Growth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix
KAUST Grant NumberKUK-C1-013-04
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AbstractWe investigate the problem of an axially loaded, isotropic, slender cylinder embedded in a soft, isotropic, outer elastic matrix. The cylinder undergoes uniform axial growth, whilst both the cylinder and the surrounding elastic matrix are confined between two rigid plates, so that this growth results in axial compression of the cylinder. We use two different modelling approaches to estimate the critical axial growth (that is, the amount of axial growth the cylinder is able to sustain before it buckles) and buckling wavelength of the cylinder. The first approach treats the filament and surrounding matrix as a single 3-dimensional elastic body undergoing large deformations, whilst the second approach treats the filament as a planar, elastic rod embedded in an infinite elastic foundation. By comparing the results of these two approaches, we obtain an estimate of the foundation modulus parameter, which characterises the strength of the foundation, in terms of the geometric and material properties of the system. © 2013 Elsevier Ltd. All rights reserved.
CitationO’Keeffe SG, Moulton DE, Waters SL, Goriely A (2013) Growth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix. International Journal of Non-Linear Mechanics 56: 94–104. Available: http://dx.doi.org/10.1016/j.ijnonlinmec.2013.04.017.
SponsorsThis publication is based on work supported in part by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) to the Oxford Centre for Collaborative Applied Mathematics (OCCAM). A.G. is a Wolfson/Royal Society Merit Award Holder and acknowledges support from a Reintegration Grant under EC Framework VII. S.O.'K. is supported by the University of Oxford Systems Biology Doctoral Training Centre, which is funded by EPSRC. We would like to thank Luis Dorfmann and Yibin Fu for interesting discussions on instabilities in nonlinear elasticity. S.O'K., D.E.M., and A.G. are members of OCCAM, D.E.M. is a member of the Centre for Mathematical Biology (CMB) and S.W. and A.G. are members of the Oxford Centre for Industrial Applied Mathematics (OCIAM). The support of these centres is gratefully acknowledged.