European Journal of Mechanics A/Solids 27 (2008) 532–547 Aspects of bifurcation in an isotropic elastic continuum with orthotropic inelastic interface J. Utzinger a,∗ , A. Menzel b,c , P. Steinmann d , A. Benallal e a Lehrstuhl für Technische Mechanik, TU Kaiserslautern, P.O.Box 3049, D-67653 Kaiserslautern, Germany b FachgebietMechanik, insbesondere Maschinendynamik, TU Dortmund, Leonhard-Euler-Str. 5, D-44227 Dortmund, Germany c Division of Solid Mechanics, Lund University, P.O. Box 118, SE-22100 Lund, Sweden d Lehrstuhl für Technische Mechanik, Universität Erlangen-Nürnberg, Egerlandstraße 5, D-91058 Erlangen, Germany e LMT-Cachan, ENS de Cachan/CNRS/Université Paris 6, 61 Avenue du Président Wilson, 94235 Cachan Cedex, France Received 21 June 2007; accepted 11 November 2007 Available online 4 March 2008 Abstract This manuscript investigates possible bifurcations into stationary wave-type solutions in situations where an isotropic elastic bulk is bonded by a non-coherent orthotropic interface to a rigid substrate. The interface is characterised by a traction–separation- law capturing elastic and inelastic material behaviour. Based on an ansatz for stationary waves at the surface of the bulk being connected to the interface, a bifurcation condition is elaborated. Thereby, the orthotropy of the interface is taken into account by considering the fully three-dimensional elastic half space and allowing for arbitrary orientations of the stationary wave-type solutions with respect to the interface co-ordinate system. The bifurcation condition is studied under the assumption of prevailing ellipticity in the bulk for a number of different examples. The results are graphically explored.  2007 Elsevier Masson SAS. All rights reserved. Keywords: Interface; Bifurcation; Boundary value problem 1. Introduction In the mesomechanical modelling of composites, interfaces between different layers of materials play a de- cisive role (Schellekens, 1992; Miehe and Schröder, 1994; Larsson and Jansson, 2002; Willam et al., 2004; Steinmann and Häsner, 2005; Utzinger et al., 2007). In particular if non-coherent interfaces are allowed for, i.e. in- terfacial displacement jumps can occur, the modelling of an appropriate traction–separation-law is a major challenge. It may even be reasonable to project all non-linearities and inelasticities of a problem into the interface law by this type of modelling. As an example, the modelling of a laminar welded specimen in a shear tension test, see Utzinger et al. (2007), is suggested. As general rule, well-established constitutive laws for the bulk, see, e.g., Lemaitre (1994), Lemaitre et al. (1994), Simo and Huges (1998), can be adapted for the constitutive modelling of interfaces. Apart from * Corresponding author. Tel.: +49 631 205 3855; fax: +49 631 205 2128. E-mail addresses: utzinger@rhrk.uni-kl.de (J. Utzinger), andreas.menzel@udo.edu (A. Menzel), andreas.menzel@solid.lth.se (A. Menzel), steinmann@ltm.uni-erlangen.de (P. Steinmann), benallal@lmt.ens-cachan.fr (A. Benallal). 0997-7538/$ – see front matter  2007 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.euromechsol.2007.11.001