly occur on the or in the nasolabial folds extending from the to the corners. Additional types include atrophic wrinkles and gravitational wrinkles, which highlight underlying structural changes. Atrophic wrinkles manifest as thin, deep lines due to volume loss in the , where reduced and fat lead to skin thinning and hollowing. Gravitational wrinkles appear as sagging folds caused by the downward pull of combined with diminished skin support from elastin degradation. Wrinkles also vary by location, influencing their appearance and severity. Periorbital wrinkles form around the eyes, such as crow's feet radiating outward from the outer corners, often exacerbated by squinting. Perioral wrinkles develop around the mouth, including vertical lines above the upper lip or marionette lines downward from the corners, typically from repetitive pursing or smiling. Neck wrinkles present as horizontal creases or bands on the neck, resulting from skin laxity in this thinner, more exposed area.

Causes of Wrinkles

Wrinkles in arise from a combination of intrinsic and extrinsic factors that disrupt the skin's structural integrity, particularly the composed of and . Intrinsic aging, also known as chronological aging, is a genetically programmed that begins in the mid-20s to early 30s, leading to gradual reductions in cell turnover, collagen production, and elastin fibers. This results in thinner, less resilient skin as fibroblasts slow their synthesis of these proteins, with genetic variations influencing the rate and severity of these changes across individuals. Over time, the loses volume and elasticity, contributing to fine lines that deepen with advancing age. Extrinsic aging, which superimposes on intrinsic processes, is predominantly driven by environmental exposures, with (UV) radiation from accounting for 70-80% of visible skin aging signs through . UV rays penetrate the skin, generating (free radicals) that damage cellular components and activate matrix metalloproteinases (MMPs), enzymes that degrade and in the . This enzymatic breakdown disrupts the , leading to fragmented fibers and solar elastosis, which manifest as coarse wrinkles, leathery texture, and pigmentation irregularities. Lifestyle factors further accelerate wrinkle formation by exacerbating oxidative damage and impairing repair. introduces free radicals and toxins that promote , reducing blood flow and oxygen delivery to cells, while simultaneously upregulating MMPs to accelerate breakdown. Diets low in antioxidants, such as vitamins C and E, fail to neutralize free radicals effectively, allowing cumulative to weaken networks and hasten extrinsic aging. Hormonal fluctuations, particularly during , contribute significantly to wrinkle development by altering composition. The decline in levels reduces synthesis and increases its turnover, resulting in up to a 30% loss of within the first five years post-, leading to thinner, drier prone to creasing. Sleep-induced wrinkles form from mechanical forces applied during prolonged facial contact with surfaces like pillows. Compression and shear stresses distort the superficial musculoaponeurotic (SMAS) layer and overlying , creating temporary folds that become more permanent with age as reduced dermal resilience impairs recovery from these distortions. Glycation, accelerated by high-sugar diets, leads to the formation of (AGEs) that covalently molecules, stiffening the and reducing its flexibility. This irreversible modification impairs 's ability to slide and recoil, promoting the rigidity and sagging associated with wrinkles.

Prevention of Wrinkles

Preventing wrinkles involves adopting proactive measures that address key modifiable risk factors, such as (UV) radiation exposure and lifestyle habits, to maintain skin elasticity and integrity over time. Sun protection remains the most effective strategy against , which accelerates wrinkle formation. Daily application of broad-spectrum with at least SPF 30 blocks UVA and UVB rays that degrade and in the . Wearing protective , such as wide-brimmed hats and long sleeves, and avoiding peak sun hours between 10 a.m. and 4 p.m. further reduces cumulative UV damage. These practices, when consistently followed from early adulthood, can significantly delay the onset of fine lines and deeper folds. A targeted skincare routine supports barrier function and counters . Moisturizers with humectants like help retain hydration, preventing the dryness that exacerbates wrinkle visibility. Topical antioxidants, including vitamins C and E, neutralize free radicals generated by environmental exposures, thereby preserving synthesis. Retinoids, such as or tretinoin, stimulate production and epidermal turnover; initiating use in one's 20s or 30s maximizes preventive benefits, though starting gradually minimizes irritation. Lifestyle modifications play a crucial role in fostering skin repair and circulation. A balanced diet rich in fruits, vegetables, and omega-3 fatty acids provides antioxidants and compounds that support dermal health and reduce glycation-related aging. Quitting restores microvascular circulation and halts the enzyme-mediated breakdown of , with visible improvements in skin texture emerging within months. Adequate , ideally 7-9 hours per night and on the back to avoid compression, allows for natural skin regeneration and minimizes sleep-induced creases. Maintaining internal and external hydration counters environmental stressors that promote wrinkle development. Drinking sufficient water—at least 8 glasses daily—enhances and hydration levels, particularly in low-water-intake individuals. Using humidifiers in dry indoor environments prevents , preserving the 's moisture barrier. Limiting alcohol consumption avoids and that impair elasticity and accelerate fine line formation. For postmenopausal women, hormonal management can mitigate estrogen decline's impact on structure. (HRT), under medical supervision, increases content and dermal thickness, reducing wrinkle depth compared to non-users. This approach is most beneficial when tailored to individual health profiles to balance skin benefits against potential risks.

