## 6 Conclusions and Prospects  
1. This study develops an elastoplastic phase field fracture model, incorporating plastic deformation mechanisms and overcoming the limitations of conventional elastic models under compressive-shear conditions. By integrating plastic strain energy and non-associated flow rules, the framework couples plasticity with phase field damage evolution, explicitly quantifying how plastic slip and shear band formation regulate crack driving forces and propagation paths. The model successfully simulates complete energy evolution processes--from elastic loading to plastic damage accumulation and unstable fracture--providing a novel theoretical tool for analyzing mesoscale rock failure mechanisms under compressive-shear stresses.
2. The numerical implementation leverages finite element discretization and nonlinear solvers, validating the model's capability to simulate complex crack propagation. The coupled interpolation of displacement and phase fields, staggered algorithms, and Newton-Raphson iterations address elastoplastic coupling nonlinearities. Benchmark tests--including single-edge notched tension and prefabricated-crack compression--demonstrate the accurate capture of crack initiation dynamics, wing crack propagation, and through-going failure. Specifically, in the elastic deformation stage, the load-displacement curve exhibits a slope error \(<5\%\) and a correlation coefficient \(\mathrm{R}^{2}>0.99\). At the peak load, the relative error between this model and data from the literature is only \(1.2\%\). These quantitative results further validate the reliability of this model.
3. The findings offer practical engineering relevance for hydraulic fracturing and underground energy storage applications. By quantifying plastic deformation's impact on crack driving forces, the model enables reliable residual strength predictions, reducing dependency on costly physical tests for the long-term stability assessments of underground structures. Additionally, full-process energy evolution simulationssupport parameter inversion in real-time monitoring systems, enhancing safety and cost-efficiency in rock engineering projects.
* Future research should focus on multifield coupling extensions and parameter optimization under dynamic loads. Integrating thermal, hydraulic, and mechanical (THM) couplings into phase field frameworks will advance the modeling of complex geological conditions. Developing data-driven parameter inversion methods and incorporating non-local plasticity theory to refine shear band width simulations are critical directions for advancing rock fracture mechanics research.  
Methodology, G.Q.; software, G.Q. and B.W.; investigation, G.Q.; writing--original draft preparation, G.Q.; writing--review and editing, J.Z. and B.W.; supervision, J.Z.; All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (grant number 52404144) and the Natural Science Basic Research Program of Shaanxi (grant number 2024)JC-YBQN-0594).  
Not applicable.  
The relevant data in this manuscript were obtained from field measurements and tests, which are real and effective.  
The authors declare no conflicts of interest.