The Frictionless Contact Problem Of Quasicrystals

With the improvement of science technology, quasicrystal has the important practical prospect be-cause of its good properties. It is a new type of functional and constructional material. As one of the important part in the field of applied mathematics mechanics, contact and fracture problems are widely exist in engineering systems. To understand the mechanical properties of quasicrystal material much bet-ter and to considerate the low friction of quasicrystal, frictionless problem of three kinds quasicrystals and its fracture problem has been researched by classical solution. The results provide a theoretical basis and reference value for the research and application of quasicrystal material.The main content of this paper is divided into three parts. In the first and second parts, friction-less contact problems of three-dimensional and one-dimensional quasicrystal are discussed by complex variable method, separately. Finally, the analytical expressions of contact stress and displacement in phonon and phason field are obtained. Numerical analysis about the results show that:(1) for the three-dimensional icosahedral quasicrystal and one-dimensional hexagonal quasicrystal, contact stress has stress concentrate phenomenon in the edge of the contact zone. (2) the influence of phonon-phason coupling coefficient R on the distribution law of contact stress is very small. When phonon-phason cou-pling coefficient R=0, the results are in agreement with the classical elastic materials. This indicates that the classical theory of contact mechanics can be also used in quasicrystals. It provides an important theo-retical basis for quasicrystal contact problem research and also verifies the correctness of the conclusions obtained in this paper.In the third part, the frictionless problem of single rigid head and dodecagonal system in two-dimensional quasicrystals has been discussed by integral transformation and dual integral equation theory. Explicit expressions for the contact stresses and displacements were obtained. Numerical analysis show that the contact stresses exhibit-1/2singularities in the edge of contact zone if the contact displacement is a constant.