Treatment of Wrinkles

Treatments for wrinkles in encompass a range of medical, cosmetic, and procedural interventions designed to reduce or eliminate visible lines by addressing underlying structural changes such as and skin laxity. These approaches target both dynamic wrinkles, caused by muscle movement, and static wrinkles, resulting from aging, with selection often depending on wrinkle type for optimal outcomes. Common methods include topical applications, injectables, surgical procedures, energy-based devices, and emerging therapies, each varying in invasiveness, duration of effect, and suitability for different skin concerns. Topical treatments form the foundation of non-invasive wrinkle management, primarily by promoting collagen production, enhancing cell turnover, and improving hydration. Retinoids, such as tretinoin, are among the most established options; tretinoin stimulates synthesis and epidermal renewal, reducing fine lines and improving skin texture, and has been FDA-approved for treatment since 1971 with subsequent recognition for . Complementary ingredients like peptides signal fibroblasts to boost and , while provides immediate hydration by binding water molecules, plumping the skin to minimize wrinkle appearance. These formulations are typically applied daily and show gradual improvements over 3-6 months, though they may cause initial . Injectable treatments offer targeted, temporary corrections for moderate to severe wrinkles. , commonly known as Botox, relaxes underlying muscles to smooth dynamic wrinkles like glabellar lines, with FDA approval for cosmetic use in 2002; effects typically last 3-6 months before requiring re-treatment. Dermal fillers, such as hyaluronic acid-based products like Juvederm, restore volume to static wrinkles and hollow areas by filling space and supporting skin structure, providing results that endure 6-18 months depending on the product's cross-linking and injection site. These minimally invasive procedures are performed in-office with and carry low risks of bruising or swelling. Surgical options provide more dramatic, long-lasting results for advanced wrinkles by physically repositioning tissues. A facelift involves elevating the skin, tightening underlying muscles and connective tissues, and removing excess fat to address sagging and deep folds, often yielding effects lasting 5-10 years. Chemical peels, using agents like , exfoliate the outer skin layers to resurface and stimulate remodeling, effectively reducing superficial wrinkles and uneven texture; light peels with 20-70% offer subtle improvements with minimal . Energy-based devices deliver controlled thermal energy to deeper layers, promoting stimulation through precise injury and healing. Laser resurfacing with CO2 or fractional ablates damaged while heating the to induce new formation, significantly improving wrinkle depth and firmness over 3-6 months post-treatment. Microneedling combined with radiofrequency creates micro-injuries and delivers heat to remodel dermal tissue, enhancing tightness and reducing fine to moderate wrinkles with effects visible after multiple sessions spaced 4-6 weeks apart. Emerging therapies leverage the body's regenerative potential for natural wrinkle reduction. Platelet-rich plasma (PRP) injections, derived from a patient's own blood, release growth factors like PDGF and TGF-β to accelerate production and tissue repair, improving skin elasticity and fine lines when administered in 3-4 sessions. LED light therapy, particularly red and near-infrared wavelengths, penetrates superficially to boost activity and synthesis without heat damage, making it suitable for mild wrinkles and suitable for home or clinical use with cumulative benefits over 8-12 weeks. These options are generally well-tolerated but require multiple treatments for sustained results.

