Wrinkling of Highly Stretched Sheets: Modeling and Analysis

Wednesday, April 10, 2019

4pm - 5pm

229 Norris Hall, Virginia Tech Campus

Tim Healey

Department of Mathematics

Cornell University

Abstract:

Transverse wrinkles often develop when a finely thin, rectangular, elastic sheet is highly stretched in the longer direction – think of a sheet of sandwich wrap. Much like the famous Euler buckling of a compressed thin rod, this can be analyzed as a bifurcation problem: The flat, unwrinkled state bifurcates to the wrinkled state as the applied macroscopic stretch is slowly increased. The problem is well known and has been widely popularized in recent years. We present some new results in this talk:

  • We propose a new class of models incorporating finite nonlinear elasticity for the membrane behavior, accompanied by small, non-zero bending stiffness.

  • Employing numerical bifurcation/continuation methods, we show that wrinkling occurs for a specific range of aspect ratios only; within that range, stable wrinkles first initiate, develop to a small maximum amplitude, and subsequently diminish and then disappear as the macroscopic strain is steadily increased. We further explore the role of inelasticity to explain some recent, rather striking experimental results, demonstrating no wrinkles during the initial stretching, with wrinkling upon unloading.

Biography:

Tim Healey works at the interface between the mechanics of nonlinearly elastic structures and solids and mathematical analysis, viz., bifurcation theory, PDE & calculus of variations. He holds degrees from the University of Missouri, Columbia (BS 1976) and the University of Illinois, Urbana-Champaign (MS 1978, PhD. 1984), during which time he studied mathematics, civil engineering, theoretical mechanics and mathematics – in that order. Before his PhD studies, he was a licensed structural engineer at a consulting firm in the Los Angeles area (1978-80). He spent one year as a visiting professor of mathematics at the University of Maryland before joining the Cornell faculty in 1985. At Cornell he has held positions in the Department of Theoretical & Applied Mechanics (1985-2008), including Chair of the Department (2000-2008), and a joint appointment in the Departments of Mathematics and Mechanical & Aerospace Engineering (2009-2014). He currently holds a full-time appointment in the Department of Mathematics at Cornell.