Calculus of Variations and Geometric Measure Theory

F. Maddalena - D. Percivale - F. Tomarelli

Elastic structures in adhesion interaction

created by maddalena on 15 Jun 2011
modified by tomarelli on 02 May 2012


Published Paper

Inserted: 15 jun 2011
Last Updated: 2 may 2012

Journal: Variational Analysis and Aerospace Engineering: Mathematical Challenges for Aerospace Design. G.Buttazzo & A.Frediani Eds
Volume: 66
Pages: 289 - 304
Year: 2012

Contributed paper in the volume 66 of series "Springer Optimization and its Applications". This volume consists of papers presented at the Variational Analysis and Aerospace Engineering Workshop II held in Erice, Italy in September 2010 at the International School of Mathematics "Guido Stampacchia".

Links: ISBN 978-1-4614-2434-5


We study a variational model describing the interaction of two 1-dimensional elastic bodies through an adhesive layer, with the aim of modeling a simplified CFRP structure: e.g. a concrete beam or a medical rehabilitation device glued to a reinforcing polymeric fiber. Different constitutive assumptions for the adhesive layer are investigated: quadratic law and two kinds of softening law. In all cases properties of the equilibrium states of the structural system are analytically deduced. In the case of adhesion with softening, the minimum length of the elastic fiber avoiding debonding failure is estimated in terms of glue carrying capacity and the constitutive parameter of the fiber

Keywords: calculus of variations, elastic structures, adhesion