3 papers
math.AP2024
A beam that can only bend on the Cantor set
Roberto Paroni, Brian Seguin
In this work we address the following question: is it possible for a one-dimensional, linearly elastic beam to only bend on the Cantor set and, if so, what would the bending energy…
math.AP2024
Sharp-interface limits for brittle fracture via the inverse-deformation formulation
Timothy J. Healey, Roberto Paroni, Phoebus Rosakis
We derive sharp-interface models for one-dimensional brittle fracture via the inverse-deformation approach. Methods of Gamma-convergence are employed to obtain the singular limits…
math.AP2017
One-dimensional von Kármán models for elastic ribbons
Lorenzo Freddi, Peter Hornung, Maria Giovanna Mora +1
By means of a variational approach we rigorously deduce three one-dimensional models for elastic ribbons from the theory of von Kármán plates, passing to the limit as the width of…