## 2 Mechanics Model
### Interaction between Delamination and Intralaminar Failure  
In this work, intralaminar failure is analyzed by the CDM model, which has the capability to predict the path of matrix crack propagation reliably, while interlaminar failure is analyzed by CZM. In general, the use of CZM together with CDM can lead to less accurate solutions for the failure of composite laminates, for it cannot capture the load transfer between cohesive interfaces and the solid elements when matrix cracks reach an interface [37; 49]. Many research works pointed out these problems in theoretical analysis or simulation results by using CDM and CZM together. To overcome the difficulties in the simulation of the interaction between failure mechanisms, researchers proposed fully-three-dimensional CDM models that represent the delamination, as well as intralaminar failure [15; 49; 56]. However, these approaches, for which delamination is considered to be same as a matrix cracking and is simulated by CDM, could not eliminate the influence of element size through-thickness on the numerical simulation result for delamination growth. The approaches, which only use CZM to represent both intralaminar and interlaminar failure mechanisms, were proposed by [3; 35; 57], but it is impossible for CZM to describe the non-prescribed matrix crack path in composites. As the matrix crack path is not known a priori in the simulation for general engineering applications, these approaches are not recommended to solve the practical problems. In [58], the approach using spring elements was also proposed to incorporate the interaction between the matrix cracks and the delamination. A significant energy interaction exists between interfacial delamination and intralaminar failure for the FE model. Once matrix fracture occurs at an element, the element has lost its cohesive traction and can be expressed as a state only with fiber. The interlaminar element adjacent to this intralaminar element can be considered as delamination failure, because there is no cohesive traction of this interlaminar element after that. When the matrix is damaged at the intralaminar element adjacent to the interlaminar element, it is used for tension and shear damage at the adjacent interface element. It shows that the energy release process in the intralaminar element is not independent of the adjacent interlaminar element. Therefore, it is necessary to set the relationship of the energy interaction between the adjacent solid element and the interface element. If this relationship of the energy interaction is not set, the fractured or damaged elements cannot induce the interface element damage. For this reason, it was difficult to predict the correct path of multicracks before. When the element adjacent to CZE is damaged, the critical energy release rate of CZE suggested in Equation (14) is reduced with the following linear relationship for the finite element modeling. \[G_{Ic}^{d}=G_{Ic}[1-\max\{D_{1},D_{2}\}],\ G_{IIc}^{d}=G_{IIc}[1-\max\{D_{1},D_ {2}\}] \tag{15}\]  
where \(G_{Ic}^{d}\), \(G_{IIc}^{d}\) are the Mode I and II critical energy release rates of CZE, respectively after intralaminar damage, and \(D_{1}\), \(D_{2}\) are the matrix damage variables at two intralaminar elements adjacent to a given CZE, which are given by Equation (5). This means that critical energy release rates of CZEs are not independent of matrix damage of the adjacent solid elements and vary with their damage variable, that is the CZEs are easily damaged with a high matrix damage level. Studies to describe the close relationship between delamination and intralaminar crack were also proposed in the past. [PERSON] et al. [33] investigated the relationship between the rate of delamination and the crack density in the mesomodel defined by the ply level by employing the stochastic method and suggested that the rate of delamination increases as the crack density increases.