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On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media
Abstract Higher order (so-called strain gradient) homogenised equations are rigorously derived for an infinitely extended periodic elastic medium with the periodicity cell of a small size e , in the
Stability and error estimates for Filon–Clenshaw–Curtis rules for highly oscillatory integrals
In this paper we obtain new results on Filon-type methods for computing oscillatory integrals of the form $\int_{-1}^1 f(s) \exp({\rm i}ks) \ {\rm d}s $. We use a Filon approach based on
A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering
TLDR
This work proposes a new robust method for the computation of scattering of high-frequency acoustic plane waves by smooth convex objects in 2D by the direct boundary integral method, using the classical combined potential approach and proves superalgebraic convergence of the numerical method as d → ∞ for fixed k.
The role of strain gradients in the grain size effect for polycrystals
Abstract The role of grain size on the overall behaviour of polycrystals is investigated by using a strain gradient constitutive law for each slip system for a reference single crystal. Variational
Propagation and localization of elastic waves in highly anisotropic periodic composites via two-scale homogenization
Abstract Wave propagation in periodic elastic composites whose phases may have not only highly contrasting but possibly also (in particular) highly anisotropic stiffnesses and moderately contrasting
Bounds and estimates for linear composites with strain gradient effects
Abstract Overall mechanical properties are studied for linear composites demonstrating a size effect. Variational principles of Hashin-Shtrikman type are formulated for incompressible composites
A ‘non-local’ variational approach to the elastic energy minimalization of martensitic polycrystals
Solid–solid phase transformations in polycrystals are considered in the context of energy minimization. The energy of a single crystal is specified by a non–convex multi–well energy function, in the
Diffraction by conical surfaces at high frequencies
Abstract We consider the scalar wave field described by the Helmholtz equation generated by a point source or by a plane wave in the presence of a conical obstacle of a rather arbitrary
A new frequency-uniform coercive boundary integral equation for acoustic scattering
A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary
On Evaluation of the Diffraction Coefficients for Arbitrary "Nonsingular" Directions of a Smooth Convex Cone
TLDR
This work develops a method for evaluating the diffraction coefficients in arbitrary "nonsingular" directions, for a class of canonical problems of plane wave diffraction by an arbitrarily shaped smooth convex cone.
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