Elastic field near the tip of an anticrack in a decagonal quasicrystalline material

• Published in: Applied mathematics and mechanics Vol. 41; no. 3; pp. 401 - 408
• Main Authors: Wang, Xu, Schiavone, P.
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.03.2020; Springer Nature B.V; School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, China%Department of Mechanical Engineering, 10-203 Donadeo Innovation Centre for Engineering,University of Alberta, Edmonton, Alberta T6G 1H9, Canada
• Edition: English ed.
• Subjects: Analytic functions; Applications of Mathematics; Classical Mechanics; Deformation; Fluid- and Aerodynamics; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; Phonons; Plane strain; Stress intensity factors; analytic continuation; O753; anticrack contraction force; O343; 32A10; 35Q74; anticrack; 74S70; decagonal quasicrystal; 74E05; 3; 74D05; elastic field
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-020-2582-8

We investigate the elastic field near the tip of an anticrack in a homogeneous decagonal quasicrystalline material subject to plane strain deformations. The phonon and phason stresses exhibit a square root singularity at the anticrack tip. Two real-valued phonon stress intensity factors and two real-valued phason stress intensity factors are introduced to scale four separate modes of deformation. We obtain four analytic functions which completely characterize the induced phonon and phason stresses as well as the displacement field. In particular, we derive a concise yet elegant representation of the anticrack contraction force.