In this paper we consider hemivariational inequalities of hyperbolic type. The existence result for hemivariational inequality is given and the existence theorem for the optimal shape design problem is shown.
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An elastic–slip interface model is proposed to investigate the effective elastic modulus of elliptical-fiber reinforced asphalt concrete, and the nonlinear factor related with the second-order term of strain is used to consider the large deformation of asphalt concrete. The representative volume element with effective isotropic medium is introduced to describe the overall properties of elliptical-fiber reinforced asphalt concrete. Combining the confor-mal mapping technique and polynomial function expanded method, a closed form solution of effective elastic modulus is obtained. Through numerical examples, the effects of inter-face material coefficients and the nonlinear factor on the effective elastic modulus under different shapes of fibers are discussed in detail. To validate the present interface model, experimental investigation on the interface effect on the elastic modulus is presented.