Related papers: Elasticity with Arbitrarily Shaped Inhomogeneity
We rigorously derive a Kirchhoff plate theory, via $\Gamma$-convergence, from a three-di\-men\-sio\-nal model that describes the finite elasticity of an elastically heterogeneous, thin sheet. The heterogeneity in the elastic properties of…
It is well known that an annular sheet could wrinkle as a result of axisymmetric tensile loads applied at the edges. In this system, regions under compression appear due to Poisson effect in the azimuthal direction yielding an incompatible…
Investigation of inhomogeneities has wide applications in different areas of mechanics including the study of composite materials. Here, we analytically study an arbitrarily-shaped isotropic inhomogeneity embedded in a finite-sized…
This paper investigates the homogenization, dimension reduction, and linearization of a composite plate subjected to external loading within the framework of non-linear elasticity problem. The total elastic energy of the problem is of order…
This paper focuses on an inverse problem associated with the plate equation which is derived from models in fluid mechanics and elasticity. We establish the unique identifying results in simultaneously determining both the unknown density…
We find a new type of boundary layers that occur at the top and bottom surfaces of an inhomogeneous plate. The boundary layers of this type never occur in homogeneous plates or plates made of layers of homogeneous materials. The thickness…
For a given class of materials, \emph{universal deformations} are those deformations that can be maintained in the absence of body forces and by applying solely boundary tractions. For inhomogeneous bodies, in addition to the universality…
We consider the cylindrical bending problem for an infinite plate as modelled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner…
A rectangular plate of dielectric elastomer exhibiting gradients of material properties through its thickness will deform inhomogeneously when a potential difference is applied to compliant electrodes on its major surfaces, because each…
Continuing a program of examining the behavior of the vacuum expectation value of the stress tensor in a background which varies only in a single direction, we here study the electromagnetic stress tensor in a medium with permittivity…
The ``Eshelby problem" refers to the response of a 2-dimensional elastic sheet to cutting away a circle, deforming it into an ellipse, and pushing it back. The resulting response is dominated by the so-called ``Eshelby Kernel" which was…
We propose a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to use diffusion tensors directly coupled to…
Under compressive creep, visco-plastic solids experiencing internal mass transfer processes have been recently proposed to accommodate singular cnoidal wave solutions, as material instabilities at the stationary wave limit. These…
In the framework of linearized elasticity, we study thin elastic composite plates with thickness $\delta$. The plates contain small, rigid rectangular plates distributed periodically along $\varepsilon$. Between two neighboring rigid plates…
We study elasticity of spontaneously orientationally-ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized for example by nematic elastomers and gels. We show that local heterogeneities and elastic…
In this paper, a method of local perturbations, previously successfully applied to decompose the problem of elasticity in the system of connected thin rods and beams [Kolpakov and Andrianov, 2013], is used to study the asymptotic behaviour…
In the late 1950's, Eshelby's linear solutions for the deformation field inside an ellipsoidal inclusion and, subsequently, the infinite matrix in which it is embedded were published. The solutions' ability to capture the behavior of an…
Liquid crystal elastomers (LCEs) marry the large deformation response of a cross-linked polymer network with the nematic order of liquid crystals pendent to the network. Of particular interest is the actuation of LCE sheets where the…
Photoelasticity is employed to investigate the stress state near stiff rectangular and rhombohedral inclusions embedded in a 'soft' elastic plate. Results show that the singular stress field predicted by the linear elastic solution for the…
Metric anomalies arising from a distribution of point defects (intrinsic interstitials, vacancies, point stacking faults), thermal deformation, biological growth, etc. are well known sources of material inhomogeneity and internal stress. By…