Effect of in-plane deformation on the cohesive failure of heterogeneous adhesives Alejandro M. Aragón a , Soheil Soghrati b , Philippe H. Geubelle a,n a Aerospace Engineering Department, University of Illinois,104 South Wright Street, Urbana, IL 61801, USA b Civil and Environmental Engineering Department, University of Illinois, 205 North Mathews Avenue, Urbana, IL 61801, USA article info Article history: Received 25 May 2012 Received in revised form 25 February 2013 Accepted 11 March 2013 Available online 29 March 2013 Keywords: Cohesive modeling Micro-to-macro analysis Generalized/extended finite element method Heterogeneous adhesives Homogenization Viscous damage model abstract The effect of in-plane deformations on the failure response of heterogeneous adhesives with a second phase of spherical elastic particles is investigated numerically using a 3D cohesive framework. The methodology includes a new interface-enriched generalized finite element scheme for the solution of structural problems with weak discontinuities, allowing for the efficient and accurate prediction of the stress and displacement fields in the adhesive based on finite element meshes that do not conform to the heterogeneities. A rate-dependent isotropic failure model is adopted to capture the failure in the matrix, while the stiff inclusions are assumed to be linearly elastic. Cohesive failure envelopes resulting from the micro-to-macro analysis are extracted for a wide variety of failure mode conditions. A study of 1611the impact of in-plane tensile and shear strains on the macroscopic failure response under tensile (mode I) loading is also presented. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction Heterogeneities are often introduced in adhesive layers to improve their failure properties and/or to provide additional functionalities. Zhao et al. (2000) showed that adding a glass fiber additive to an epoxy-based adhesive stabilized crack propagation in double cantilever beam (DCB) specimens. White et al. (2001) explored the autonomic healing capabilities of polymers containing a micro-encapsulated healing agent, and showed that up to 75% of the virgin fracture toughness could be recovered. Kinloch (2003) showed that adding rubber particles as a second phase in polymeric adhesives could greatly improve their fracture toughness. Dean et al. (2004) presented a numerical model for the study of these rubber-toughened polymers, considering the effect of rubber particle cavitation. Meguid and Sun (2004) showed that carbon nanotubes and alumina powder fillers in an epoxy adhesive improve up to certain point the debonding properties of the interface. Finally, Zhao and Hoa (2007) studied the effect of particle sizes in the toughening response of epoxy polymers, and provided a fracture model for their characterization. In all these and other related cases, adding heterogeneities in the adhesive layer leads to complex failure processes, including cavitation (Dean et al., 2004), particle or fiber debonding (Kawaguchi and Pearson, 2003), micro-crack nucleation (Guarino et al., 1999), propagation and coalescence (Ramanathan et al., 1997; Tang and Kou, 1998). By collapsing the thin adhesive layer to a surface, cohesive modeling is a natural approach to analyze the failure response of bonded structures. Various cohesive models have been proposed over the past two decades based on a wide range Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jmps Journal of the Mechanics and Physics of Solids 0022-5096/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jmps.2013.03.003 n Corresponding author. Tel.: +1 217 244 7648; fax: +1 217 244 0720. E-mail addresses: alejandro.aragon@fulbrightmail.org (A.M. Aragón), ssoghra2@illinois.edu (S. Soghrati), geubelle@illinois.edu (P.H. Geubelle). Journal of the Mechanics and Physics of Solids 61 (2013) 1600–1611