Study on the similarity of elasticity and ideal plasticity response of thin plate under impact loading

For the impact similarity problem of the scaled model and the prototype usually have different materials with elastic and plastic properties, the differences of material properties and the coexistence of elastoplastic in different deformation stages will lead to the failure of the previous impact similarity theory. Based on the theory of the thin plate impact problem, the similarity law of impact response was derived by using the method of equation similarity analysis for the material with the linear elastic and ideal rigid-plastic properties. The basic equations of the thin plate structure, such as the energy conservation equation and the strain-displacement equation, were analyzed using equation similarity analysis methods, and the similarity scaling factor of the ideal elastic-plastic thin plate structure was derived. Based on the equation similarity analysis methods, a thickness compensation method that can simultaneously consider the similarity of elastic deformation and plastic deformation was proposed.For the impact similarity problem of the scaled model and the prototype using different ideal elastoplastic materials, this methodcan be used to calculate the geometric sizes and load conditions of the scaled model through the material properties when the response of the scaled model is similar to that of the prototype.Two finite element models of circular plate mass impact and circular plate velocity impact were established.The geometric sizes and load conditions of the scaled model were calculated through the thickness compensation method when the prototype uses aluminum alloy and the scaled model uses different materials such as steel, brass, etc. The applicability of the thickness compensation method was verified by the response of prototype and scaled model.The results show that the structural response of the scaled model obtained by the thickness compensation method can accurately predict the impact response of the prototype, even though the scale model and the scale model use different materials.