B-bar FEMs for anisotropic elasticity

The topological derivative in anisotropic elasticity

A comprehensive treatment of the topological derivative for anisotropic elasticity is presented, with both the background material and the trial small inhomogeneity assumed to have arbitrary anisotropic elastic properties. A formula for the topological derivative of any cost functional defined in terms of regular volume or surface densities depending on the displacement is established, by combi...

Anisotropic elasticity of experimental colloidal Wigner crystals.

Colloidal particles interacting via a long-range repulsion can, in contrast to hard-sphere systems, exhibit crystalline ordering at low volume fraction. Here we experimentally investigate the structure and properties of such "colloidal Wigner crystals." We find a body-centered-cubic crystalline phase at volume fractions of ϕ≳15%, which exhibits large fluctuations of individual particles from th...

Anisotropic elasticity of magnetically ordered agarose gel.

The physical properties of agarose gel prepared under strong magnetic fields were investigated. The storage modulus was measured by the reflection method with an ultrasonic pulse. The measurement results of the gel's elasticity indicate that agarose gel has anisotropic properties. The elasticity and its anisotropy depend on the concentration of the gel and the magnetic field to which it is expo...

Sharp trace regularity for an anisotropic elasticity system

In this paper, we establish an optimal trace regularity theorem, also known as the hidden regularity theorem [L2], for the anisotropic linear elasticity equation on a bounded domain Ω with Lipschitz boundary. In its simplest form it provides a space-time L estimate for the trace of the normal derivative for the solution. Over the years, such sharp trace regularity theorems have proven to be cru...

An alternative to the Kelvin decomposition for plane anisotropic elasticity