Abstract
A class of two-phase composite materials with a biperiodic structure is investigated by the methods of complex analysis. Two interface conditions -continuity of normal component of a desired vector w and tangential component of ρw at the contact boundary as well as the double-periodicity condition - are involved in rigorous form. The exact analytic solution of the corresponding generalized Riemann boundary-value problem is obtained. The explicit values of the effective parameters, namely effective resistivity and dissipation of energy of an elementary cell and resistivities along the symmetry axes are calculated in closed analytic form. The coincidence of our formulae with the well-known effective resistivity (conductivity) formula of Keller (1964), Dykhne (1970) and Mendelson (1975) and the dissipation formula of Dykhne (1970) is shown in the case of square checkerboard field. The Keller (1963) identity is generalized for the heterogeneous structure studied.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
