2017/02/28 by Salem Al Mosleh, Christian D. Santangelo, Christian Santangelo
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · Physics and Astronomy · #Advanced Materials and Mechanics #Cellular Mechanics and Interactions #Classical mechanics #Continuum mechanics #Curvature #Geometry #Isometry (Riemannian geometry) #Mathematical analysis #Mathematics #Nonlinear system #Physics #Quantum mechanics #Structural Analysis and Optimization #Surface (topology) #cond-mat.soft
paper · pdf · doi:10.1103/physreve.96.013003
published as Phys. Rev. E 96, 013003 (2017)
openalex publication_date 2017/07/10 · arxiv created 2018/06/01 · arxiv updated 2018/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Thin shells are characterized by a high cost of stretching compared to bending. As a result isometries of the midsurface of a shell play a crucial role in their mechanics. In turn, curves on the midsurface with zero normal curvature play a critical role in determining the number and behavior of isometries. In this paper, we show how the presence of these curves results in a decrease in the number of linear isometries. Paradoxically, shells are also known to continuously fold more easily across these rigidifying curves than other curves on the surface. We show how including nonlinearities in the strain can explain these phenomena and demonstrate folding isometries with explicit solutions to the nonlinear isometry equations. In addition to explicit solutions, exact geometric arguments are given to validate and guide our analysis in a coordinate-free way.