A 3D–1D Young measure theory of an elastic string

Article type: Research Article

Authors: Freddi, Lorenzo^; | Paroni, Roberto

Affiliations: Dipartimento di Matematica e Informatica, Università di Udine, via delle Scienze 206, 33100 Udine, Italy E‐mail: freddi@dimi.uniud.it | Dipartimento di Architettura e Pianificazione, Università di Sassari, Palazzo del Pou Salit, Piazza Duomo, 07041 Alghero, Italy E‐mail: paroni@uniss.it

Note: [] Corresponding author.

Abstract: A variational limit defined on the space of one‐dimensional Young measures is obtained from three‐dimensional elasticity via dimension reduction. The physical requirement that the energy becomes infinite when the volume locally vanishes is taken into account. The rate at which it blows up characterizes the domain of the limit energy. The obtained limit problem uniquely determines the energy density of the elastic string.

Journal: Asymptotic Analysis, vol. 39, no. 1, pp. 61-89, 2004