Although the majority of computational works in the field employ the primal, displacement-based, variant of the finite element method (FEM), its application to imperfectly bonded assemblies suffers from specific difficulties. In particular, an interface is introduced into the model in the form of an inelastic cohesive element, characterized by a finite value of interfacial stiffness. In order to correctly reproduce the perfect interfaces, the stiffness needs to be very large, which manifests in spurious traction oscillations and hence an inaccurate prediction of damage initiation. A low stiffness value, on the other hand, allows for mutual interpenetration of individual constituents, resulting in a non-physical distribution of mechanical fields. Furthermore, it is now well-understood that an efficient treatment of contact among adjacent domains, even for the frictionless approximation, is relatively difficult in the framework of primal FEM techniques.

Our approach attempts to eliminate the above mentioned problems. It is a rate-independent energy-based model which uses the principles of isotropic damage mechanics to model the evolution of interfacial damage [1]. A mixed-mode constitutive model with linear softening is implemented.

The continuous formulation is converted to the time-incremental problem, which is subsequently discretized using the FEM method. By adopting the alternate minimization strategy due to Bourdin [2], the problem is converted into the dual form, expressed in terms of interfacial forces that enforce the displacement compatibility. For the perfect bonding case, the resulting system is equivalent to the original finite element tearing and interconnecting (FETI) method due to Farhat and Roux [3]. For imperfect interfaces, we recover the modified FETI equations first proposed by Kruis and Bittnar [4], which are complemented with a simple projection technique to ensure the frictionless contact conditions. In both cases, the system is well-suited for the treatment using the preconditioned conjugate gradient algorithm.

As a proof-of-concept for this approach, two numerical examples of two-layered laminated beams failing due to mode-II and mixed-mode delaminations were successfully validated against available experimental data.

1

M. Kocvara, A. Mielke, T. Roubicek, "A Rate-Independent Approach to the Delamination Problem", Mathematics and Mechanics of Solids, 11(4), 423-447, 2006. doi:10.1177/1081286505046482

2

B. Bourdin, "Numerical implementation of the variational formulation for quasi-static brittle fracture", Interfaces and Free Boundaries, 9(3), 411-430, 2007. doi:10.4171/IFB/171

3

C. Farhat, F.X. Roux, "A method of finite element tearing and interconnecting and its parallel solution algorithm", International Journal for Numerical Methods in Engineering, 32(6), 1205-1227, 1991. doi:10.1002/nme.1620320604

4

J. Kruis, Z. Bittnar, "Reinforcement-Matrix Interaction Modeled by FETI Method", in "Domain Decomposition Methods in Science and Engineering XVII", Springer, 567-573, 2008. doi:10.1007/978-3-540-75199-1_71

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