2001/08/20 by B. A. DiDonna, Brian DiDonna · 4 citations
Engineering · Physics and Astronomy · #Composite Structure Analysis and Optimization #Dynamics and Control of Mechanical Systems #Elasticity and Material Modeling #cond-mat
paper · pdf · doi:10.1103/physreve.66.016601
42 pages, latex, doctoral dissertation, to be submitted to Phys Rev E
arxiv created 2001/08/20 · openalex publication_date 2002/07/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When a thin elastic sheet crumples, the elastic energy condenses into a network of folding lines and point vertices. These folds and vertices have elastic energy densities much greater than the surrounding areas, and most of the work required to crumple the sheet is consumed in breaking the folding lines or "ridges." To understand crumpling it is then necessary to understand the strength of the ridges. In this work, we consider the buckling of a single ridge under the action of inward forcing applied at its ends. We demonstrate a simple scaling relation for the response of the ridge to the force prior to buckling. We also show that the buckling instability depends only on the ratio of strain along the ridge to the curvature across it. Numerically, we find for a wide range of boundary conditions that ridges buckle when our forcing increases their elastic energy by 20% over their resting state value. We also observe a correlation between neighbor interactions and the location of initial buckling. Analytic arguments and numerical simulations are employed to prove these results. Implications for the strength of ridges as structural elements are discussed.