On the energetic formulation of the Gurtin and Anand model in strain gradient plasticity
Line defect evolution in finite-dimensional manifolds
March 2012, 17(2): 553-574. doi: 10.3934/dcdsb.2012.17.553
Adhesive flexible material structures
Francesco Maddalena 1, , Danilo Percivale 2, and Franco Tomarelli 3,
Dipartimento di Matematica Politecnico di Bari, via Re David 200, 70125 Bari, Italy
Dipartimento di Ingegneria della Produzione Termoenergetica e Modelli Matematici, Università di Genova, Piazzale Kennedy, Fiera del Mare, Padiglione D, 16129 Genova, Italy
Dipartimento di Matematica "Francesco Brioschi", Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
Received November 2010 Revised June 2011 Published December 2011
We study variational problems modeling the adhesion interaction with a rigid substrate for elastic strings and rods. We produce conditions characterizing bonded and detached states as well as optimality properties with respect to loading and geometry. We show Euler equations for minimizers of the total energy outside self-contact and secondary contact points with the substrate.
Keywords: nonlinear elasticity., adhesion, Calculus of variations.
Mathematics Subject Classification: Primary: 49K10, 49Q10; 74G55 Secondary: 74B20; 74G6.
Citation: Francesco Maddalena, Danilo Percivale, Franco Tomarelli. Adhesive flexible material structures. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 553-574. doi: 10.3934/dcdsb.2012.17.553
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Francesco Maddalena Danilo Percivale Franco Tomarelli