## 4 Analysis of Mechanical Properties and Energy Absorption Performance of Confined Compression
### Analysis of Energy Absorption Performance  
Solid materials will undergo deformation when subjected to external loads, and this deformation process is the process of external forces doing work. Due to energy conservation, the energy is absorbed by the object under load, and the energy absorbed due to deformation caused by external forces is called deformation energy or strain energy. In the lateral compression test of this experiment, the stress-strain curve of the EPP concrete reflects its obvious energy absorption characteristics. From the elastic-plastic section and compression platform section of the curve, the EPP concrete specimen is compressed under external force (load), and the external force (load) does work on the specimen, absorbing energy and dissipating it in various forms such as pore deformation, fragmentation, collapse and friction of concrete fragments. The strain energy of the EPP concrete during compression and the related calculation formula are demonstrated by the shaded area in Figure 16 and Formula (6), respectively. Figure 14: Relationship between dense volume strain and EPP content. Figure 13: Relationship between dense volume strain, ultimate compressive strain and EPP volume content. Figure 15: Relationship between ultimate compressive strain and EPP content. The energy absorption per unit volume and the related calculation formula are also shown in Figure 17 and Formula (7), respectively. \[W=\int\limits_{0}^{\delta_{d}}F(\delta)d\delta \tag{6}\]  
\[W_{V}=\int\limits_{0}^{\theta_{d}}\sigma(\theta)d\theta \tag{7}\]  
where \(W\) stands for the strain energy (j), \(W_{V}\) denotes the deformation energy per unit volume, i.e., strain energy density (KJ/m\({}^{3}\)), \(F\) signifies the pressure force test value (kN), \(\delta\) is the compressive deformation value of the EPP concrete specimen (mm), \(\sigma\) represents the stress value (kPa), \(\theta\) is the volume strain value of the EPP concrete specimen and \(\delta_{d}\) refers to the vertical deformation value corresponding to the dense volume strain. The energy absorption of the EPP concrete occurs in two stages, namely, the elastic-plastic deformation and the pore collapse compaction. Accordingly, the energy \(W_{V}\) absorbed per unit volume can be argued to consist of two parts: (1) the energy \(W_{V1}\) which is absorbed by the elastic-plastic section and (2) the compressed energy \(W_{V2}\) absorbed by the platform segment, the mathematical relationship and the calculation formulae, of which are shown in Formulas (8)-(10). \[W_{V}=W_{V1}+W_{V2} \tag{8}\]  
\[W_{V1}=\int\limits_{0}^{\theta_{V}}\sigma(\theta)d\theta \tag{9}\]  
Figure 16: Schematic diagram of strain energy of EPP concrete. Figure 17: Schematic diagram of strain energy per unit volume of EPP concrete. \[W_{V2}=\int\limits_{\theta_{cc}}^{\theta_{d}}\sigma(\theta)d\theta \tag{10}\]  
where \(\theta_{cc}\) stands for the volume strain value corresponding to the confined compressive strength \(f_{cc}\), and \(\theta_{d}\) denotes the dense volume strain. The energy absorption indexes \(W_{V1}\) and \(W_{V2}\) were obtained by piecewise integrating the stress-volume strain curves of A1-A6, the schematic diagram of which is shown in Figure 13:0 The results obtained from the calculation of the strain energy density are also provided in Figure 13:1  
Figure 13:2 Piecewise integral diagram of confined compressive stress–volume strain of concrete specimens with different EPP volume content. (**a**) A1 group: EPP volume content of 28%. (**b**) A2 group: EPP volume content of 35%. (**c**) A3 group: EPP volume content of 42%. (**d**) A4 group: EPP volume content of 50%. (**e**) A5 group: EPP volume content of 57%. (**f**) A6 group: EPP volume content of 64%. As can be seen in Figure 18, an increase in the EPP particle content resulted in a gradual increase in the total strain energy density, which is an indication of the higher EPP content, the more obvious energy absorption characteristics and the better energy absorption performance of the EPP concrete.