Mechanics Reveals the Biological Trigger in Wrinkly Fingers

Abstract

Fingertips wrinkle due to long exposure to water. The biological reason for this morphological change is unclear and still not fully understood. There are two main hypotheses for the underlying mechanism of fingertip wrinkling: the 'shrink' model (in which the wrinkling is driven by the contraction of the lower layers of skin, associated with the shrinking of the underlying vasculature), and the 'swell' model (in which the wrinkling is driven by the swelling of the upper layers of the skin, associated with osmosis). In reality, contraction of the lower layers of the skin and swelling of the upper layers will happen simultaneously. However, the relative importance of these two mechanisms to drive fingertip wrinkling also remains unclear. Simulating the swelling in the upper layers of skin alone, which is associated with neurological disorders, we found that wrinkles appeared above an increase of volume of [Formula: see text] Therefore, the upper layers can not exceed this swelling level in order to not contradict in vivo observations in patients with such neurological disorders. Simulating the contraction of the lower layers of the skin alone, we found that the volume have to decrease a [Formula: see text] to observe wrinkles. Furthermore, we found that the combined effect of both mechanisms leads to pronounced wrinkles even at low levels of swelling and contraction when individually they do not. This latter results indicates that the collaborative effect of both hypothesis are needed to induce wrinkles in the fingertips. Our results demonstrate how models from continuum mechanics can be successfully applied to testing hypotheses for the mechanisms that underly fingertip wrinkling, and how these effects can be quantified.

Post-buckling evolution of wavy patterns in trapezoidal film/substrate bilayers

“…Bifurcation curves of the microscopic model (4) and macroscopic model(7). The analytical critical load = 2 agrees with the numerical solutions.…”

“…Furthermore, spatially graded wrinkles are not straightly ribbed along direction but have a wavy curvature perpendicular to the taper edges, indicating that the wave direction varies as well. This is mainly due to stress relaxation along the edges and is actually distinguished from the analytical assumption on 1D sinusoidal wrinkles in models (4) and (7). Note that such orthogonality between the boundary and instability patterns seems a generic feature, which have been previously observed in experimental fluid mechanics [34].…”

“…Quantitative understanding and prediction of wrinkling pattern formation and evolution is of great importance not only for comprehensive knowledge on morphogenesis of growing soft tissues widely observed in nature and biological systems [1][2][3][4][5][6][7], but also for large industrial application areas including functional surface patterning design [8,9], micro/nano-fabrication of flexible electronic devices [10,11], microlens arrays production [12], adaptive aerodynamic drag control [13,14], mechanical property measurement of material characteristics [15], and the design of moisture-responsive wrinkling devices with tunable dynamics [16] and reversible optical writing/erasure functional surface [17]. Previous works are mainly concerned with 2D or 3D rectangular film/substrate systems and suggest that wrinkling patterns strongly depend on applied loading [18][19][20][21][22][23][24][25][26][27][28].…”

Quantitative predictions of diverse wrinkling patterns in film/substrate systems

“…Surface morphological instabilities of a soft material with a stiff thin surface layer have raised considerable research interests during past few years. Abundant examples can be found in various types of living creatures across length scales such as blooming process of hornbeam leaves 1 , hierarchical wrinkling of skins 2 and fingers 3 , folding of growing tubular organs 4 and human brain development 5 , morphological buckling of fruits and vegetables 6 – 8 , and differential growth of bacterial biofilms 9 . Besides, in modern industry, surface wrinkling can be widely applied in large area ranging from micro/nano morphological patterning control 10 – 12 , fabrication of flexible electronic devices 13 , 14 , mechanical self-assembly of islands on nano-particles 15 , defect localization in elastic surface crystals 16 , wet surface chemical patterning of micro-spheres 17 , multi-periodic surface topography of coated materials 18 , adaptive aerodynamic drag control 19 , 20 , mechanical property measurement of material characteristics 21 , to the design of moisture-responsive wrinkling devices with tunable dynamics 22 and reversible optical writing/erasure functional surface 23 .…”

On the buckling and post-buckling of core-shell cylinders under thermal loading

“…Quantitative characterization of wrinkling process for film/substrate systems has motivated considerable research interests during past few years for understanding and predicting pattern formation both in nature ( Mahadevan and Rica, 2005;Efimenko et al, 2005;Yin et al, 2009;Wang and Zhao, 2015;Zhang et al, 2016;Sáez and Zöllner, 2017 ) and in modern industry ( Brau et al, 2011;Cai et al, 2011;Cao and Hutchinson, 2012;Sun et al, 2012;Zang et al, 2012;Xu et al, 2014;2015a;2015b;Fu and Cai, 2015;Xu and Potier-Ferry, 2016a;Huang et al, 2016 ). Broad applications range from micro/nano-fabrication of flexible electronic devices with functional surface patterning ( Bowden et al, 1998;Rogers et al, 2010;Li, 2016 ), microlens arrays production ( Chan and Crosby, 2006 ), adaptive aerodynamic drag control ( Terwagne et al, 2014 ), to the mechanical property measurement of material characteristics ( Howarter and Stafford, 2010 ).…”