## 1 Introduction  
Composite laminates are widely used as a structural material as they are lightweight and bear high loads. Slender composite laminates commonly fail under delamination which has been widely studied, and many analytical theories have been developed to understand this complex phenomenon [1, 2]. The theories focus primarily on the energy release rate (ERR), the energy that is required for a unit length of crack to propagate. The analytical theories are based on different assumptions that are made to simplify the 3D problem where delamination takes place on a plane (2D delamination). Here, the crack propagates between two sub-laminates (upper and lower part of the composite laminate) and can be simplified by transforming the 2D delamination problem into a 1D problem [3]. In particular, the two sub-laminates are considered as composite beams, and the crack propagates on a single line between the two sub-beams. Beam kinematic equations are derived using the conventional plate theory (CLT), where shear effects are not considered [4, 5], or the first-order shear deformation theory (FSDT), where shear effects are considered. Both CLT and FSDT are formulated under the plane strain or plane stress assumptions. The 1D delamination problem is the most common case found in the literature and many theories have been presented considering different interface boundary conditions [6], i.e., different assumptions for the continuity of displacements and rotations of the bonded surface between the two sub-beams. The most straightforward case is when the interface between the two sub-beams is considered to be totally rigid [7]. Here, both the relative displacements and the relative rotations at the crack tip are zero. This case is mentioned as the conventional composite beam theory or rigid joint model [8]. Even though the assumption of zero relative displacements and rotations simplifies significantly the formulation, it can highly influence the predictions of the ERR [9; 10] and should be avoided. The shear deformable theory (or semi-rigid joint model) is a generalization of the conventional composite beam theory and is able to capture the crack-tip rotations [11]. This model considers that only the relative displacements at the crack tip are zero, and the relative rotations are released. This considerably improves the predictions of the ERR and has been extensively used [3; 12; 13; 14]. However, when local phenomena are considered, the imposition of zero relative displacements can lead to inaccuracies regarding the distribution of stresses close to the crack tip [15]. This problem is addressed by the interface deformable theory (or flexible joint model) [15], where both relative displacements and rotations are allowed between the two sub-beams. The flexible joint model is a general version of the \"beams on elastic foundation\" model developed for symmetric beams [9; 16; 17]. The three aforementioned theories are initially formulated under generic loading conditions and then expressed for specific delamination tests. The boundary conditions that are considered for delamination tests express the forces that are applied on each sub-beam. For mode I opening tests, such as the Double Cantilever Beam (DCB) [18] test, only external loads are considered since there is no contact between the two plates. However, for mode II in-plane shear tests, such as the End-Notched Flexure (ENF) [19] and the End-Loaded Split (ELS) [20] test, a contact force appears between the two sub-beams and should be considered in the formulation. The effects of this force on the ERR were investigated in the work of [PERSON] [21]. The approach that [PERSON] followed for the estimation of the contact force was based on the rigid joint model and was specifically applied for a three-layered laminate where the upper part and the lower part were considered to be individually symmetric. Residual thermal stresses were considered in the formulation but extension-bending coupling phenomena and shear stresses were neglected.