带裂纹十次对称二维准晶平面弹性的无摩擦接触问题

Abstract

With the classical complex function method, a frictionless contact problem of 2D decagonal quasicrystal semiplane elasticity with arbitraryform cracks was addressed under the action of a rigid convex basal punch. Based on complex expressions of stresses and displacements of 2D decagonal quasicrystals, the problem was converted into solvable boundary value problems with analytic functions, and then reduced to a class of Riemann boundary problems. Solutions to the Riemann boundary problems give the stress functions in closed form, the explicit expressions of the stress intensity factors at crack tips and the contact stress distribution under the punch. The expression of the contact stress shows that, it has singularity at the edge of the contact zone and the crack tips. Without the effect of the phason field, the obtained results match well with those classical conclusions for elastic materials. Numerical examples illustrated the solutions to the frictionless contact problem in 2D decagonal quasicrystal semiplane elasticity with a vertical crack and a horizontal straight crack under a rigid punch. The work provides a theoretical reference for the application of quasicrystalline materials.