## 3 Analysis and Results
### Numerical Analysis of the Anchoring Performance of DBS Slips
#### 3.1.2 Analysis of Calculation Results Between the Slip Snail and Slip Block  
Utilizing the established computational model, a finite element analysis of the DBS slip setting mechanism was conducted. This study comparatively evaluates the mechanical performance between nail-type and block-type slip configurations through the quantitative analysis of von Mises stress distribution in slip and casing and interfacial contact pressure evolution during plug setting.  
Contact pressure distributions between the two slip types (nail type and block type) and casings were calculated and illustrated separately in Figure 5 under seating forces. The peak contact pressure at the slip insert/casing wall interface attained 2338.5 MPa when employing the nail-type slip. In comparison, the contact pressure distribution exhibited greater uniformity along the upper slip segment, where the peak interfacial pressure reached 1161.3 MPa at the block-type slip tooth/casing contact zone.  
The contact pressure distribution analysis reveals that the nail-type slip exhibited concentrated stress near the interfacial contact zone, with peak pressures reaching 1879 MPa. In contrast, the block-type slip demonstrate significantly improved pressure distribution uniformity, maintaining a peak interfacial pressure of 776 MPa. Both slip components utilized identical material with a yield strength of 981 MPa. Notably, the peak stress on the nail-type slip exceeds the material yield strength by 93.4%, indicating a high likelihood of pronounced plastic deformation in the slip nail. Such deformation could potentially culminate in slip anchoring failure during downhole operations.  
The stress distribution along the casing wall for the two structural slip configurations is depicted in Figure 6. For the casing integrated with embedded slip nails, the peak contact pressure reaches 1277.9 MPa (73.2% above yield strength), whereas the casing with embedded slip blocks exhibits a peak pressure of 946.9 MPa (28.3% above yield). The yield strength of the casing material is specified as 738 MPa. The simulation results indicate that  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parts** & **Modulus of Elasticity/MPa** & **Poisson’s Ratio** & **Yield Strength** \\ \hline Slip Body & 70,000 & 0.35 & 350 \\ Slip blocks/Slip nails & 230,000 & 0.26 & 981 \\ Casing & 210,000 & 0.26 & 738 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material parameters of each component of DBS.  
Figure 5: Contact pressure distributions between the two slip types and casings. (**a**) Nail type. (**b**) Block type.  
the block-type slip configuration demonstrates superior anchoring performance compared to the block-type slip design.  
Finite element analysis (FEA) was conducted on two existing slip configurations to characterize the equivalent stress states of the slip-casing systems. Simulation results indicate that the nail-type slip configuration induces significantly higher stresses in both the slip elements and the casing wall, leading to insufficient anchoring stability. In contrast, the block-type slip configuration demonstrates uniform stress distribution across the slip-casing interface, enabling superior anchoring performance. However, the influence of the critical structural parameters (e.g., tooth profile angle, contact surface roughness) of the slip block on anchoring efficiency remains undefined, necessitating further exploration to optimize parameter combinations for enhanced reliability.