Local contact behavior between elastic and elastic–plastic bodies

The loading–unloading behavior of local contact between elastic body and elastic-ideally plastic body is studied analytically and numerically. An analytical model is derived based on the simulating results pertinent to Brinell indentation and elastic–plastic beam impact. The observed linear and nonlinear contact characters from simulations are introduced into the proposed analytical model. The contact law is expressed in much easier formulations by four normalized contact variables, normalized average contact pressure H¯, relative strain Λ, normalized contact area c2 and relative contact force Ψ. The elastic loading is following Hertz contact theory. The linear contact laws for the elastic–plastic and fully plastic loadings and the nonlinear contact laws for the finite deformation loading are introduced in term of the finite element (FE) contact simulations pertinent to Brinell indentation. The coefficients in the contact law are determined by fitting the FE contact simulations and by satisfying the continuous conditions. The more suitable regime of Hertz solution and a refined force–indentation relation of unloading are introduced as well into the analytical model according to the FE impact simulations. The model is finally verified with the FE simulation and experiment of elastic-ideally beam struck by elastic sphere. The analytical model shows a very good agreement between the FE-simulations and the experimental data for either low or moderate velocity impacts, while Stronge model is dependent upon impact velocity. The loading and unloading laws are highly accurate, even for the finite contact deformation in which the nearly 90% of cross section has yielded and the contact radius a (normalized by the indenter radius R) is up to a/R = 0.217.