many earthquakes occur in iran every year and some of these earthquakes cause loss of life and property. consequently earthquake is one of challenging topics not only in iran but also in other active tectonic regions in the world. investigating the mechanism of earthquake as a natural disaster is the first and important step. to study earthquakes, different information such as geometry and beha...

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...

The effects of thermal elastic fluctuations in rubbery materials are examined. It is shown that, due to their interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation, compared to that of classical rubber elasticity. To leading order, this mechanism provides a simple and generic explanation for the peak structure of Mo...

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...

We draw upon existing knowledge of twinning and slip mechanics to develop a diffraction analysis model that allows for empirical quantification of individual deformation mechanisms to the macroscopic behaviors of low symmetry and phase transforming crystalline solids. These methods are applied in studying elasticity, accommodation twinning, deformation twinning, and slip through neutron diffrac...

Abstract. We model the coupled system formed by an incompressible, irrotational fluid and a nonlinear elastic body. We work with large displacement, small deformation elasticity (or St Venant elasticity), which makes the problem very interesting from the physical point of view. The elastic body is three-dimensional Ω ∈ R, and thus it can not be reduced to its boundary Γ (like in the case of a m...

It is typical in smectic liquid crystals to describe elastic deformations with a linear theory when the elastic strain is small. In smectics, certain essential nonlinearities arise from the requirement of rotational invariance. By employing the Bogomol'nyi, Prasad, and Sommerfield decomposition and relying on boundary conditions and geometric invariants, we have found a large class of exact sol...