# Impact Fracture and Fragmentation of Glass via the 3D Combined Finite-Discrete Element Method +
## 1 Introduction  
It is a well-known fact that a great number of traffic accidents result in windshield breakage that unduly causes great harm to automobile to both passengers and pedestrians. Due to the consequences of these accidents, a forensics approach was developed wherein analysts can use windshield fracture patterns to reconstruct some aspects of accidents [1]. Needless to say, the study of automobile glass impact fracture mechanisms is of theoretical and practical importance to the automobile industry as it affects passenger protection, passive safety measures, and traffic accident reconstruction. Current automobile windshield safety analysis standards heavily rely upon both experimental and analytical approaches to meet Federal guidelines for breakage standards. Due to computational mechanic's advancements, numerical methods offer an alternative approach that is proving to be effective for the study of automobile glass fracture. Given the critical nature and need for computational methods that can effectively capture glass breakage many efforts have been undertaken. [PERSON] et al. simulated the impact of a sphere into a glass plate and the behavior of a windscreen during a roof crash via the finite element method (FEM), where failed elements were deleted from the calculation after the strainwas greater than a pre-set failure strain [2]. [PERSON] et al. presented a computational technique for the modeling of laminated glass using an explicit finite element code. In their work, different material models, element techniques, and the influence of the mesh were discussed [3]. [PERSON] et al. used the extended finite element method (XFEM) to characterize radial crack and circumferential crack propagations of windshield cracking under low-speed impacts [4]. [PERSON] et al. proposed a failure criterion for laminated glass under impact loading [5]. The criterion was implemented into a commercial finite element code and was validated by comparing against experiments. [PERSON] et al. simulated the mechanical behavior of a windshield-laminated glass given the impact of a pedestrian's head using an element deletion approach implemented in a commercial finite element code [6]. Different finite element models were tested and the numerical results were verified against experimental data. [PERSON] et al. utilized a cohesive zone model based computational framework for the modeling of impact fracture on automotive laminated glass [7]. [PERSON] et al. investigated radial multi-cracking phenomenon in laminated glass subject to dynamic loading using XFEM [8]. [PERSON] et al. modeled automotive windshield impact fracture behavior via an intrinsic cohesive approach [9]. The numerical results were compared against the element deletion method and experimental observations. In all the above mentioned work, the simulations were conducted in the context of the finite element method (FEM). In the meantime, computational mechanics of discontinuum approaches have also been extensively utilized to simulate the glass impact fracture processes. [PERSON] et al. simulated the dynamic fracture behavior of laminated glass using a 2D discrete element method (DEM) implementation, where both the glass and polyvinyl butyral (PVB) film were divided into identical circular discrete elements [10; 11]. [PERSON] et al. investigated the impact fracture behavior of automobile glasses using a 3D particle-based DEM, wherein the advantage of laminated glass in passenger safety was thoroughly demonstrated [12]. In order to simulate the large deformation of the PVB layer in laminated glass, [PERSON] and [PERSON] developed a numerical framework that combined particle-based DEM and explicit FEM, where the mechanical response accounted for glass fracture by using DEM while the large deformation of the PVB was modeled using FEM [13].