title: Edge wrinkling in elastically supported pre-stressed incompressible isotropic plates.
abstract: The equations governing the appearance of flexural static perturbations at the edge of a semi-infinite thin elastic isotropic plate, subjected to a state of homogeneous bi-axial pre-stress, are derived and solved. The plate is incompressible and supported by a Winkler elastic foundation with, possibly, wavenumber dependence. Small perturbations superposed onto the homogeneous state of pre-stress, within the three-dimensional elasticity theory, are considered. A series expansion of the plate kinematics in the plate thickness provides a consistent expression for the second variation of the potential energy, whose minimization gives the plate governing equations. Consistency considerations supplement a constraint on the scaling of the pre-stress so that the classical Kirchhoff-Love linear theory of pre-stretched elastic plates is retrieved. Moreover, a scaling constraint for the foundation stiffness is also introduced. Edge wrinkling is investigated and compared with body wrinkling. We find that the former always precedes the latter in a state of uni-axial pre-stretch, regardless of the foundation stiffness. By contrast, a general bi-axial pre-stretch state may favour body wrinkling for moderate foundation stiffness. Wavenumber dependence significantly alters the predicted behaviour. The results may be especially relevant to modelling soft biological materials, such as skin or tissues, or stretchable organic thin-films, embedded in a compliant elastic matrix.
authors.affiliation: School of Mathematics, Statistics Applied Mathematics, National University of Ireland Galway, Galway, Ireland; School of Mechanical Materials Engineering, University College Dublin, Belfield, Dublin 4, Ireland.
authors.forename: Michel
authors.identifier: 0000-0002-6266-1221
authors.initials: M
authors.lastname: Destrade
authors.affiliation: School of Computing and Mathematics , Keele University , Keele, Staffordshire ST5 5BG, UK.
authors.forename: Yibin
authors.initials: Y
authors.lastname: Fu
authors.affiliation: Dipartimento di Ingegneria Enzo Ferrari, via Vignolese 905, 41125 Modena, Italy.
authors.forename: Andrea
authors.identifier: 0000-0002-9657-5903
authors.initials: A
authors.lastname: Nobili
keywords: buckling; edge wrinkles; foundation; incremental deformation; pre-stressed plate