## 5 Validation of Numerical Model of Test Impact Force
Considering the elastic-plastic nature of the contact material and the material hardening under the dynamic loading conditions (the process of the elastic-plastic change of the material), in order to simplify the calculation process, the elastic-plastic property of the material was simplified to satisfy the hypothetical condition. Furthermore, the relationship between the stress of the yield pressure and the radius of the contact surface at the initial yield time can be established by combining Equations (1)-(3), as shown in Equation (4). \[\rm P_{y}=\frac{2E_{y}}{\pi R} \tag{4}\]  
where \(\rm P_{y}\) (MPa) is the stress of the yield pressure in the plastic area of the collision contact surface; \(\rm r_{y}\) (m) is the radius of the contact surface at the initial yield time. According to the [PERSON] contact theory, it is assumed that the falling sandbag satisfies the [PERSON] yield criterion [17]. The calculation formula for the stress of the yield pressure in the plastic area of the collision contact surface is as shown in Equation (5). \[\rm P_{y}=C_{v}Y \tag{5}\]  
where \(\rm C_{v}\) is the contact coefficient, \(\rm C_{v}=1.234+1.256\rm\gamma\); \(\rm\
u\) is the Poisson ratio of the contact material; \(\rm Y\) (MPa) is the yield strength of the contact material. Equations (2)-(5) were solved simultaneously to obtain the initial yield compression of the normal deformation \(\rm\delta_{y}\) (m). Substituting the result into Equation (1), we can obtain the initial yield compressive stress of the normal direction \(\rm P_{y}\) (kPa). The contact material can be assumed as an ideal elastic-plastic material by the Thornton theory [18]. In addition, the relationship between the compressive stress of the elastic-plastic contact compression at the normal deformation and the normal compressive deformation was defined, as shown in Equation (6):  
\[\rm P_{ep}=P_{y}+2\pi R\rm P_{y}\left(\delta-\delta_{y}\right) \tag{6}\]where \(\rm P_{ep}\) (kPa) is the compressive stress of the elastic-plastic contact compression at the normal deformation; \(\rm P_{y}\) (kPa) is the initial yield compressive stress of the normal direction, \(\rm P_{y}=\frac{4}{3}ER^{\frac{1}{2}}\delta\frac{3}{\dot{y}};\delta_{y}\) (m) is the initial yield compression of the normal deformation. Through the analysis of energy conservation, it can be seen that the kinetic energy generated by the falling sandbag was mainly composed of the local elastic deformation energy, the elastic-plastic deformation energy of the contact area and the overall bending deformation energy of the composite wall [19]. Integrating the conservation of momentum into the equation, the maximum compression of the normal deformation under consideration of elastic-plastic deformation can be obtained, as shown in Equation (7):  
\[\frac{1}{2}mv_{1}^{2}+\frac{1}{2}mv_{2}^{2}=\int_{0}^{\delta_{y}}P_{\rm e}( \delta)d\delta+\int_{\delta_{y}}^{\delta_{\rm max}}P_{\rm ep}(\delta)d\delta+ \frac{24P_{\rm ep}^{2}\left(1-\
u_{2}^{2}\right)}{\pi^{4}E_{2}h^{3}ab\left( \frac{1}{\delta^{2}}+\frac{1}{b^{2}}\right)} \tag{7}\]  
where \(\delta_{\rm max}\) (m) is the maximum compression of the normal deformation under consideration of elastic-plastic deformation. By solving the integral Equation (7), one can determine the \(\delta_{\rm max}\). Considering the strength characteristics and the impact resistance of various materials in the test, an empirical deformation magnification factor \(\kappa\) was given. Substituting \(\delta_{\rm max}^{*}=\kappa\delta_{\rm max}\) into Equation (6), the maximum impact force of the collision after considering the elastic-plastic theory can obtained. After considering the coupling effect of the experimental composite materials, the modified parameter reduction coefficients of LSKLCW were given. The maximum impact force calculation model was obtained through the joint solution process, as shown in Equation (8).