Necessary and Sufficient Elastic Stability Conditions in Various Crystal Systems

While the Born elastic stability criteria are well-known for cubic crystals, there is some confusion in the literature about the form it should take for lower symmetry crystal classes. We present here closed form necessary and sufficient conditions for elastic stability in all crystal classes, as a concise and pedagogical reference to stability criteria in non-cubic materials

An analytical study of effects on aeroelasticity on control effectiveness

Various uses of the Elastic Stability Derivative (ELASRAD) program are described. Topics include structural influence coefficient matrices of wings, arrow wing structural analysis, and graphic display of wing structures. The rigid and elastic stability derivatives were calculated for Transonic Aircraft Technology Project aircraft

Drag enhancement and drag reduction in viscoelastic flow

Creeping flow of polymeric fluid without inertia exhibits elastic instabilities and elastic turbulence accompanied by drag enhancement due to elastic stress produced by flow-stretched polymers. However, in inertia-dominated flow at high \mbox{Re} and low fluid elasticity $El$, a reduction in turbulent frictional drag is caused by an intricate competition between inertial and elastic stresses. Here, we explore the effect of inertia on the stability of viscoelastic flow in a broad range of control parameters $El$ and (\mbox{Re}, \mbox{Wi}). We present the stability diagram of observed flow regimes in \mbox{Wi}-\mbox{Re} coordinates and find that instabilities' onsets show unexpectedly non-monotonic dependence on $El$. Further, three distinct regions in the diagram are identified based on $El$. Strikingly, for high elasticity fluids we discover a complete relaminarization of flow at Reynolds number of the order of unity, different from a well-known turbulent drag reduction. These counterintuitive effects may be explained by a finite polymer extensibility and a suppression of vorticity at high \mbox{Wi}. Our results call for further theoretical and numerical development to uncover the role of inertial effect on elastic turbulence in a viscoelastic flow.Comment: 8 pages, 6 figure

Linear Stability Analysis for Plane-Poiseuille Flow of an Elastoviscoplastic fluid with internal microstructure

We study the linear stability of Plane Poiseuille flow of an elastoviscoplastic fluid using a revised version of the model proposed by Putz and Burghelea (Rheol. Acta (2009)48:673-689). The evolution of the microstructure upon a gradual increase of the external forcing is governed by a structural variable (the concentration of solid material elements) which decays smoothly from unity to zero as the stresses are gradually increased beyond the yield point. Stability results are in close conformity with the ones of a pseudo-plastic fluid. Destabilizing effects are related to the presence of an intermediate transition zone where elastic solid elements coexist with fluid elements. This region brings an elastic contribution which does modify the stability of the flow

On the stability of equilibrium of continuous systems Technical report no. 65-1

Stability of equilibrium of linear elastic continuum - Galerkin metho

Absence of Two-Dimensional Bragg Glasses

The stability to dislocations of the elastic phase, or ``Bragg glass'', of a randomly pinned elastic medium in two dimensions is studied using the minimum-cost-flow algorithm for a disordered fully-packed loop model. The elastic phase is found to be unstable to dislocations due to the quenched disorder. The energetics of dislocations are discussed within the framework of renormalization group predictions as well as in terms of a domain wall picture.Comment: 5 pages, REVTEX, 3 figures included. Further information can be obtained from [email protected]

Determining the anisotropic traction state in a membrane by boundary measurements

We prove uniqueness and stability for an inverse boundary problem associated to an anisotropic elliptic equation arising in the modeling of prestressed elastic membranes.Comment: 6 page