# Study on Dynamic Mechanical Properties and Failure Pattern of Thin-Layered Schist
## 4 Numerical Simulation  
### Model and Parameters  
Schist is a typical metamorphic rock; the rock mass is relatively broken, and it is difficult to take a relatively complete stone, resulting in a large dispersion of the laboratory test analysis results [28]. In order to further analyze the dynamic mechanical properties and failure pattern of thin-layered schist and discuss the influence of the schistity angle and schistity spacing, the SHPB test is numerically simulated using ANSYS/LS-DYNA 18.0. The simulation model comprises four components corresponding to the actual test system:--the bullet, incident bar, transmission bar, and specimen (Figure 8)--all of which are represented by the three-dimensional solid unit, SOLID164. The model is meshed by the mapping method. The model of the bullet, incident bar, and transmission bar is, respectively, divided into 40, 100 and 80 parts along the radial direction. The specimen model grid was divided into 30 parts to ensure the damage effect of rock mass. The mesh coordination between the incident rod, the transmission rod and the rock specimen can make the simulation results more accurate. A total of 215,400 model units were divided. Figure 7: Variation law between the mean dissipated energy and schistity angle. AUTOMATIC_NODES_TO_SURFACE is used between the bullet and the incident rod, and ERODING_SURFACE_TO_SURFACE is used between the specimen and the incident rod and transmission rod. The symmetric penalty function algorithm is adopted for the contact surface, and the penalty function factor of the contact stiffness _f_s is 0.8. The unit failure method (MAT_ADD_EROSION) is used to simulate rock sample fracture. The bullet, incident bar, and transmission bar in the SHPB system are made of 40 Cr alloy steel, which adopts the *MAT_ELASTIC model. The detailed material parameters are \(\rho=7900\) kg/m\({}^{3}\), \(E=210\) GPa, and \(\
u=0.3\). The *MAT_JOHNSON_HOLMQUIST_CONCRETE model is a constitutive model used to simulate the damage and failure of concrete or rock under high load, high strain rate and large deformation [29]. The yield surface equation of the HJC model is described by the dimensionless equivalent stress \(\sigma^{\star}\), and the expression is as follows:  
\[\sigma^{\star}=\Big{[}A(1-D)+BP^{\star}N\Big{]}(1+\text{Cln}\varepsilon^{\star}) \tag{3}\]  
where \(\sigma^{\star}=\sigma/f_{c}\) is normalized equivalent yield strength. \(\sigma\) is equivalent strength. \(f_{c}\) is quasi-static uniaxial compressive strength. \(A\) is normalized viscous strength. \(B\) is the normalized pressure hardening coefficient. \(C\) is the influence coefficient of the strain rate. \(D\) is the damage degree. \(N\) is the pressure hardening coefficient. \(P^{\star}\) is dimensionless pressure, which is the ratio of hydrostatic pressure to compressive strength. \(\varepsilon^{\star}\) is the dimensionless strain rate. In this study, this model will be used to study the nonlinear dynamic characteristics of thin-layered schist. According to the SHPB test results of thin-layered schist, specimens with schistoids angles of \(90^{\circ}\) fracture due to shear failure, and the effect of schistoids is small. Therefore, based on the SHPB laboratory test results, Table 2 displays the HJC parameters of schist. Due to the unavailability of HJC parameters for the schistory structure from the SHPB test, we utilized a parameter reduction method to calculate and make a comparison with the test results. Reduction coefficients of 0.4, 0.35, 0.3, 0.25, and 0.2 were employed for comparison purposes. Figure 9 illustrates the comparison between the stress-strain curve obtained through numerical simulation using a reduction coefficient of 0.35 and