## 2 Materials and Methods  
The EMC-ASED criterion is applied here to a wide range of materials with different levels of nonlinear behavior. All tests were previously completed by the authors and reported in the literature (see the corresponding references), with different purposes than those pursued in this research, but the application of the EMC-ASED criterion analyses is here presented for first time (except for one case, as mentioned below), providing a comprehensive overview of the EMC-ASED potential as a fracture assessment tool. The materials and conditions are as follows:  
* PA6 (Durethan, Lanckess, Germany), see [7; 14] for details, with basically linear-elastic behaviour, even in the stress-strain curve of the tensile test, and fully linear behaviour in the presence of defects (for both crack and notch-type defects. SENB specimens). Tensile tests were performed according with [15], whereas fracture tests followed [16]. Both types of tests were completed at 20 \({}^{\circ}\)C, with the thickness and the width being 4 and 10 mm, respectively, in all cases. Before being tested, the specimens were dried in an oven at 100 \({}^{\circ}\)C, to avoid any trace of moisture. * SGFR-PA6 (Short Glass Fiber Reinforced PA6, see [7; 14; 15; 16] for details), with 5 wt.% of fibre content. The short fibres were oriented in the longitudinal direction of the specimens, had an average length of 300 \(\upmu\)m and a diameter of 10 \(\upmu\)m, with their tensile strength, elastic modulus and density being 3450 MPa, 72.5 GPa and 2.6 gr/cm\({}^{3}\), respectively. This material has a slightly nonlinear tensile curve, with the load-displacement curves of the fracture tests performed on SENB specimens (for both cracked and notched specimens) being fully linear. Again, the tests were completed at 20 \({}^{\circ}\)C, with the thickness and the width of the specimens being 4 and 10 mm, respectively. The specimens were also dried in an oven, at 10 \({}^{\circ}\)C to avoid any trace of moisture. * SGFR-PA6 (Short Glass Fiber Reinforced PA6, see [7; 14; 15; 16] for details), with 50 wt.% of fibre content. In this case, the tensile curve is clearly nonlinear, and the load-displacement curve of the fracture tests performed on SENB specimens is basically linear (fulfilling linear-elastic fracture mechanics conditions). The characteristics of the fibres and the specimens were analogous to those mentioned above. * PMMA (see [10; 15; 16; 17] for a wide description of experimental procedure, material properties and critical loads), with moderate nonlinear tensile curve and predominantly linear-elastic curves in notched conditions (with fully linear-elastic behaviour in cracked conditions. SENB specimens). Both tensile and fracture tests were performed at 20 \({}^{\circ}\)C in 4 mm thick specimens, with the width being 10 mm. * AI/075-T651 (TL orientation) with linear-elastic behaviour in cracked conditions (CT specimens), moderate nonlinear behaviour in tensile behaviour and intermediate situations in the presence of notches. Details (material properties and experimental critical loads) may be found in [12; 18], with the proper EMC-ASED criterion being applied in [13]. Tensile and fracture tests were performed by following [19] and [20], respectively. Fracture tests were performed at room temperature, with the width and the thickness of the specimens being 40 and 20 mm, respectively. * Steel S275 JR at \(-\)120 \({}^{\circ}\)C, operating within its Lower Shelf region (T\({}_{0}=-\)26 \({}^{\circ}\)C [21]) and, thus, presenting dominant linear-elastic behaviour in cracked conditions. However, it develops significant nonlinear behaviour in tensile tests. Thus, this material is in an analogous situation of AI/075T651. The basic fracture (CT specimens) and tensile characterisation of this material, and the corresponding experimental critical loads, may be consulted in [8; 19; 20; 22]. The thickness and the width of the fracture specimens were 25 and 50 mm, respectively.