Non-linear hyperelastic response of reinforced elastomers is modeled using a novel three-dimensional mixed finite element method with a nonlocal pressure field. The element is unconditionally convergent and free of spurious pressure modes. Nonlocal pressure is obtained by an implicit gradient technique and obeys the Helmholtz equation. Physical motivation for this nonlocality is shown. An impli...

Single-walled carbon nanotubes (SWCNTs) in an elastic medium under a longitudinal magnetic field have piqued the interest of researchers as elements utilized nanoelectro-magneto-mechanical systems (NEMMS). This work presents vibration analysis embedded SWCNTs using nonlocal second-order strain gradient elasticity theory. Considering surface effect, characteristic equation motion for SWCNT polym...

We investigate the transient dynamics of a sheared suspension neutrally buoyant particles under pressure-imposed conditions, subject to sudden change in shear rate or external pressure. Discrete Element Method simulations show that, depending on flow parameters (particle and system size, initial volume fraction), early stress response may strongly differ from prediction Suspension Balance Model...

We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure. These properties allow for accurate computations of stationary states and long-time asymptotics demonstrated by suitably chosen test cases in which these features of the scheme are essential. The proposed scheme is able to cope with non-smooth stationary st...

We investigate a class of nonlocal conservation laws with the nonlinear advection coupling both local and nonlocal mechanism, which arises in several applications such as the collective motion of cells and traffic flows. It is proved that the C solution regularity of this class of conservation laws will persist at least for a short time. This persistency may continue as long as the solution gra...

In this work, we investigate the existence and nonexistence of nonnegative solutions to a class nonlocal elliptic systems set in bounded open subset , where gradients unknowns act as source terms (see $(S)$ below). Our approach can be also used treat other nonlinear with different structures. This work extends previous results obtained local case by fourth author his coworkers, points significa...