Wrinkles in Other Organisms

Wrinkles in Animals

In non-human animals, wrinkles often represent evolutionary adaptations that enhance survival through , sensory functions, or , though they can also arise from genetic mutations or aging processes similar to those observed in collagen degradation. These skin features vary by , reflecting diverse physiological needs in terrestrial, aquatic, and arboreal environments. In large mammals such as elephants and rhinoceroses, thick, wrinkled serves a critical role in by increasing surface area for heat dissipation and retaining moisture for evaporative cooling. African elephants (Loxodonta africana) possess a cracked that traps water and mud, facilitating prolonged cooling in arid habitats where sweating is absent; this structure enhances heat exchange efficiency by increasing water retention for evaporative cooling, with the sculptured allowing 4-5 to 10 times greater moisture retention than flat surfaces. Similarly, white rhinoceroses (Ceratotherium simum) exhibit folded with a well-developed vascular bed beneath an approximately 1 mm thick , allowing efficient temperature regulation through moisture retention and insulation against environmental extremes. These adaptations likely evolved to mitigate overheating during prolonged activity in hot climates. The Chinese Shar-Pei dog breed exemplifies genetically induced wrinkles resulting from a duplication in the HAS2 gene, which overproduces hyaluronan and leads to excessive skin folding, particularly pronounced in puppies and persisting into adulthood on the head, neck, and limbs. While this trait defines the breed's morphology, the deep folds create moist, enclosed spaces prone to bacterial proliferation, resulting in recurrent skin infections () and , where eyelids invert and irritate the . Pathological consequences often necessitate surgical interventions, such as the Stades forced granulation procedure on the upper or Hotz-Celsus corner tacking, to correct eyelid malposition and prevent corneal ulceration. Functional wrinkles appear in various species for sensory or behavioral purposes. In , water-immersion wrinkling of —triggered by prolonged exposure—enhances grip on wet surfaces by channeling away and increasing , reducing the force needed to handle slippery objects by aligning it with dry conditions; this trait, observed across including macaques, suggests an adaptive response to in rainy environments. Facial skin movements in domestic cats (Felis catus) and dogs (Canis lupus familiaris), involving subtle folds around the eyes, mouth, and whiskers, contribute to over 270 distinct expressions in cats and facilitate emotional signaling, such as slow blinks for affiliation or ear flattening for distress, aiding social communication and sensory perception. In avian species like wild turkeys (Meleagris gallopavo), the wattle—a fleshy, vascular lobe beneath the —undergoes dynamic swelling and color changes (from pale to bright red) during mating displays, forming temporary folds that amplify visual signals to attract females and deter rivals by indicating health and arousal. Aging-related wrinkles in animals stem from progressive and degradation in the , paralleling human mechanisms but varying by species due to metabolic rates and lifespan. Small mammals like mice exhibit accelerated thinning and wrinkle formation, with content dropping up to 40% in aged models due to reduced synthesis and increased activity; in contrast, longer-lived species such as axolotls (Ambystoma mexicanum) show slower dermal remodeling with persistent regenerative capacity.

Wrinkles in Plants

In xerophytic plants, such as cacti in the family Cactaceae, folded or ribbed stem structures function as wrinkle-like adaptations to minimize water loss through transpiration. These ribs and tubercles allow the plant to expand or contract radially without excessively increasing surface area, thereby limiting exposure to dry air and reducing evaporative loss; for instance, in species like Echinocactus platyacanthus, the thick cortex (up to 300 mm) maintains hydration while the folded epidermis provides mechanical support during volume changes. Similarly, leaf venation patterns in many plants create natural creases and ridges that enhance structural integrity, acting as trusses to resist bending and wind damage while optimizing light capture for photosynthesis. In monocot leaves, for example, longitudinal V-folds or crosswise pleats form ridge-and-valley configurations that increase flexural stiffness without adding substantial mass. Developmental wrinkling occurs in young leaves due to differential growth rates between cell layers, leading to mechanical that puckers the surface and expands the effective area for light interception. This uneven expansion, driven by anisotropic stresses in the and mesophyll, helps young leaves achieve a three-dimensional form that boosts during early , as seen in various dicot and monocot species. In pathological contexts, viral infections like (CMV) induce leaf wrinkling as a stress response by disrupting function and signaling, causing distortion and reduced ; symptoms include mottled, puckered leaves that reflect cellular imbalance and impaired growth. Environmental similarly triggers temporary furrowing or rolling in leaves, such as in (Triticum aestivum), where turgor loss in bulliform cells folds the lamina to decrease exposed surface area, conserving and maintaining viability during midday . Wrinkling in aging fruits, exemplified by prunes (dried plums) and raisins (dried grapes), results from dehydration-induced collapse of cell walls, particularly through degradation and reconfiguration of networks. As water is lost, calcium-crosslinked low-methoxyl aggregates irreversibly, reducing the tissue's ability to reswell and causing surface folding due to microstructural shrinkage and loss of turgor; this process alters mechanical properties, making the skin brittle while concentrating sugars. Evolutionarily, wrinkled bark in trees like oaks (Quercus spp.) serves protective roles against herbivores and , with thick, furrowed layers insulating the from heat and deterring browsing by creating an uneven, tannin-rich barrier. Cracks form as the expands annually, generating tension that splits the outer bark, a that enhances resistance in pyrophytic species by allowing rapid wound closure.

