); zhouhao32111301([EMAIL_ADDRESS] (H.Z. ); [EMAIL_ADDRESS] (C.G. ); 1 [EMAIL_ADDRESS] (H.D. ); [EMAIL_ADDRESS] (X.D.) Xiaochun Yin  
1 School of Physics, Nanjing University of Science and Technology, Nanjing 210094, China; [EMAIL_ADDRESS] (H.Y. ); [EMAIL_ADDRESS] (Y.G. ); [EMAIL_ADDRESS] (C.W. ); zhouhao32111301([EMAIL_ADDRESS] (H.Z. ); [EMAIL_ADDRESS] (C.G. ); 1 [EMAIL_ADDRESS] (H.D. ); [EMAIL_ADDRESS] (X.D.) Xiaochun Yin  
1 School of Physics, Nanjing University of Science and Technology, Nanjing 210094, China; [EMAIL_ADDRESS] (H.Z. ); [EMAIL_ADDRESS] (Y.G. ); [EMAIL_ADDRESS] (C.W. ); zhouhao32111301([EMAIL_ADDRESS] (H.Z. ); [EMAIL_ADDRESS] (C.G. ); 1 ding_huxieng@njusts. contact problem [11; 12; 13; 14]. [PERSON] [15] derived the contact force-indentation relation for the loading and unloading phases on the basis of a spherical-shell extension model [2] applied to the rod [16] and beam [17] impacts. [PERSON] and [PERSON] [18] presented an elastic-plastic contact law to solve the coefficients of recovery for sphere-plate elastic-plastic impacts [19]. [PERSON] [20] proposed a simplified elastic-plastic contact law to compute the coefficient of recovery of a particle impact with a vessel wall. The existing theoretical contact laws are mainly provided for the quasi-static impacts of rigid spheres against elastic-plastic bodies. According to different selection methods of \(\sigma_{Y}\), which is the yield strength of the softer material [21; 22; 23], the contact type can be divided into three types: the indention type when \(\sigma_{Ys}>\sigma_{Yb}\), the flattening type when \(\sigma_{Ys}<\sigma_{Yb}\), and the combined type when \(\sigma_{Ys}=\sigma_{Yb}\). For an elastic-plastic material indented by a rigid sphere or an elastic-plastic sphere pressed by a rigid flat, the Hertz contact law [24] can be adopted before the inception of plastic yielding, and the pressure is assumed to have an elliptic distribution. Many theoretical loading and unloading laws exist for indentation contact [2; 25; 26] and flattening contact [27; 28; 29]. However, the contact between two elastic-plastic bodies is more complex, and, until now, most studies of elastic-plastic contact behaviors have focused on the elastic-plastic materials contacted by a rigid sphere or a rigid flat, and the force-indentation relationship laws in combined contact types are scarce [30; 31]. To consider the deformations of the contact between two elastic-plastic bodies, [PERSON] et al. [31] tried to adopt the yield stress ratio of the two contacting bodies as a controlling parameter. They proposed a complicated theoretical contact law that has not been sufficiently examined. Furthermore, [PERSON] et al. [32; 33] found that the compliance of the indenter cannot be neglected even though the ratio of elastic moduli between the indenter and indented material is at least three times. In experiments performed by [PERSON] et al. [34], it was found that, by using even extremely stiff material with the compressive yield stress of 3690 MPa, the compressive yield stress decreased by about 39% compared to that of the rigid indenter. To account for the elastic deformation of the indenter, [PERSON] et al. [25] presented an implicit indentation model, and [PERSON] et al. [35] and [PERSON] [36] presented an explicit loading law. However, a highly applicable method that can consider the indenter elastic-plastic deformation is still lacking. The present study performs the systematic FE simulations for sphere-half space elastic-plastic impact at low speed, and a new linear contact law is proposed for the deformation characteristics. Section 2 introduces the linear contact law and finite element model. In Section 3, the influence of elastic-plastic contact deformation of the spherical indenter is considered. In Section 4, a new linear contact law is presented. Finally, the conclusions are presented in Section 5.