research

Cross-posted to Biocurious a blog about biology through the eyes of physicists.

Polarization switching-induced shielding or anti-shielding of an electrically permeable crack in a mono-domain ferroelectric material with the original polarization direction perpendicular to the crack is simulated by a phase field model based on the time-dependent Ginzburg-Landau equation. The domain wall energy and the long-range mechanical and electrical interactions between polarizations are taken into account. The phase field simulations exhibit a wing-shape- switched zone backwards the crack tip.

A stiff skin forms on surface areas of a flat polydimethylsiloxane (PDMS) upon exposure to focused ion beam (FIB) leading to ordered surface wrinkles. By controlling the FIB fluence and area of exposure of the PDMS, one can create a variety of patterns in the wavelengths in the micrometer to submicrometer range, from simple one-dimensional wrinkles to peculiar and complex hierarchical nested wrinkles. Examination of the chemical composition of the exposed PDMS reveals that the stiff skin resembles amorphous silica. Moreover, upon formation, the stiff skin tends to expand in the direction perpendicular to the direction of ion beam irradiation. The consequent mismatch strain between the stiff skin and the PDMS substrate buckles the skin, forming the wrinkle patterns. The induced strains in the stiff skin are estimated by measuring the surface length in the buckled state. Estimates of the thickness and stiffness of the stiffened surface layer are estimated by using the theory for buckled films on compliant substrates. The method provides an effective and inexpensive technique to create wrinkled hard skin patterns on surfaces of polymers for various applications. Click here for access to the full article. See also the press release: Applied scientists create wrinkled 'skin' on polymers

This paper presents some developments related to the idea of covariance in elasticity. The geometric point of view in continuum mechanics is briefly reviewed. Building on this, regarding the reference configuration and the ambient space as Riemannian manifolds with their own metrics, a Lagrangian field theory of elastic bodies with evolving reference configurations is developed. It is shown that even in this general setting, the Euler-Lagrange equations resulting from horizontal (referential) variations are equivalent to those resulting from vertical (spatial) variations. The classical Green-Naghdi-Rivilin theorem is revisited and a material version of it is discussed. It is shown that energy balance, in general, cannot be invariant under isometries of the reference configuration, which in this case is identified with a subset of R^3. Transformation properties of balance of energy under rigid translations and rotations of the reference configuration is obtained. The spatial covariant theory of elasticity is also revisited. The transformation of balance of energy under an arbitrary diffeomorphism of the reference configuration is obtained and it is shown that some nonstandard terms appear in the transformed balance of energy. Then conditions under which energy balance is materially covariant are obtained. It is seen that material covariance of energy balance is equivalent to conservation of mass, isotropy, material Doyle-Ericksen formula and an extra condition that we call ‘configurational inviscidity’. In the last part of the paper, the connection between Noether’s theorem and covariance is investigated. It is shown that the Doyle-Ericksen formula can be obtained as a consequence of spatial covariance of Lagrangian density. Similarly, it is shown that the material Doyle-Ericksen formula can be obtained from material covariance of Lagrangian density.