Elasto-Gravity Bending: Energy and Equilibrium

This lecture covers the concept of elasto-gravity bending in thin sheets, focusing on the bending energy and equilibrium shapes under gravity. The instructor explains the linearized limit of small deformations and the bending energy equations for two-dimensional sheets. The lecture delves into the bending modulus, stiffness under bending deformations, and large deformations. It also discusses the total energy functional for a thin strip bent under gravity, equilibrium shapes, and differential equations. The non-dimensionalization of equations and the determination of the elasto-gravity lengthscale are explored. The lecture concludes with numerical methods to solve nonlinear differential equations and determine the bending modulus and specific bending stiffness of paper sheets.