Related papers: The convexity of inclusions and gradient's concent…
In composite material, the stress may be arbitrarily large in the narrow region between two close-to-touching hard inclusions. The stress is represented by the gradient of a solution to the Lam\'{e} system of linear elasticity. The aim of…
In high-contrast elastic composites, it is vitally important to investigate the stress concentration from an engineering point of view. The purpose of this paper is to show that the blowup rate of the stress depends not only on the shape of…
This paper is concerned with the stress concentration phenomenon in elastic composite materials when the inclusions are very closely spaced. We investigate the gradient blow-up estimates for the Lam\'{e} system of linear elasticity with…
In the region between two closely located stiff inclusions, the stress, which is the gradient of a solution to the Lam\'{e} system with partially infinite coefficients, may become arbitrarily large as the distance between interfacial…
For two neighbouring stiff inclusions, the stress, which is the gradient of a solution to the Lam\'{e} system of linear elasticity, may exhibit singular behavior as the distance between these two inclusions becomes arbitrarily small. In…
We consider the Lam\'{e} system arising from high-contrast composite materials whose inclusions (fibers) are nearly touching the matrix boundary. The stress, which is the gradient of the solution, always concentrates highly in the narrow…
A long-standing area of materials science research has been the study of electrostatic, magnetic, and elastic fields in composite with densely packed inclusions whose material properties differ from that of the background. For a general…
We establish upper bounds on the blow-up rate of the gradients of solutions of the Lam\'{e} system with partially infinite coefficients in dimensions greater than two as the distance between the surfaces of discontinuity of the coefficients…
In the region between close-to-touching hard inclusions, the stress may be arbitrarily large as the inclusions get closer. The stress is represented by the gradient of a solution to the Lam\'e system of linear elasticity. We consider the…
In high-contrast composite materials, the electric field concentration is a common phenomenon when two inclusions are close to touch. It is important from an engineering point of view to study the dependence of the electric field on the…
We establish upper bounds on the blow up rate of the gradients of solutions of the Lam\'e system with partially infinite coefficients in dimension two as the distance between the surfaces of discontinuity of the coefficients of the system…
We study the insulated conductivity problem with inclusions embedded in a bounded domain in $\mathbb{R}^n$. It was known that in the setting of strictly convex inclusions, the gradient of solutions may blow up as the distance between…
In the perfect conductivity problem, it is interesting to study whether the electric field can become arbitrarily large or not, in a narrow region between two adjacent perfectly conducting inclusions. In this paper, we show that the…
A high-contrast two-phase nonlinear composite material with adjacent inclusions of $m$-convex shapes is considered for $m>2$. The mathematical formulation consists of the insulated conductivity problem with $p$-Laplace operator in…
We investigate higher derivative estimates for the Lam\'e system with hard inclusions embedded in a bounded domain in $\mathbb{R}^{d}$. As the distance $\varepsilon$ between two closely spaced hard inclusions approaches zero, the stress in…
We study the stress concentration, which is the gradient of the solution, when two smooth inclusions are closely located in a possibly anisotropic medium. The governing equation may be degenerate of $p-$Laplace type, with $1<p \leq N$. We…
We are concerned with the field concentration between two nearly-touching inclusions with high-contrast material parameters, which is a central topic in the theory of composite materials. The degree of concentration is characterised by the…
In high-contrast composites, if an inclusion is in close proximity to the matrix boundary, then the stress, which is represented by the gradient of a solution to the Lam\'{e} systems of linear elasticity, may exhibits the singularities with…
In the perfect conductivity problem of composite material, the electric field concentrates in a narrow region in between two inclusions and always becomes arbitrarily large when the distance between inclusions tends to zero. To characterize…
We study the insulated conductivity problem which involves two adjacent convex insulators embedded in a bounded domain. It is known that the gradient of solutions may blow up as the distance between the two inclusions tends to zero.…