## 1 Introduction  
Stitched composites, which can be fabricated by inserting high-strength threads in through thickness direction into the preforms prior to resin consolidation process, have been widely used in various engineering fields, especially in aerospace, marine, motor sport, military, and specialist construction, due to their excellent impact resistance and compression-after impact strength [1]. By now, there is a great deal of studies that are related to the mechanical properties of stitched composites, which are fundamentally important in design phases. [PERSON] proposed a finite element based unit cell model to simulate the in-plane and out-of-plane properties of the stitched composite laminates [2; 3]. Two modes of fracture toughness of laminates stitched with a one-sided stitching technique were plain experimentally studied [4]. [PERSON] experimentally studied the damage mechanisms of the stitched composites, which include tensile and compressive properties [1; 5; 6]. [PERSON] investigated the influence of the stitching pattern on the mechanical properties of glass fiber non-crimp fabric composites [7]. During their service, it is common that the stitched composite structures subjected to multiple forms of low-velocity impact loading conditions, such as objects falling down on composites and a flying fragment with low-velocity impact on composites, which will result in the immeasurable impact damage inside the material and reduce its service safety. Therefore, the failure and residual strength after low-velocity impact of stitched composites are very important in their service and maintenance phases. During the past several years, there are many studies on the response behavior of the stitched composites that suffered low-velocity impact. [PERSON] analyzed the effects of stitched density on low-velocity impact damage of cross-woven carbon fiber reinforced silicon carbide composites (two-dimensional (2D) C/SiCs) [8]. [PERSON] explored the effects of through-the-thickness on the Mode I inter-laminar fracture toughness and the performance of low-velocity of flax/epoxy composite laminates [9; 10; 11]. [PERSON] studied the impact response of the three-dimensional (3D) stitched sandwich composite [12]. [PERSON] studied the impact damage and subsequent damage propagation problems, and the effects of stitch density and stitch thread thickness of the stitched composites [13; 14; 15; 16; 17]. [PERSON] experimentally investigated the stitched laminates that were subjected to low-velocity impact and the consequent compression behaviors [18]. [PERSON] studied the impact and post impact behavior of stitched woven-knit hybrid composites by experiments [19]. [PERSON] used a Finite Element model that was based on the use of progressive damage schemes to simulate the effect of stitching on the delamination resistance of laminated composites subjected to low-velocity impact [20]. [PERSON] proposed a 3D dynamic finite-element model to simulate the damage development process and the influence factors of stitched laminates that were subjected to low-velocity impact [21]. However, the studies on the residual strength after low-velocity impact of stitched composites are still immature. Normally, there are three main equivalent methods used to predict the residual strength after low-velocity impact of composites. The first equivalent method is the softening inclusion method [22], in which the impact damage is equivalent to softening inclusion before the analysis of residual strength. The second equivalent method is the sub-layer buckling method [23], in which the impact damage is treated as the buckling of multiple sub-layers before the analysis of residual strength. The third equivalent method is the opening equivalence method [24], in which the impact damage is equivalent to the elliptical orifice panel before the analysis of residual strength. The above three equivalent methods are used widely due to their simplexes.