Wrinkling of a compressed hyperelastic half-space with localized surface imperfections

Fu

Abstract

We consider a variant of the classical Biot problem concerning the wrinkling of a compressed hyperelastic half-space. The traction-free surface is no longer flat but has a localized ridge or trench that is invariant in the x1-direction along which the wrinkling pattern is assumed to be periodic. With the x2-axis aligned with the depth direction, the localized imperfection is assumed to be slowly varying and localized in the x3-direction, and an asymptotic analysis is conducted to assess the effect of the imperfection on the critical stretch for wrinkling. The imperfection introduces a length scale so that the critical stretch is now weakly dependent on the wave number. It is shown that the imperfection increases the critical stretch (and hence reduces the critical strain) whether the imperfection is a ridge or trench, and the amount of increase is proportional to the square of the maximum gradient of the surface profile.

• Acceptance Date: Aug 5, 2020
• Publication Date: Nov 1, 2020
• Journal: International Journal of Non-Linear Mechanics
• Print ISSN: 0020-7462
• Publisher: Elsevier
• DOI: https://doi.org/10.1016/j.ijnonlinmec.2020.103576
• Keywords: Elastic half-space; Wrinkling; Bifurcation; Nonlinear elasticity
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0020746220302389?via%3Dihub