Anisotropy of Random Two-Dimensional Composites with Circular Inclusions
Mityushev V. Nauryzbayev N. Nurtazina K.
2024Tbilisi International Centre of Mathematics and Informatics (TICMI)
Lecture Notes of TICMI
2024#25137 - 146 pp.
The problem of macroscopic anisotropy of random two-dimensional composite reinforcement with particles is considered. The investigation is based on the exact solution to the RiemannHilbert and R-linear problems for a multiply connected domain with circular inclusions, along with approximate analytical formulas for boundary value problems involving harmonic and biharmonic functions. The anisotropy terms start with the coefficient c2 on f2 in the power expansion of the effective tensor with respect to the concentration f of circular inclusions. This coefficient c2 is explicitly expressed by the structural sums e2 and (Formula presented.). Universal relations, e2 = π and (Formula presented.), apply to any macroscopically isotropic composite with the changing parameter f. The deviation of e2 and e(1) 3 for the random location of inclusions is studied. It is demonstrated that elastic composites described by biharmonic functions are more isotropically unstable for geometric perturbations than conductive composites described by harmonic functions.
Macroscopic anisotropy , random two-dimensional composite , structural sums
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Cracow University of Technology, Warszawska St., 24, Krakow, 31-155, Poland
Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Satpayev St., 2, Astana, Kazakhstan
Cracow University of Technology
Faculty of Mechanics and Mathematics
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