# Energy Dissipation and Stress Equilibrium Behavior of Granite under Dynamic Impact
## 1 Introduction  
The stress uniformity of rock material under impact loading is one of the most meaningful indicators in the rock dynamic study by the Split Hopkinson pressure system. The dynamic characteristics of rock are influenced by the size effect, shape effect, strain rate effect, various environments, etc. of the specimen [1]. Moreover, the crack morphology, intrinsic relationships, macro- and microcracks, and dynamic equilibrium of rock can be studied by the dynamic compressive test and the Brazilian disc test, which use the Split Hopkinson pressure system [2]. The stress uniformity is to evenly reflect the distributed stress in the specimen and the deformation of the rock specimen under the impact loading. Additionally, the stress equilibrium statement usually exists before the rock is broken. Research on the rock dynamic characteristics of strain rate effect and size effect under the impact loading has been verified extensively. Regarding the strain rate effect, [PERSON] al., experimented with high strain rate on four types of glasses and the high strain rate was shown to have a big influence on glass dynamic characteristics [3]. Borosilicate performed higher destructive strain and compressive strength and energy absorption. [PERSON] et al., used DIC to monitor the strain rate from 30 s\({}^{-1}\) to 200 s\({}^{-1}\) of ultra-high-performance concrete under impact compressive tests, and found that the strain rate and stress equilibrium tend to be constant at 200 MPa [4]. [PERSON] et al., conducted the compressive strength and specific energy absorption of different asphalt/water-to-cement ratios increased with increasing strain rate, and built a model of statistically continuous damage constitution [5]. [PERSON] et al., used the triaxial SHPB system to study the sandstone under the confining pressure of 5 MPa, 7.5 MPa, 10 MPa, 12.5 MPa, and 15 MPa with a strain rate of 40-160 s\({}^{-1}\). It was found that the peak strain was independent from the confining pressure, but increased with strain. The secant modulus was independent from the confining pressure and strain rate [6]. The size effect has also been studied widely. [PERSON] et al., performed the carbon fiber polymer and confined the length-diameter ratios of 0.5 and 2 in SHPB test. The results showed that the concrete specimens had no significant effect on strain rate [7]. [PERSON] et al., studied different length-diameter ratios of coal specimen and proposed a new approach to determine the stress equilibrium [8]. Among length-diameter ratios of 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1, the critical length-diameter ratios of 0.6, 0.3, and 0.4 are optimal. By comparing the stress states and damage patterns of cylindric and cubic specimens, [PERSON] et al., proposed conversion factors for the compressive strength of cylinders and cubes that vary with the strain rate [9]. At present, there are many studies on rock dynamic behavior and energy dissipation, while there are few studies on energy dissipation and stress equilibrium time under impact loading with different length-diameter ratios. They have simply investigated the effect of damage characteristic based on fractal rock mechanics and fracture mechanics theory [10]. [PERSON] et al., defined a stress balance coefficient and performed Hopkinson tests on coal samples with length-to-diameter ratios of 0.3-0.9 to study the stress uniformity and deformation behavior during dynamic compression [11]. [PERSON] et al., monitored the strain behavior of granite impact damage by DIC, and the strain was 0.52% before reaching the stress equilibrium [12]. The Hopkinson's test allows for a variety of analyses of strain rates and fracture patterns of rock specimens. For harder rocks such as granite, longer stress equilibrium time can be maintained before damage. However, there are no more studies on the relationship between rock crushing dissipation energy and stress equilibrium. To this end, research is needed on combing the energy equilibrium factor to define the stress uniformity of granite specimens.