Asymptotic analysis of a junction of hyperelastic rods

Article type: Research Article

Authors: Hernández-Llanos, Pedro^{; *}

Affiliations: Departmento de Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile. E-mail: pedrohernandez@udec.cl

Correspondence: [*] Corresponding author. E-mail: pedrohernandez@udec.cl.

Abstract: In this article we obtain a 1-dimensional asymptotic model for a junction of thin hyperelastic rods as the thickness goes to zero. We show, under appropriate hypotheses on the loads, that the deformations that minimize the total energy weakly converge in a Sobolev space towards the minimum of a 1D-dimensional energy for elastic strings by using techniques from Γ-convergence.

Keywords: Junctions, thin structures, hyperelasticity, nonlinear elasticity, thin rods, asymptotic analysis

DOI: 10.3233/ASY-211683

Journal: Asymptotic Analysis, vol. 126, no. 3-4, pp. 303-322, 2022