## 5 Inverse Stress-Slip Law Identification  
The method utilised in this paper to inversely identify the stress-slip law of adhesive anchors is based on the Sequentially Linear Analysis (SLA) [23; 24], which was specifically developed to overcome the difficulty of snap-back behaviour [25; 26]. This method aims at identifying the stress-slip law; no assumptions are needed in terms of a tensile strength and a functional form since the procedure directly outputs the determined stress-slip relation. Figure 10a shows the mesh of the model used for the stress-slip law identification. Four-node quadrilateral axisymmetric finite elements and interface elements with a linear approximation of the displacement jump were utilised. The damage is assumed to be localised in zero-thickness cohesive interface elements [27]. The material outside the potential crack paths is assumed to be linear-elastic.  
Figure 10: Mesh of the numerical model (**a**), numerical fitting of the experimental result (**b**), and stress-slip law building process (**c**).  
Figure 9: Difference between load displacements curves having: unloaded end (dashed blue line), loaded end (red dash-dotted line), and stroke displacement (solid green line).  
In order to use this method, the experimentally measured load-displacement curve needs to be known. In each step, a reference load \(L\), which needs to be larger than the maximum load observed experimentally, is applied in the model. Since a sequence of linear (secant) steps is assumed, the response is a straight line. The critical load multiplier \(\lambda\) is then obtained as the minimum of (i) the intersection of the calculated and experimental load-displacement curves, the point A in Figure 10b, or (ii) the value by which the normal stress, induced in any integration point by the reference load \(L\), would have to be scaled to become equal to its current critical strength, given by the already determined TS diagram, point B in Figure 10c. Once the critical multiplier is determined, the load \(L\), stress, and strain fields are scaled. In case (i), the extension of stress-slip relation is recorded. Then, the stiffness in the critical element (element in which the minimum \(\lambda\) was found) is decreased, and the process continues to identify the next points in the stress-slip relation. Note that the initial stiffness of the computational model has to be the same as the experimentally measured stiffness. For more details regarding the inverse analysis, the interested reader is referred to [23; 24].  
The experimental data obtained for Cored specimens of bonded lengths 30 and 40 mm are further employed since no damage in concrete is assumed during the inverse analysis. Figure 11a shows the results of the inverse analysis compared with the one (a cored configuration specimen with 30 mm of embedment depth) of the experimentally obtained load-displacement curves. Furthermore, the smoothed interface stress-slip relations and their means are depicted in Figure 11b. The ideal stress-slip law would be the same for all concrete and geometrical parameters. The stress-slip laws obtained for the cored configuration, with an embedment depth of 30 mm (C-30 in Figure 11b) and 40 mm (C-40 in Figure 11b), are very similar to each other, especially in the post-peak part. Using the Cored configuration and controlling the test with the displacement at the unloaded end made it possible to obtain a precise softening behaviour.