Damage analysis of fiber composites Part I: Statistical analysis on fiber scale

Generalized Finite Element Methods — Main Ideas, Results and Perspective

“…Let S ω j ∩Γ 1 (x) be the sector subtending this arc, and let γ ωj ∩Γ1 be the angle of this sector. Suppose each ω j is convex, d j = diam (ω j ), and supposeω j is a disk of diameterd j ≥ dj κ 2 , whose closure lies in ω j . Assume…”

Gradient Estimates for the Perfect Conductivity Problem

“…For a fixed 0 < k < ∞, the C m,α (D i )-norm of the solution might tend to infinity as ε → 0. Babuska, Anderson, Smith and Levin [4] were interested in linear elliptic systems of elasticity arising from the study of composite material. They observed numerically that, for solution u to certain homogeneous isotropic linear systems of elasticity, ∇u L ∞ is bounded independently of the distance ε between D 1 and D 1 .…”

Estimates for the electric field in the presence of adjacent perfectly conducting spheres

“…If the inclusions are perfect conductors (k = +∞) or insulators (k = 0), then the gradient blows up at the rate of −1/2 , as shown by Babuska et al [3] by numerical evidence. See also [5,8,11].…”

“…Because of the symmetry of the configuration, x 1 and x 2 play the same roles, and hence it suffices to consider the cases when H = x 1 and H = x 3 .…”

“…Introduction. Frequently in two phase composites, inclusions are located very closely and may even touch; see [3]. It is therefore natural and important to find out if the electric field in the presence of closely spaced inclusions can be arbitrarily large or not.…”