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Heterogeneous materials exhibit anisotropy which is influenced by factors such as individual phase properties and microstructural configuration that form crucial descriptors of heterogeneity. A review of anisotropy indices proposed in the…
We seek the response, in particular the spectral absorptance, of a rigidly-backed periodically-(in one horizontal~~ direction) ~inhomogeneous ~layer ~composed ~of ~alternating rigid and macroscopically-homogeneous porous portions, submitted…
Auxetic materials are characterized by a negative Poisson's ratio, $\mathrm{\nu}$. As the Poisson's ratio becomes negative and approaches the lower isotropic mechanical limit of $\mathrm{\nu = -1}$, materials show enhanced resistance to…
In seismic waveform inversion, the reconstruction of the subsurface properties is usually carried out using approximative wave propagation models to ensure computational efficiency. The viscoelastic nature of the subsurface is often…
Materials with negative Poisson ratio have the counter-intuitive property of expanding laterally when they are stretched longitudinally. They are accordingly termed auxetic, from the Greek auxesis meaning to increase. Experimental studies…
This paper investigates the effects of plasticity on the effective fracture toughness. A layered material is considered as a modelling system. An elastic-plastic phase-field model and a surfing boundary condition are used to study how the…
This paper is devoted to the exploration of rectangular finite elements' ability to model the stress-strain state of isotropic and orthotropic materials with a negative Poisson's ratio, known as auxetic materials. By employing linear…
Uniform convergence of empirical norms - empirical measures of squared functions - is a topic which has received considerable attention in the literature on empirical processes. The results are relevant as empirical norms occur due to…
We consider the inverse problem of determining the possible presence of an inclusion in a thin plate by boundary measurements. The plate is made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. The…
We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic…
One considers linearly thermoelastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated inclusions. Effective properties (such as compliance and thermal…
We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…
This paper presents an auxetic medium, consisting of a two-dimensional perforated sheet where the holes are arranged in a repetitive pattern. The hexagonal disposition of the perforations makes the medium isotropic in the plane. It is shown…
This paper investigates the asymptotic behaviors of time-harmonic acoustic waves generated by an incident wave illuminating inhomogeneous medium inclusions with high-contrast material parameters. We derive sharp asymptotic estimates and…
Spatially referenced data often have autocovariance functions with elliptical isolevel contours, a property known as geometric anisotropy. The anisotropy parameters include the tilt of the ellipse (orientation angle) with respect to a…
Particulate materials include powders, emulsions, composites, and many others. This is why measuring these has become important for both industry and scientific applications. For industrial applications, the greatest need is to measure…
This work is a natural extension of the authors previous work, Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation, theoretical fundamentals and applications, which established the foundation for…
Using a Cauchy integral formulation of the boundary integral equations, we simulate the erosion a porous medium comprised of up to 100 solid bodies embedded in a Stokes flow. The grains of the medium are resolved individually and erode…
The hardness of materials plays an important role in material design. There are numerous experimental methods to measure the hardness of materials, but theoretical prediction of hardness is challenging. By investigating the correlation…