Related papers: Modified Eshelby tensor for an anisotropic matrix …
In the first part of the book, we classify the automorphic representations of {\rm GSp}(2) which are invariant under tensor product with a given quadratic id\`ele class character, via the lifting of automorphic representations of twisted…
In this study, we present a precise anisotropic interpolation error estimate for the Morley finite element method (FEM) and apply it to fourth-order elliptic equations. We do not impose the shape-regularity mesh condition in the analysis.…
The paper presents a numerical study for the finite element method with anisotropic meshes. We compare the accuracy of the numerical solutions on quasi-uniform, isotropic, and anisotropic meshes for a test problem which combines several…
A microscopic expression of the residual electrical resistivity tensor is derived in linear response theory for Rashba electrons scattering at a magnetic impurity with cylindrical or non-cylindrical potential. The behavior of the…
In this paper, we replace the asymptotic enrichments around the crack tip in the extended finite element method (XFEM) with the semi-analytical solution obtained by the scaled boundary finite element method (SBFEM). The proposed method does…
Short pitch deformed helix ferroelectric liquid crystals have numerous applications as active materials in displays, optical telemetry and biomedical devices. In this paper, we derive convenient analytical formulas to calculate the…
In this paper, we extend the recently proposed extended scaled boundary finite element method (xSBFEM)~\cite{natarajansong2013} to study fracture parameters of interfacial cracks and cracks terminating at the interface. The approach is also…
In this study, the fundamental framework of analytical micromechanics is generalized to consider nano-composites with both interface stretching and bending effects. The interior and exterior Eshelby tensors for a spherical nano-inclusion,…
We introduce a novel TRUNC finite element in n dimensions, encompassing the traditional TRUNC triangle as a particular instance. By establishing the weak continuity identity, we identify it as crucial for error estimate. This element is…
The elastoresistivity tensor $m_{ij,kl}$ relates changes in resistivity to strains experienced by a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity…
We introduce and analyze a new mixed finite element method with reduced symmetry for the standard linear model in viscoelasticity. Following a previous approach employed for linear elastodynamics, the present problem is formulated as a…
We present a stable finite element method for incompressible nonlinear elasticity based on a four-field mixed formulation involving the displacement, displacement gradient, first Piola--Kirchhoff stress and pressure. Unlike existing…
Conditions for a maximum or minimum of Poisson's ratio of anisotropic elastic materials are derived. For a uniaxial stress in the 1-direction and Poisson's ratio $\nu$ defined by the contraction in the 2-direction, the following three…
The direct calculation of the elastic and piezoelectric tensors of solids can be accomplished by treating homogeneous strain within the framework of density-functional perturbation theory. By formulating the energy functional in reduced…
We show how the St.Venant compatibility relations for strain in three dimensions lead to twinning for the cubic to tetragonal transition in martensitic materials within a Ginzburg-Landau model in terms of the six components of the symmetric…
We discuss elastic tensegrity frameworks made from rigid bars and elastic cables, depending on many parameters. For any fixed parameter values, the stable equilibrium position of the framework is determined by minimizing an energy function…
A new finite element method (FEM) using meshes that do not necessarily align with the interface is developed for two- and three-dimensional anisotropic elliptic interface problems with nonhomogeneous jump conditions. The degrees of freedom…
A continuum mechanical theory incorporating an extension of Finsler geometry is formulated for fibrous soft solids. Especially if of biologic origin, such solids are nonlinear elastic with evolving microstructures. For example, elongated…
The description of the behavior of a material subjected to multi-physics loadings requires the formulation of constitutive laws that usually derive from Gibbs free energies, using invariant quantities depending on the considered physics and…
Selectively heating a microscopic colloidal particle embedded in a soft elastic matrix is a situation of high practical relevance. For instance, during hyperthermic cancer treatment, cell tissue surrounding heated magnetic colloidal…