Related papers: Analytical solution of a plane strain pure bending…
We formulate a phenomenological elasto-plastic theory to describe a solid undergoing a structural transition from a square (p4mm) to an oblique (p2) lattice in two dimensions. Within our theory, the components of the strain may be…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonmagnetic, linearly polarized, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the…
The origin of "giant" flexoelectricity, orders of magnitude larger than theoretically predicted, yet frequently observed, is under intense scrutiny. There is mounting evidence correlating giant flexoelectric-like effects with parasitic…
A dual hybrid Virtual Element scheme for plane linear elastic problems is presented and analysed. In particular, stability and convergence results have been established. The method, which is first order convergent, has been numerically…
We developed a lattice dynamical theory of an atomically-thin compressional piezoelectric resonator. Acoustic and optical dynamic displacement response functions are derived and account for frequency-dependent electromechanical coupling.…
The Lattice Boltzmann Method (LBM), e.g. in [ 1] and [2 ], can be interpreted as an alternative method for the numerical solution of partial differential equations. Consequently, although the LBM is usually applied to solve fluid flows, the…
The equations of a planar elastica under pressure can be rewritten in a useful form by parametrising the variables in terms of the local orientation angle, $\theta$, instead of the arc length. This ``$\theta$-formulation'' lends itself to a…
Mindlins systematic procedure of power series expansion for deriving one and two dimensional equations of elastic beams and plates is extended to layered beams and plates with interface slips by adding a step function term to the power…
The quasistatic, Prandtl-Reuss perfect plasticity at small strains is combined with a gradient, reversible (i.e. admitting healing) damage which influences both the elastic moduli and the yield stress. Existence of weak solutions of the…
Budiansky's nonlinear shell theory is particularized to a 2D setting, and thereupon generalized to a fully nonlinear, statically and kinematically exact, theory of strain-gradient elasticity of beams. The governing equations are displayed…
The stressed state of flattened thin elastic sheet, as well as that of translationally symmetric 3D solids, are effectively 2D problems. This paper study equilibrium state-of-stress in metrically-incompatible 2D elastic materials. The…
The present work attempts to present a consistent and efficient approach to piezoelectric laminated beams. The influence of hypotheses on three-dimensional sectional deformations and stress distributions on the estimate of the beam…
Recent works have shown that in contrast to classical linear elastic fracture mechanics, endowing crack fronts in a brittle Green-elastic solid with Steigmann-Ogden surface elasticity yields a model that predicts bounded stresses and…
The energy-based definition provides a viable resolution to the longstanding confusion on the proper definition of $n$-th order rigidity and flexibility in geometric constraint systems. Applying an energy-based local rigidity analysis to…
Poisson-Boltzmann theory is the cornerstone for soft matter electrostatics. We provide novel exact analytical solutions to this non-linear mean-field approach, for the diffuse layer of ions in the vicinity of a planar or a cylindrical…
The problem of the strain of smectics subjected to a force distributed over a line in the basal plane has been solved.
According to the classical theory of elasticity, a plate subjected to a bending moment always deflects with symmetric tensile and compressive strains in its two sides, without overall deformation perpendicular to the bending moment. Here,…
A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed…
Motivated by recent advances in the inverse design of electromagnetic materials, we develop two methods for manipulating flexural waves on thin elastic plates. Firstly, we derive a technique for determining plate pinning or mass-loading of…
We derive a large-strain plate model that allows to describe transient, coupled processes involving elasticity and solvent migration, by performing a dimensional reduction of a three-dimensional poroelastic theory. We apply the model to…