# Material Point Simulation Method for Concrete Medium Fracture and Fragmentation under Blast Loading
## 3 An Improved HJC Model Considering the Segmentation of the DIF Function
### The Improved Method of the HJC Model  
In addition to the above shortcomings, a large number of research results have shown that the HJC model can well reflect the influence of low strain rates on the dynamic strength of concrete but cannot accurately describe the significant enhancement effect of concrete dynamic strength under high strain rate conditions. That is, the dynamic strength calculated by the DIF function in the HJC model under high strain rate conditions deviates greatly from experimental results. Therefore, based on the Hopkinson bar, this article carried out dynamic uniaxial compression and dynamic split tension experiments on concrete to obtain the dynamic compressive and tensile strengths of concrete under high strain rates and improved the DIF function in the HJC model in combination with experimental data, making it have segmentation. That is, there is a critical strain rate. When the strain rate is lower than the critical strain rate, the strain rate effect on the strength of concrete is not obvious, but when the strain rate is higher than the critical strain rate, the degree to which the strength of concrete increases with the strain rate is significantly improved. The SHPB experiment is the primary method of studying the mechanical properties of materials at high strain rates (10\({}^{2}\)\(\sim\)10\({}^{4}\) s\({}^{-1}\)). A modern conventional SHPB consists of a gas gun (cannon or launching device), a bullet, an incident bar, a transmission bar, an energy absorption device, and a data acquisition system (as shown in Figure 4). Large cubic concrete samples were cast for core drilling. At the end of the 28-day curing period, the mass concrete specimens were sent to a professional processing plant, where they were cored, cut to size, and ground. It was then processed into \(\Phi\)50 mm \(\times\) 25 mm disc-shaped specimens (as shown in Figure 5). The two loading sections of the processed specimens are smooth enough and have parallelism within the tolerance range of 0.01 mm. The dynamic compression and dynamic Brazilian splitting experiments were carried out by the SHPB experimental device. Throughout the experiment, it is required that the cross-sectional area of the specimen always be smaller than or equal to that of the rod. In addition, the incident rod must be long enough (more than twice the length of the bullet) to avoid overlapping of incident and reflected waves, and the material must remain within the elastic range during the experiment. To improve the accuracy of the test, it is also required that the contact surface between the rod and the specimen remain flat and parallel to each other throughout the experiment. Figure 4: Conventional Hopkinson bar experiment system. The concrete specimen is loaded between the incident and transmission bars. The bullet is propelled by high-pressure gas and is fired from the launching device at a certain velocity, striking the incident bar and generating a pressure pulse in the incident bar known as the incident wave (measured by the resistance strain gauge attached to the incident bar). The pressure pulse propagates forward in the incident bar, and when it reaches the interface between the incident bar and the specimen, the entire specimen is compressed due to the inertial effect of the specimen and the transmission bar. Meanwhile, due to the wave impedance difference between the bar and specimen, the incident wave is partially reflected as a reflected wave back to the incident bar, and the other part passes through the specimen as a transmission wave and enters the transmission bar. The reflected wave is also measured by the resistance strain gauge attached to the incident bar, and the transmission wave is measured by the resistance strain gauge attached to the transmission bar. By processing the measured incident wave, reflected wave, and transmission wave, the deformation and failure of the material can be obtained, as can the dynamic performance data of the material.