Modelling Propagating Bloch Waves in Magnetoelectroelastic Phononic Structures with Kagomé Lattice Using the Improved Plane Wave Expansion

We studied the dispersion diagram of a 2D magnetoelectroelastic phononic crystal (MPnC) with Kagomé lattice. The MPnC is composed of BaTiO3–CoFe2O4 circular scatterers embedded in a polymeric matrix. The improved plane wave expansion (IPWE) approach was used to calculate the dispersion diagram (only propagating modes) of the MPnC considering the classical elasticity theory, solid with transverse isotropy and wave propagation in the xy plane. Complete Bragg-type forbidden bands were observed for XY and Z modes. The piezoelectric and the piezomagnetic effects significantly influenced the forbidden band widths and localizations. This investigation can be valuable for elastic wave manipulation using smart phononic crystals with piezoelectric and piezomagnetic effects.

The J-Integral for Gradient Theory of Piezoelectricity

The size-dependent features concerning the mechanical behavior of the micro/nanoelectronic structures are well known from experiments. They are described by the strain-gradient effect in this paper since the classical elasticity theory fails to capture the size effect of the nanostructures. The electric field-strain gradient coupling is considered in the constitutive equations of the material and the governing equations are derived with the corresponding boundary conditions using the variational principle. The path independent J-integral is derived for fracture mechanics analysis of piezoelectric solids described by the gradient theory.

Bending of a Cosserat Elastic Bar of Square Cross Section: Theory and Experiment

Pure bending experiments on prismatic bars of square cross section composed of reticulated polymer foam exhibit deformation behavior not captured by classical elasticity theory. Perhaps the clearest example of this is the observed sigmoidal deformation of the bars' lateral surfaces, which are predicted by classical elasticity theory to tilt but remain planar upon pure moment application. Such foams have a non-negligible length scale compared to the bars' cross-sectional dimensions, whereas classical elasticity theory contains no inherent length scale. All these facts raise the intriguing question: is there a richer, physically sensible, yet still continuum and relatively simple elasticity theory capable of modeling the observed phenomenon in these materials? This paper reports our exploration of the hypothesis that Cosserat elasticity can. We employ the principle of minimum potential energy for homogeneous isotropic Cosserat linear elastic material in which the microrotation vector is taken to be independent of the macrorotation vector (as prior experiments indicate that it should be in general to model such materials) to obtain an approximate three-dimensional solution to pure bending of a prismatic bar having a square cross section. We show that this solution, and hence Cosserat elasticity, captures the experimentally observed nonclassical deformation feature, both qualitatively and quantitatively, for reasonable values of the Cosserat moduli. A further interesting conclusion is that a single experiment—the pure bending one—suffices to reveal directly, via the observation of surface deformation, the presence of nonclassical elastic effects describable by Cosserat elasticity.

Effect of Surface Stress on the Deformation of an Half-Plane Applied to Nanometer Materials

Based on the two distinct solutions, as classical solution for an elastic half space containing a circular hole at nanoscale, the complex variable and superposition method was proposed and employed to investigate the state of stress and displacement in an half space with surface tension for nanoelastic material.The results indicate some characteristics in half space which are different from those in classical elasticity theory .

The Analysis of the Effect of Surface Stresses at Nanoscale

Based on classical elasticity theory, the effects of surface stresses on the nanosized contact problem in an elastic half-plane which contains a nanocylindrical hole are analyzed. Meanwhile, the effects of surface energy of the contact nanosized surface are considered. The complex variable function method is applied to derive the fundamental solution of the contact problem. As example, the deformation induced by a distributed traction of cosine function on the nanosized surface is analyzed in detail. The results tell some interesting characteristics in contact mechanics, which are different from those in classical elasticity theory.

Spherical Wave Propagation in a Poroelastic Medium with Infinite Permeability: Time Domain Solution

Exact time domain solutions for displacement and porepressure are derived for waves emanating from a pressurized spherical cavity, in an infinitely permeable poroelastic medium with a permeable boundary. Cases for blast and exponentially decaying step pulse loadings are considered; letter case, in the limit as decay constant goes to zero, also covers the step (uniform) pressure. Solutions clearly show the propagation of the second (slow)p-wave. Furthermore, Biot modulusQis shown to have a pronounced influence on wave propagation characteristics in poroelastic media. Results are compared with solutions in classical elasticity theory.

Sudden Pressurization of a Spherical Cavity in a Poroelastic Medium

Governing equations of poroelastodynamics in time and frequency domain are derived. The continuity equation complements the momentum balance equations. After reduction for spherical symmetry (geometry and loading), the governing equations in frequency domain are solved by introducing wave potentials. The wave propagation velocities are obtained as the real parts of the characteristic equation of the coupled ODE system. Time domain solution for Dirac type boundary pressure is obtained through numerical inversion of transformed solutions. The results are compared to the solution in classical elasticity theory found in the literature.

When Small is Different: The Case of Membranes Inside Tubes

ABSTRACTRecently, classical elasticity theory for thin sheets was used to demonstrate the existence of a universal structural behavior describing the confinement of sheets inside cylindrical tubes. However, this kind of formalism was derived to describe macroscopic systems. A natural question is whether this behavior still holds at nanoscale. In this work, we have investigated through molecular dynamics simulations the structural behavior of graphene and boron nitride single layers confined into nanotubes. Our results show that the class of universality observed at macroscale is no longer observed at nanoscale. The origin of this discrepancy is addressed in terms of the relative importance of forces and energies at macro and nano scales.