# Elastoplastic Constitutive Model for Energy Dissipation and Crack Evolution in Rocks
## 6 Discussion  
This study successfully constructed an elastoplastic constitutive model for rock energy dissipation and crack evolution, validating the model's effectiveness through numerical simulations and comparisons with experimental data on argillaceous siltstone. Our research indicates that dissipated energy equals the integral of the stress-strain curve minus the elastic strain energy, which can be quantitatively described using strength parameters. Additionally, the crack volumetric strain is equal to the plastic volumetric strain and can be indirectly quantified using the dilatancy angle. This finding provides a solid theoretical basis for the elastoplastic modeling of rock energy dissipation and crack evolution.  
Compared to existing elastoplastic constitutive models in the literature, while previous models have made significant progress in characterizing the nonlinear mechanical behavior of rocks [9; 10; 11; 12], they generally overlook the crucial role of energy dissipation and crack evolution in the strain failure process of rocks. Our proposed model effectively describes the energy dissipation and crack evolution process by introducing the concepts of dissipated energy [29; 30; 31; 32; 33] and plastic volumetric strain [40; 41; 43; 44], providing a stronger advantage in describing and predicting actual rock failure processes. Furthermore, existing studies often limit themselves to secondary developments based on single material models [4; 7; 8], whereas our research derives a three-dimensional finite difference format of the model, clarifying the incremental iterative relationships among various mechanical parameters and their detailed computational process in FLAC [30], thus facilitating effective numerical algorithm implementation and providing theoretical support for the widespread application of the model.  
The results of this study have significant implications for rock mechanics and related engineering fields. Firstly, the constructed model can effectively predict the mechanical response of rocks under different loading conditions, providing theoretical guidance for mining, underground engineering, and other domains. Secondly, the quantitative relationship between energy dissipation and crack evolution proposed in the model offers new insights for the design and assessment of rock materials. In the future, this model could be applied to more complex rock engineering projects to enhance the prediction accuracy and reliability.  
Despite the achievements of this study, several limitations remain. Firstly, the analysis of the model primarily focuses on shear failure during the triaxial compression of rocks, without considering the effects of tensile failure. Secondly, the model has shortcomings inaccounting for the influences of strain rate, temperature, humidity, and other environmental factors on rock behavior. Additionally, the model was verified only using argillaceous siltstone and did not fully leverage the information on dissipated energy and crack volumetric strain to enhance the physical understanding of experimental phenomena. Future research should aim to overcome these limitations to further expand the model's applicability and practical use.  
In summary, this study provides a theoretical foundation, algorithm implementation, and experimental validation for the elastoplastic constitutive model of rock energy dissipation and crack evolution, with hopes for validation and development in broader applications in the future.