# Impact Fracture and Fragmentation of Glass via the 3D Combined Finite-Discrete Element Method +
## 2 Overview of the Combined Finite-Discrete Element Method
### Continua-Discontinua Transition  
In FDEM, cohesive zone models are usually used to simulate the fracture and fragmentation in solids [20]. In the cohesive zone models, the mechanical response of the solid material is decomposed into a solid matrix part and an interfacial part that represents multi-scale processes taking place behind the fracture front (e.g., breaking of bonds between grains). In the solid matrix part, the finite element method along with constitutive laws (e.g., elastic, plastic, continuum damage models) are used to simulate the solid's bulk deformation, while fracture and fragmentation are handled in the interfacial part via cohesive elements or cohesive points that are assumed to coincide with the finite element boundary [20]. The mechanical response of the cohesive elements/points are dominated by the so-called \"traction-separation\" constitutive law. To control when and how the cohesive elements/points are introduced into the system, different cohesive zone models have been developed and implemented in FDEM.  
One group of cohesive zone models is called the intrinsic cohesive zone model [35]. In this model, the cohesive elements/points are inserted in advance between two adjacent elements to connect those two originally adjacent elements. In order to enforce the continuity of the material, \"strain-hardening\" with a sufficiently large initial slope must be introduced in the \"traction-separation\" curve, which reduces the stiffness of the system artificially. Another group of cohesive zone models are called the extrinsic cohesive zone model [36]. In the extrinsic models, the cohesive elements are dynamically inserted into the system according to the stress state. The extrinsic models avoid the artificial compliance seen in the intrinsic model approach, however they may end up being \"time-discontinuous\" at the point when the material is transitioning from continua to discontinua.  
In the earlier versions of FDEM, the combined single smeared crack model [37; 38], which belongs to the family of intrinsic cohesive zone models, was developed for the simulation of fracture and fragmentation. Originally, the combined single smeared crack model was aimed at mode I loaded cracks only and it was implemented in 2D [37]. In 2010, that crack model was extended to 3D for both mode I and mode II fractures and this extended 3D crack model was implemented in the open-source FDEM code Y-code [14; 39]. Since then, with the open distribution of Y-code, this 3D crack model has been widely used in different research groups for different topics.  
The latest version of FDEM features a unified cohesive zone model [40]. Similar to the traditional extrinsic cohesive zone model, the unified cohesive zone model dynamically inserts the cohesive element into the system based on the local stress state. However, the transition from continua to discontinua is smoothly achieved and as such, the unified cohesive zone model eliminates the \"time-discontinuous\" issue. Moreover, within the unified cohesive zone model the point of transition from continua to discontinua is controllable. Both the intrinsic cohesive zone model and enhanced extrinsic cohesive model can be retrieved from the unified model through the introduction of a threshold parameter [40]. Thus, the unified cohesive zone model, which unifies the intrinsic and extrinsic cohesive zone models, has all the advantages of both approaches while overcoming most of the disadvantage of existing cohesive zone models [40].