4. Conclusions
The theoretical base and a semi-analytical model (SAM) for simulating the dynamic contact of a rigid sphere and the surface of a multiferroic magnetoelectroelastic (MEE) film under transient applied force has been developed. The research has yielded analytical frequency response functions (FRFs) and their conversion into influence coefficients (ICs) for the MEE film subjected to a set of generalized normal force and generated surface electric/magnetic charges under the influence of changing loading velocity in a dynamic process. The research has also further developed the fast numerical techniques, such as the conjugate gradient method (CGM) and the fast Fourier transform (FFT), for efficient numerical solutions to the dynamic contact behaviors of the thin-film material, including the distributions and variations of contact pressure and electric/magnetic potentials, as well as subsurface stresses. The combined influences of loading velocity, film thickness, and sphere radius on the dynamic MEE responses have been investigated, and the numerical results lead to the following conclusions.
1). The dynamic contact characteristics, including the applied force and electric/magnetic potentials under the triangular loading speed variation are slightly smaller than those under the sinusoidal loading velocity variation in the early stage of the loading cycle, while the trend reverses in the later stage. The contact characteristic values increase with the maximum velocity and sphere radius, but decrease with film thickness.
2). The von Mises stress become larger and the location of the maximum von Mises stress departs further away from the contact surface as loading velocity increases in one loading cycle. A thicker film results in a smaller stress. On the other hand, a larger sphere radius induces a smaller stress under the same peak velocity
