Schwarz’s alternating method in a matrix form and its applications to composites

Dependence of effective properties upon regular perturbations

“…Gorb and Berlyand [26] considered the asymptotic behavior of the effective properties of composites with close inclusions of optimal shape. For two-dimensional composites, the recent work by Mityushev, Nawalaniec, Nosov, and Pesetskaya [48] studies the effective conductivity of two-phase random composites with non-overlapping inclusions whose boundaries are C 1,α curves. In Lee and Lee [39], the authors have studied how the effective elasticity of dilute periodic elastic composites is affected by its periodic structure.…”

Perturbation analysis of the effective conductivity of a periodic composite

“…Gorb and Berlyand [25] considered the asymptotic behavior of the effective properties of composites with close inclusions of optimal shape. For 2D composites, we also mention the recent work by Mityushev, Nawalaniec, Nosov, and Pesetskaya [42], where the authors have applied the generalized alternating method of Schwarz in order to study the effective conductivity of two-phase random composites with non-overlapping inclusions whose boundaries are arbitrary Lyapunov's curves. In Lee and Lee [37], the authors have studied how the effective elasticity of dilute periodic elastic composites is affected by its periodic structure.…”