# Experimental and Numerical Investigation of the Mesoscale Size Effect in Notched Woven Composites
## 4 Conclusions  
In order to study the complex stress field from open hole concentration in a twill composite material, a 2D shell model that describes the material at tow level was developed in this work. The model was found to be effective in representing the complex stress and strain distributions in a woven composite material subject to stress concentration. Thanks to its low computational cost, the model was well-suited to be implemented in parameter optimization and FEMU schemes. An advantage over conventional multiscale methods is that a mesoscale-level stress analysis can be carried out without requiring knowledge of microscale-level material properties. On the contrary, only coupon-level tests need to be performed, fully exploiting the spatial resolution of DIC instead of using smaller-scale tests to obtain a higher level of detail.  
A prerequisite for good elastic parameter calibration was found to be a proper separation of the horizontal and vertical tows in the two materials. If this is not achieved, the longitudinal and transverse elastic moduli tend towards an average--the modulus of the homogeneous material. The new approach proposed builds the numerical model from an image of the real specimen, directly captured on the test fixture by the same cameras used for DIC. The spatial correspondence of empirically and numerically determined strain fields is therefore ensured by design, as highlighted in Figure 1. This technique may be handily applied to the numerical study of any problem where considering mesoscale mate  
Figure 10: The two effects on stress ratios for increasing hole diameters. (**a**) Curves are the local tensile strength \(S_{1}\) versus unnotched strength \(S_{1}^{0}\), remote stress versus maximum stress, their superposed effect, and the macro-level trend of ultimate nominal tensile stress; (**b**) close-up of the last two curves.  
rial heterogeneity in woven fiber composites is necessary, such as to analyze the effect ofply shift on open-hole stress concentration.  
A curve analogous to the reduction in nominal tensile strength was determined from the tow-level stresses (Figure 10b). The reduction was interpreted as the combination of two mesoscale-level effects: stress concentration, which increases stress in a volume of material with dimensions comparable to the characteristic size of the notch, and stress localization, which dramatically increases the stress in a small volume of material close to the hole. Due to the size effect, the consequences of these two phenomena on material strength are diametrically opposed. The larger affected volume decreases material strength, which can be interpreted as the result of an increased probability of encountering a pre-existing defect in the material large enough to cause failure at the local stress level. On the other hand, stress localization radically increases stress in a very small volume close to the notch, leading to an improvement in local material strength, which favorably scales with hole size.  
The combination of these two effects results in a macroscale-level behavior, which is consistent with traditional semi-empiric models like the point stress criterion. The change in slope of the nominal tensile strength versus notch size curve was interpreted as a result of different scaling effects on the detrimental stress concentration and beneficial strain localization effects, with the latter effect being amplified for increasing hole diameters.  
Conceptualization, A.F.; methodology, A.F., C.B.N. and A.C.; investigation, A.F. and R.C.; writing--original draft preparation, A.F.; writing--review and editing, A.F., C.B.N., A.C., D.S.P. and G.B.; supervision, D.S.P. and G.B. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.