Comput Mech DOI 10.1007/s00466-014-0991-7 ORIGINAL PAPER NURBS- and T-spline-based isogeometric cohesive zone modeling of interface debonding R. Dimitri · L. De Lorenzis · P. Wriggers · G. Zavarise Received: 30 October 2013 / Accepted: 27 January 2014 © Springer-Verlag Berlin Heidelberg 2014 Abstract Cohesive zone (CZ) models have long been used by the scientific community to analyze the progressive dam- age of materials and interfaces. In these models, non-linear relationships between tractions and relative displacements are assumed, which dictate both the work of separation per unit fracture surface and the peak stress that has to be reached for the crack formation. This contribution deals with isogeo- metric CZ modeling of interface debonding. The interface is discretized with generalized contact elements which account for both contact and cohesive debonding within a unified framework. The formulation is suitable for non-matching dis- cretizations of the interacting surfaces in presence of large deformations and large relative displacements. The isoge- ometric discretizations are based on non uniform rational B-splines as well as analysis-suitable T-splines enabling local refinement. Conventional Lagrange polynomial discretiza- tions are also used for comparison purposes. Some numerical examples demonstrate that the proposed formulation based on isogeometric analysis is a computationally accurate and efficient technology to solve challenging interface debonding problems in 2D and 3D. Keywords Cohesive zone modeling · Contact · Debonding · Isogeometric analysis · NURBS · T-splines R. Dimitri (B ) · G. Zavarise Dipartimento di Ingegneria dell’Innovazione, Università del Salento, Lecce, Italy e-mail: rossana.dimitri@unisalento.it L. De Lorenzis Institut für Angewandte Mechanik, Technische Universität Braunschweig, Braunschweig, Germany P. Wriggers Institut für Kontinuumsmechanik, Leibniz Universität Hannover, Hannover, Germany 1 Introduction Interfacial debonding often results in failure of laminated or generally jointed structures. Laminated structures are widely used e.g. for aerospace, civil and mechanical applications due to their good thermo-electro-mechanical performances combined with low weight and high toughness. The devel- opment of damage at the interfaces between laminae results in the formation and growth of interlaminar cracks through a non-linear and irreversible process which is known as debonding. A widely used modeling approach to simulate the onset and the propagation of debonding is represented by cohesive zone (CZ) models. These interpret the progressive decay of the cohesive forces and the formation of traction-free sur- faces at a bi-material interface or within a material or at the interlaminar interface in a laminated structure, provided that the path of the potential crack is known a priori [2, 43]. CZ models were originally introduced by [7, 22] as an alternative approach to singularity driven fracture mechanics and have been widely used to describe the fracture process in a number of materials, such as ductile [32, 33, 54, 55, 59] or composite materials [3, 4, 9, 11, 37, 43]. The numerical application of CZ models for debonding problems within finite element frameworks, however, has shown some difficulties because of the localization of the fracture process zone (FPZ) ahead of the crack tip. Unless a sufficiently fine mesh discretizes the process zone of a cohe- sive crack, local softening in the interface elements results in a sudden release of the elastic strain energy stored in the surrounding bulk material. This causes a sequence of arti- ficial (non physical) snap-through or snap-back branches in the global load-deflection response, which leads to failure of a standard Newton–Raphson iterative scheme [1]. The sim- plest strategy to circumvent this problem consists in reducing 123