is the Maxwell relaxation time [24]. This relaxation time is a convenient approximation to the timescale of deformation where the transition from purely viscous behavior to purely elastic behavior occurs. The purely viscous response of a silicate melt is termed “liquid” behavior whereas the purely elastic response is termed “glassy” behavior. The term silicate melt is used to describe molten si...

A mathematical theory of time-dependent dislocation mechanics of unrestricted geometric and material nonlinearity is reviewed. Within a ‘small deformation’ setting, a suite of simplified, but interesting, models, namely a nonlocal Ginzburg Landau, a nonlocal level set, and a nonlocal generalized Burgers equation are derived. In the finite deformation setting, it is shown that an additive decomp...

A mathematical theory of time-dependent dislocation mechanics of unrestricted geometric and material nonlinearity is reviewed. Within a “small deformation” setting, a suite of simplified and interesting models consisting of a nonlocal Ginzburg Landau equation, a nonlocal level set equation, and a nonlocal generalized Burgers equation is derived. In the finite deformation setting, it is shown th...

A novel physics-inspired model is proposed for image structure representation. The deformable elastic grid is defined on digital images. The attracting force between adjacent points is defined according to the gray-scale difference, which is the source of force causing the deformation of the elastic grid. The final shape of the grid after deformation can represent image structure information, b...

Elastic deformation on the surfaces of molecular crystals can be imaged using a variant of lateral force microscopy in which the tip is scanned parallel to the cantilever axis. The shear force transverse to this direction has a distinctly different origin than the friction force as determined by the tip velocity and temperature dependence of the cantilever torque. An elastic deformation model f...

The static deformation of gravitating elastic earth model is studied in some detail. It is found that the problem becomes well posed if we discard the stress-strain relation in the liquid core. A convenient formulation, in which derivative of density does not appear, is proposed in the liquid core by introducing a new variable. Static solutions obtained by the present theory are compared with d...

Fibronectin (FN) textiles are built as nanometer-thick fabrics. When uniaxially loaded, these fabrics exhibit a distinct threshold between elastic and plastic deformation with increasing stretch. Fabric mechanics are modeled using an eight-chain network and two-state model, revealing that elastic properties of FN depend on conformational extension of the protein and that plastic deformation dep...

The paper introduces a new alternative towards fabrication of auxetic metamaterials (materials with negative Poisson’s ratio) controlled by geometric transformations. These transformations are derived from the theory of small (infinitesimal) elastic deformation superimposed on finite elastic deformations. By using this theory, a cylindrical region filled with initial deformed foam is transforme...

We used a novel diffraction-based method to extract the local, atomic-level elastic strain in nanoscale amorphous TiAl films during in situ transmission electron microscopy deformation, while simultaneously measuring the macroscopic strain. The complementary strain measurements revealed significant anelastic deformation, which was independently confirmed by strain rate experiments. Furthermore,...

The paper presents a new parameter-free approach to non-rigid image registration, where displacements, obtained through a mapping of boundary structures in the source and target image, are incorporated as hard constraints into elastic image deformation. As a consequence, our approach does not contain any parameters of the deformation model (elastic constants). The approach guarantees the exact ...