Calculus of Variations and Geometric Measure Theory

R. Paroni - M. Picchi Scardaoni

From elastic shallow shells to beams with elastic hinges by $\Gamma $-convergence

created by picchiscardaoni on 05 Jul 2024


Published Paper

Inserted: 5 jul 2024
Last Updated: 5 jul 2024

Journal: Zeitschrift für angewandte Mathematik und Physik
Volume: 75
Number: 4
Year: 2024
Doi: 10.1007/s00033-024-02280-1
Links: journal link


In this paper, we study the $\Gamma $ -limit of a properly rescaled family of energies, defined on a narrow strip, as the width of the strip tends to zero. The limit energy is one-dimensional and is able to capture (and penalize) concentrations of the midline curvature. At the best of our knowledge, it is the first paper in the $\Gamma $ -convergence field for dimension reduction that predicts elastic hinges. In particular, starting from a purely elastic shell model with “smooth” solutions, we obtain a beam model where the derivatives of the displacement andor of the rotation fields may have jump discontinuities. Mechanically speaking, elastic hinges can occur in the beam.

Keywords: shallow shell, ribbons, elastic hinges, tape spring