Journal of Elasticity最新文献

This paper studies surface waves called Bleustein–Gulyaev (BG) waves in piezoelectricity. They propagate along the surface of a homogeneous piezoelectric half-space whose constituent material has (C_{6}) hexagonal symmetry, where the surface is subject to the mechanically-free and electrically-closed condition. We revisit the Barnett–Lothe integral formalism for general piezoelectricity and give straightforward proofs, which only use the positive definiteness of the elasticity tensor and of the dielectric tensor, to derive fundamental properties of the Barnett–Lothe tensors. This leads us to obtain a criterion for the existence of subsonic surface waves. Moreover, when the waves propagate in the direction of the 1-axis along the surface of the piezoelectric half-space (x_{2}le0) of (C_{6}) hexagonal symmetry whose 6-fold axis of rotational symmetry coincides with the 3-axis, we compute explicitly the phase velocity of the BG waves and investigate its perturbation, i.e., the shift in the velocity due to a perturbation of the material constants which need not have any symmetry.

Simple fiber reinforcing patterns can serve to guide deformations in specialized ways if the material experiences expansion due to some sort of swelling phenomenon. This occurs even when the only activation is via the material swelling itself; the fibers being a passive hyperelastic material embedded in a swellable hyperelastic matrix. Using anisotropic hyperelasticity where the usual incompressibility constraint is generalized to model swelling, we consider such fiber guided deformation in the context of a circular cylinder subject to uniform swelling. The material is taken to be transversely isotropic with a fiber pattern corresponding to helical spirals in each cross section. This paper extends previous work which had examined a traction free outer radius that expanded while the inner radius was held fixed. Because of the spiral pattern, the tube in these previous studies exhibited increasing twist as the swelling proceeded. The problem considered here takes both inner and outer radius as free surfaces, thus causing the amount of radial expansion itself to be unknown. It is found that the spiral fiber pattern again induces a twist, and that this pattern also influences the nature of the radial expansion.

In the setting of either compressible or incompressible Finite Elastostatics, Agmon’s condition may be formulated in terms of an algebraic Riccati equation. These equations are studied under the assumption of Strong Ellipticity.

A dual variational principle is defined for the nonlinear system of PDE describing the dynamics of dislocations in elastic solids. The dual variational principle accounting for a specified set of initial and boundary conditions for a general class of PDE is also developed.

Dilational materials, for which the angles between pairs of material fibers are preserved under deformations, are an important class of metamaterials. Although these materials are typically made by assembling discrete elemental building blocks in repeating patterns, continuum mechanics provides a powerful tool for exploring their macroscopic properties and response. We present an analysis of the constraint, the constitutive relation, and the equilibrium equations for homogeneous and isotropic dilational elastic material surfaces. We also describe the possibility of penalizing deviations from local area preservation to yield a framework for approximating isometric deformations of unstretchable elastic material surfaces.