In this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, ‘breathing-like’ deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

10aCrawling motility10aDirectional surfaces10aFrictional interactions10aLiquid crystal elastomers10aSoft biomimetic robots1 aDeSimone, Antonio1 aGidoni, Paolo1 aNoselli, Giovanni uhttp://www.sciencedirect.com/science/article/pii/S002250961530043000709nas a2200169 4500008004100000245011000041210006900151260003000220300001200250490000700262520014000269653002500409100002600434700002100460700002200481856003600503 2012 en d00aLinear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions0 aLinear elasticity obtained from finite elasticity by Gammaconver bGauthier-Villars;Elsevier a715-7350 v293 aThe energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

10aNonlinear elasticity1 aAgostiniani, Virginia1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/4267