Effect of initial impact energy on contact stiffness in linear contact law of low velocity elastic-plastic impact

Abstract

In this paper, the loading force-indentation curve of low-velocity impact between an elastic-plastic plate and an elastic-plastic sphere by finite element (FE) analysis is investigated. The impactor mass and impact velocity are varied to cover a wide range of initial impact energies. The comparisons between the linear contact law using theoretical contact stiffness and the FE results show much difference. Based on the observation of FE data, the practical contact stiffness is strongly affected by the initial impact energy due to the nonlinearity of practical contact stiffness in the elastic-plastic impact. The definition of the equivalent contact stiffness is proposed to obtain the practical contact stiffness for the elastic-plastic impact accurately. The relations between theoretical and equivalent contact stiffness are massively calculated by FE covering a wide range of initial impact energies. Based on the FE results of the relations, a coefficient to revise the theoretical contact stiffness is suggested and a piecewise expression of the coefficient is presented by curve-fitting approach. It is demonstrated that the revised contact stiffness agrees well with the practical contact stiffness. This revised contact stiffness is of great value in predicting the maximum impact force in low velocity elastic-plastic impact between elastic-plastic bodies.