In this work, a finite-element formulation for modeling mixed-mode delamination in layered structures, consisting of two-node Timoshenko beam finite elements with quadratic linked interpolation and corresponding 4-node interface elements is presented and compared to a more common approach where linear Lagrange interpolation is used. The principal novelty of the proposed approach is that the vertical displacements of the beam elements, as well as the transversal relative displacements of the interface elements, are interpolated using a quadratic linked interpolation that also takes into account the nodal cross-sectional rotations of the beam elements. At the same time, the axial displacements and cross-sectional rotations are interpolated using linear Lagrange polynomials. A bilinear cohesive zone model is embedded in the interface finite elements for delamination modes I and II. Numerical analyses based on the examples from the literature with metal joints show that the formulation with quadratic linked interpolation improves the convergence and robustness of the solution with respect to the approach with linear interpolation. On the other hand, in case of composites with stiff adhesives this formulation exhibits a peculiar behavior with spurious oscillations of the normal interface tractions that leads to a poor performance in mode-I and mixed-mode tests. This problem can be easily solved by canceling the quadratic term in the interpolation function and using the standard Lagrange interpolation in such cases.

A fast and simple finite element model is presented in this paper to simulate the crack propagation in notched beam structures with two layers and one interface medium in Mode I delamination. The truss elements from FEAP element library are endowed with a user material law describing the bilinear cohesive zone model (CZM) with the material unloading path defined by embedding a history variable in the response. The layer is modelled with linear elastic Timoshenko beam elements. The method is used for damage growth and damage propagation simulations in interfaces with both ductile and brittle materials. The method is robust for ductile interfaces, but for brittle interfaces more specific numerical techniques are required. The results are evaluated using available analytical and numerical solutions and a good agreement is achieved.

Fracture resistance of structural adhesive joints is key for their application in the industry. Mode-I adhesive joint delamination is the most severe type of fracture and the possibility of this outcome should be avoided whenever possible. In this work we are investigating mode-I delamination of plate-like specimens, where the width is comparable to the length. In such cases anticlastic bending of the plates takes place on the debonded part and the crack front is a curve rather than a straight line. We model the interface by means of discrete non-linear truss elements with embedded exponential traction-separation law [1]. Such choice is justified because in this test, only pure mode-I (opening) displacements occur at the interface, which in our case will cause axial elongation of the truss elements. The plates are modelled using 4-node plate finite elements derived by the assumed shear strain approach that pass the general constant-bending patch test [2]. Cohesive-zone interface parameter identification is performed by a direct method (J-integral) [3] and by virtual experiments regression. Numerical tests have been performed and the exponential cohesive-zone interface model compared against the bi-linear in terms of precision, robustness and computing time. The results confirm the experimentally observed behaviour with anticlastic bending of the arms and the curved crack front.