## 1 Introduction  
Woven fabrics and their composites have been widely used in engineering due to the outstanding mechanical performance [1; 2]. Recently, wet compression molding of woven composites has attracted more attention because of its high efficiency in the manufacturing process [3]. The shear deformation, the dominant mode of a woven fabric in the forming process, is closely related to the yarn reorientation which is critical for the mechanical properties of a composite. It is noted that a blank holder is commonly used to provide a tensile force in a preforming process so that wrinkle onset can be postponed [4]. Moreover, the shear stiffness of a woven fabric can be significantly affected by applying a tensile force along yarns [5; 6]. Thus, it is critical to establish a model that can account for tension-shear coupling for the large shear deformation of a woven fabric. Approaches to investigate the shear behavior of a woven fabric can be classified into three categories [7]: experimental testing, numerical simulation, and analytical modeling. In the first category, many kinds of experimental configurations have been reported [8; 9]. For the second category, numerical simulations of woven fabrics have also been widely investigated, for example, [PERSON] et al. [10], [PERSON] et al. [11], and [PERSON] et al. [12]. Experiments are essential for the understanding of mechanical properties of materials. However, it is too expensive to obtain all the properties of a material under various load cases only upon experiments. Conversely, numerical simulations and analytical models can predict mechanical behaviors of a material based on some basic test results, which significantly accelerates the application process of a material. Furthermore, compared with numerical methods, analytical models are superior in computational efficiency and understanding of physical mechanism. Thus, this work mainly focuses on analytical models. Analytical models for shear behavior of woven fabrics can be split into two categories: kinematic models and mechanical models. The kinematic models [13; 14] are succinct, but they cannot account for the effect of mechanical behaviors of yarns on the deformation of woven fabrics. To tackle this problem, mechanical models were developed. Mechanical models can be roughly divided into two families: continuum models and discrete models. With respect to the former family, [PERSON] et al. [15] proposed a continuum mechanics model for woven fabrics, where the bending, tension, and shear behaviors of yarns are modeled by virtual springs. The parameters of the virtual springs are obtained from experiments directly, meaning that the coupling between tension and shear properties is only involved implicitly. [PERSON] et al. [16] developed a continuum material model for woven fabrics, where the shear and tension stresses are decoupled by using a non-orthogonal coordinate system. However, the interaction between shear and tension properties still exists but is not considered. [PERSON] et al. [17] proposed an anisotropic hyper-elastic model for the preforming process of woven fabrics, where the tension-shear coupling effect was studied. Nevertheless, the coupling factors are directly obtained by fitting experimental data, meaning that the coupling mechanism is not fully revealed. In the range of discrete models, [PERSON] and [PERSON] [18] presented an analytical model to investigate the tension-shear coupling in woven fabrics. In their work, the effect of transverse in-plane compression of yarns on the shear property is considered indirectly by the friction dissipation energy, which may underestimate its contribution. [PERSON] et al. [19] pointed out that the shear dissipation energy can be divided into three parts: yarn sliding, yarn compression, and yarn rotation. However, no tensile forces along yarns were studied in the work of [PERSON] et al. [19]. [PERSON] et al.