Better energies for low-dimensional elastic systems under combined bending and stretching
Schedule
Monday, April 11, 2022
00:00 UTC
Eduardo Vitral
Dr.
University of Nevada, Reno
Host: SLAAM by UC Merced
Recording
Open recording
Event Information
Recording
Available
Host
SLAAM by UC Merced
Duration
70 minutes
Abstract
We present new kinematic bending measures and quadratic energies for isotropic elastic plates and shells, with certain desirable features not present in commonly employed models in mechanics and soft matter. These are justified both by simple physical arguments related to the through-thickness variation in strain, and through a detailed reduction from a three-dimensional energy quadratic in stretch. The measure of plate bending is a dilation-invariant surface tensor that couples stretch and curvature in a natural extension of primitive generalized bending strains for straight rods. The extension to naturally-curved rods and shells, for which the pure stretching of a curved rest configuration is not a dilation, contrasts with previous ad hoc postulated forms. Our results provide a clean basis for simple models of low-dimensional elastic systems, and should enable more accurate probing of the structure of singularities in soft sheets and membranes.
Topics
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