## 1 Introduction
Through experimental and numerical investigations, [PERSON] [16] concluded that defects like fiber buckling and wrinkling are caused by inter-ply shear stress induced during shape forming. To minimize this inter-ply shear stress, adjacent plies have to easily slip over one another. Research findings depict that during composite forming, inter-ply slippage relaxes inter-ply shear stress, thereby reducing fiber buckling and wrinkling [17; 18]. [PERSON] et al. [19] conducted experimental analysis about the effects of blank temperature, pressure load, and ply pullout speed on the inter-ply shear properties of a glass/PPcomposite blank and drew the conclusion that shear stress increases for lower temperatures and reduces for decreasing ply pullout speed. [PERSON] et al. [20] investigated plausible causes of wrinkling defects during forming. According to their report, the relative fiber orientation angle of adjacent plies has a remarkable effect on wrinkling development. [PERSON] et al. [21] reported the mechanism through which wrinkle is incurred during composite forming. In their report, it was shown that the incursion of wrinkles is also related to in-plane fiber misalignment. [PERSON] et al. [22] presented a technique for determining the forming parameters such as temperature, forming speed, and pressure required to minimize inter-ply shear resistance. [PERSON] et al. [23] conducted a comparative study on uni-directional polyetheretherketone (UD/PEEK) and 8-harness satin polyphenylene sulfide (8 HS/PPS) composite materials and concluded that the materials with higher inter-ply shear stress cause severe wrinkling during doubly-curved structure forming. However, due to multiple forming parameters such as the relative fiber orientation angle of adjacent plies, blank temperature, pressure load, and inter-ply slip velocity, it is very complex to determine how and to what extent inter-ply shear stress should be reduced to achieve defect-free products. [PERSON] et al. [24], in their one-dimensional ply pullout experiment, listed out forming speed, blank temperature, and pressure load as the parameters influencing inter-ply slippage. [PERSON] et al. [25], in an attempt to achieve wrinkle-free forming of a composite laminate, reported that the relative fiber orientation angle of adjacent plies has a significant influence on the formability of composite structure. Performing physical experiment for the ranges of these forming parameters is economically costly and time consuming. To ease this costly task, developing a surrogate model that emulates the functional dependency of inter-ply shear stress on forming parameters is vital. Implementing surrogate model based analysis in composite materials becomes a disparate alternative to tedious physical experiments. This paradigm shift is apparent in many of recently published papers [26; 27; 28; 29]. [PERSON] et al. [26] applied a surrogate model to the cure process of composite laminate so as to remarkably reduce the computational time. [PERSON] et al. [27] also implemented a surrogate model to approximate the mechanical response of composite laminate, thereby demonstrating the computational efficiency and accuracy of the surrogate model. [PERSON] et al. [28] employed a surrogate model to the meso-scale mechanical response of a composite structure containing wrinkle defects. In an attempt to determine the performance of defective composite structures and their failure modes, [PERSON] et al. [29] utilized a surrogate model. Hence, in this study, the mathematical model of inter-ply shear stress, as a function of the aforementioned forming parameters, was formulated and analyzed. The formulation of this mathematical model is based on the surrogate modeling technique. The surrogate model construction and validation procedure taken in this study are as follows: In Section 2, the parameters' specification and their random combination techniques are described. Based on the random combination, the finite element modeling of the composite sheet is explained.