The classical phase-field model represents a coupling of an Allen-Cahn type nonlinear equation with a standard diffusion equation and has been proposed to describe uniform phase separation in a pure substance. This research considers an extension of that model which incorporates a more accurate approximation to the diffuse interface between states of matter through the use of a nonlocal operato...

For classical elasticity, the constitutive equations (Hooke’s law) have the same functional form for both homogeneous and nonhomogeneous materials. However, for straingradient elasticity, such is not the case. This paper shows that for strain-gradient elasticity with volumetric and surface energy (Casal’s continuum), extra terms appear in the constitutive equations which are associated with the...

The nonlocal Kuramoto-Sivashinsky equation arises in the modeling of the flow of a thin film of viscous liquid falling down an inclined plane, subject to an applied electric field. In this paper, the authors show that, as the coefficient of the nonlocal integral term goes to zero, the solution trajectories and the maximal attractor of the nonlocal Kuramoto-Sivashinsky equation converge to those...

The lateral free vibration of micro-rods initially subjected to axial loads based on a nonlocal continuum theory is considered. effects long-range interaction fields the natural frequencies and modes are examined. A simply supported micro-rod taken as an example; linear responses observed by two different methods, including separation variables multiple scales analysis. relations between mode d...

On the local systems hamiltonian in the weakly nonlocal Poisson brackets. Abstract We consider nonlocal field-theoretical Poisson brackets containing the operator of integration in the nonlocal part. The main attention is given to the nonlocal brackets of Hydrodynamic Type for which we introduce the Physical and Canonical forms. We use the Canonical form of these brackets for the investigation ...

In this paper, mechanics of continuum with general form nonlocality in space and time is considered. Some basic concepts nonlocal are discussed. General fractional calculus (GFC) vector (GFVC) used as mathematical tools for constructing media time. Balance equations mass, momentum, energy, which describe conservation laws continuum, derived by using the fundamental theorems GFC. The balance equ...

This paper investigates the lateral vibration of single-layered graphene sheets based on a new theory called doublet mechanics with a length scale parameter. After a brief reviewing of doublet mechanics fundamentals, a sixth order partial differential equation that governs the lateral vibration of single-layered graphene sheets is derived. Using doublet mechanics, the relation between natural f...

From its early days the SPH method has been criticised for shortcomings namely tensile instability and consistency. Without thorough understanding of attempts were made to make classical consistent stable which resulted in local Total Lagrangian forms similar finite element method. In this paper we derived analysed a nonlocal similarity with Bazant’s imbricate continuum. addition, provides comp...