A mathematical model for a pseudo-plastic welding joint

Oana Iosifescu (1) , Pongpol Juntharee (2) , Christian Licht (2) , Gérard Michaille (1, 3)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 M3 - Modélisation Mathématique en Mécanique
3 UNIMES - Université de Nîmes

An elementary situation in welding involves the perfect assembly of two adherents and a strong adhesive occupying a thin layer. The bulk energy density of the hyperelastic adherents grows superlinearly while that of the pseudo-plastic adhesive grows linearly with a stiffness of the order of the inverse of its thickness epsilon. We propose a simplified but accurate model by studying the asymptotic behavior, when epsilon goes to zero, through variational convergence methods: at the limit, the intermediate layer is replaced by a pseudo-plastic interface which allows cracks to appear.

Mots clés: elasticity; energy; gamma-convergence; welding joint

Domaines: Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]

Oana Iosifescu, Pongpol Juntharee, Christian Licht, Gérard Michaille. A mathematical model for a pseudo-plastic welding joint. Analysis and Applications, 2009, 7, pp.243-267. ⟨10.1142/S0219530509001372⟩. ⟨hal-00574669⟩