Boundary Value Problems of Potential Functions in Decagonal Quasicrystals

Abstract EN

A unified form of potential functions in decagonal quasicrystals (QCs) and conformal mappings are applied in a novel way to solve the boundary value problems emanating from the generalized theory of elasticity for decagonal QCs.

By executing the reduction of boundary value problem to function equations, two crack problems are investigated.

In the first one, an approximate analysis for bending specimen with a crack is given.

In the other, a finite width strip with single edge crack of decagonal QCs is analytically estimated.

Using the basic idea underlying Dugdale’s crack model, the extent of cohesive force zone in each of the two cases is analytically derived.