An interface crack with mixed electrical conditions at it faces in 1D quasicrystal with piezoelectric effect

Abstract

An interface crack in 1D piezoelectric quasicrystalline space is considered. Both conducting and mixed conducting-permeable electric conditions at the crack faces are studied. The matrix–vector representations of the phonon, phason and electric quantities via the sectional-holomorphic function are derived. Two types of electrical conditions at the crack faces are considered – conducting case and mixed conducting-permeable case. A Riemann problem of linear relationship and a combined Dirichlet–Riemann boundary value problem are derived. Exact analytical solutions of the mentioned problems are presented and the simple analytical formulas for all required values are given and numerically illustrated.

Keywords:

• Interface crack
• quasicrystal
• piezoelectric effect
• mixed electric conditions
• analytical solution

Additional information

Funding

This work was sponsored by a public grant overseen by the French National Research Agency as part of the “Investissements d’Avenir” through the IMobS3 Laboratory of Excellence [ANR-10-LABX-0016] and the IDEX-ISITE initiative CAP 20-25 [ANR-16-IDEX-0001], program WOW.