# Experimental and Numerical Investigation of the Mesoscale Size Effect in Notched Woven Composites
## 1 Introduction  
Digital Image Correlation (DIC) is a well-established method to obtain full-field strain measurements during mechanical testing on the surfaces of material coupons and components. This measurement technique is often applied when performing tests on heterogeneous materials, where data with fine spatial resolution are needed, and for identifying local material properties [1]. Due to their intrinsic heterogeneity and anisotropy, stress concentration in composite materials is a complex problem, the study of which has greatly benefited from full-field techniques; previous works have used electronic speckle pattern interferometry [2], the grid method [3], and digital image correlation [4]. A common application of full-field measurements to this problem is for validating a finite element analysis, by comparing the measured strain field with the numerical results [2, 3]. The tensile strength of hole-notched composites is a classic example of size effect. In general, this effect is the dependence of mechanical behavior on the scale of the problem, typically observed in brittle and quasi-brittle materials [5]. Failure in these materials is determined by the presence of statistically distributed defects; the probability of a defect large enough to cause failure depends on the volume of the material [6]. Early studies handled this problem with semi-empirical models, aimed at predicting the decrease in failure properties at specimen or component level, with criteria such as the point stress or the average stress in a region [7]. These criteria remain useful due to their ease of application, and are still been extended to recently developed composites [8, 9, 10] or used tocheck the accuracy of newly developed numerical methods [11]. Later studies [3; 12; 13; 14] have focused on the damage and failure mechanisms with full-field measurements, often using the mixed experimental-numerical approach. In a unique approach, [PERSON] et al. used DIC and FEM to perform a stress analysis in a twill fabric composite under open-hole tension [15]. However, most studies have focused on unidirectional fiber composites. To the best of the authors' knowledge, there has not been research on using the capabilities of direct image correlation to systematically study size effect in widely used heterogeneous composite materials such as woven fabric composites. Another application of full-field strain measurements is the determination of parameters for material models, once again using mixed experimental-numerical methods [9; 16; 17; 18; 19]. These methods are usually a variant of the so-called Finite Element Model-Updating schemes. A Finite Element Model (FEM) is iteratively solved, and the resulting strains in output are compared to the experimental ones in an objective function, appropriately formulated to evaluate the discrepancy in the specific problem. At every step, an optimization algorithm updates the model with the values of the material parameters to be identified, attempting to minimize the objective function. When a pre-determined convergence criterion is reached, the resulting optimized parameters are retained [16]. This approach has already been used by [20] at a theoretical proof-of-concept level to identify material properties of microscale composite constituents. The objectives of the present work are two-fold. First, to develop a FEMU method capable of preserving the mesoscale material heterogeneity captured by DIC measurements. Second, to use this method to extend the understanding of size effect in heterogeneous fiber-reinforced composites from macroscale to mesoscale. This work, therefore, proposes a study of the hole size effect at local level, with full-field knowledge of the stress in the material obtained from the DIC-determined strain field. An innovative integrated experimental-numerical approach is developed, making use of image processing tools and DIC from modeling to validation.