Wrinkles in Materials and Physics

Wrinkles in Fabrics and Textiles

Wrinkles in fabrics and textiles form primarily through the disruption of bonds within structures, particularly in cellulosic materials like . When exposed to and moisture, such as during washing or wear, water molecules penetrate between polymer chains in the , breaking the intermolecular bonds that maintain the fabric's smooth alignment. This allows the chains to slip and shift under mechanical stress, creating creases. Upon drying, the bonds reform in the new, folded positions, locking in the wrinkles. Natural fibers, such as and , are particularly prone to wrinkling due to their hydrophilic properties, which facilitate absorption and bond disruption. 's cellulose structure readily swells with water, promoting chain slippage, while 's protein-based offers slightly more resilience but still yields under prolonged stress. In contrast, synthetic fibers like exhibit greater resistance to wrinkling owing to their non-polar, smooth molecular chains that form fewer bonds and repel , maintaining structural integrity even after compression or drying. Several factors exacerbate wrinkle formation in textiles, including environmental conditions and handling practices. High promotes moisture retention in fibers, softening them and increasing susceptibility to creasing during activities like prolonged sitting or improper storage in folded states. Mechanical actions, such as tumbling in dryers, further induce wrinkles by combining compression with uneven . Fabric weave also plays a role; plain weaves, common in shirting, are more wrinkle-prone than weaves, which distribute stress more evenly due to their diagonal interlacing pattern. To mitigate wrinkling, chemical finishes have been developed since the , with dimethylol dihydroxyethyleneurea (DMDHEU) emerging as a key agent that cross-links cellulose chains, restricting their slippage and enhancing recovery from deformation. This urea-formaldehyde derivative, applied via padding and curing, forms a rigid network within the fiber, improving durability to laundering. Permanent press fabrics extend this approach by incorporating treatments during , where thermosetting resins are impregnated into the material post-weaving but pre-sewing, then cured under heat to set shape retention properties. In fashion and daily use, wrinkles compromise aesthetic appeal by conveying dishevelment, prompting reliance on to restore flatness. applies (typically 100–200°C, varying by type) and to soften bonds, allowing manual realignment before they reform upon cooling, thus smoothing the fabric. This practice underscores broader cultural preferences for crisp appearances in and social contexts, though recent trends occasionally embrace subtle creases for a relaxed aesthetic.

Physics of Wrinkling

Wrinkling in thin elastic sheets arises as a instability when compressive stresses surpass the material's , resulting in the formation of periodic out-of-plane folds that relieve in-plane compression. This phenomenon is governed by the competition between bending energy, which favors smoother surfaces, and energy, which is minimized by allowing localized deformations under compression. In the seminal analysis by Cerda and Mahadevan, the wrinkling pattern emerges far from the instability threshold, where nonlinear geometric effects dominate, leading to a characteristic wavelength determined by the sheet's thickness and the applied confinement. For thin films deposited on compliant substrates, the wrinkle pattern is characterized by a critical that balances the film's resistance against the substrate's elastic response. The governing relation is given by λ=2π(BhY)1/4,\lambda = 2\pi \left( \frac{B h}{Y} \right)^{1/4}, where BB is the film's modulus, YY is the of the substrate, and hh is the substrate thickness; this formula arises in the elastic foundation model, where the substrate provides a restoring proportional to Y/hY/h. Experimental validation of this scaling has been observed in systems where the substrate thickness modulates the wrinkle periodicity, confirming the theoretical prediction for moderate compressions. In natural systems, such as the pruney wrinkles on fingertips after prolonged immersion, epidermal contraction relative to the underlying mimics this film-on-substrate instability, producing periodic folds with wavelengths on the order of millimeters. Technologically, engineered wrinkled surfaces exploit these principles for functional applications; for instance, controlled in thin films creates hierarchical topographies that enhance , such as gratings for tunable antireflection coatings, or improve in dry-contact systems, including gecko-inspired tapes where wrinkles facilitate conformal contact on rough substrates. Under sustained or increasing compression, initial delocalized wrinkles can transition to localized creases, where deformation concentrates into sharp, permanent folds to further minimize the total . This post-buckling behavior is modeled through energy minimization, accounting for the nonlinear coupling between and , with the crease forming when the compressive strain exceeds a threshold determined by the sheet's and properties. The localization arises from an in the wrinkle , driven by the geometric nonlinearity that amplifies release in folded regions. Experimental studies illustrate these principles across diverse systems; for example, wrinkles form in drying coatings due to differential shrinkage between surface and bulk layers, producing hierarchical patterns as compressive stresses build during solvent evaporation. Similarly, in stretched sheets, out-of-plane ripples emerge under tensile loading, with their evolution governed by van der Waals interactions and substrate effects, leading to periodic undulations that persist even at low strains. In both cases, large deformations highlight the role of nonlinear geometry, where the out-of-plane deflection introduces higher-order terms in the strain energy, enabling stable wrinkled states far beyond linear predictions.

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