Contact Problems Of One-Dimensional Hexagonal Quasicrystals Aperiodical Plane

Quasicrystal becomes reinforcement or coating of some structural materials because of its excellent physical properties and brittle trait.In the process of using materials,contact is inevitable.In order to avoid the early formation of fatigue crack and prolong the service life of materials,it has theoretical value to study the contact problem.In the actual engineering field,periodic contact problem and contact problems with cracks have more practical significance.Based on the one-dimensional quasicrystal as an example and using complex variable method,this paper discusses the two kinds of contact problems,which provides the reference for the study of mechanics of quasicrystal material.This paper is mainly composed of two parts.The first part,the frictionless,adhesive and frictionally periodic contact problem of one-dimensional hexagonal quasicrystal aperiodical plane are discussed.Firstly,it supposed that stress and displacement are with a? period,meanwhile the stress is bounded at infinity(displacement is not necessarily bounded).Then the periodic contact problem is transformed into the Riemann-Hilbert boundary value problem based on Hilbert kernel integral formula of half plane,so as to obtain the closed form solutions.Further,as an application,for the frictionless and frictionally cases,the explicit solutions of contact stress were given under the action of three common basal punches(strraight horizontal,straight inclined and circular basal punches);for the adhesive one,the analytic solution of contact stress was given in the case of the wedge shaped periodic displacement on the contact boundary.The second part,the frictionless,adhesive and frictionally contact problem of aperiodical half-plane with cracks in one-dimensional hexagonal quasicrystal are studied.Firstly,it is assumed that the external stress primary vector of stress and displacement in the infinite distance and playing role in both sides of the crack are zero,then through reasonable stress functions decomposition and elimination method,the problem is attributed to the solvable Riemann's boundary value problem,finally solved in closed form.The distribution of stress intensity factor in the crack tip and the contact stress under the punch are given.