Small deformations of a viscoelastic body are considered through the linear Maxwell and Kelvin-Voigt models in the quasi-static equilibrium. A robust mixed finite element method, enforcing the symmetry of the stress tensor weakly, is proposed for these equations on simplicial tessellations in two and three dimensions. A priori error estimates are derived and numerical experiments presented. The...

here we denote by σ the stress tensor, by ε the linearized strain tensor, by B(x) the compliance tensor and by ∂φ(·, x) the subdifferential of a convex function φ(·, x). This relation accounts for elasto-viscoplasticity, including a nonlinear version of the classical Maxwell model of viscoelasticity and the Prandtl–Reuss model of elastoplasticity. The constitutive law is coupled with the equati...

The electrostatic interaction among molecules solvated in ionic solution is governed by the Poisson-Boltzmann equation (PBE). Here the hypersingular integral technique is used in a boundary element method (BEM) for the three-dimensional (3D) linear PBE to calculate the Maxwell stress tensor on the solvated molecular surface, and then the PB forces and torques can be obtained from the stress ten...

The governing equations of three dimensional elasticity problems include the six Beltrami-Michell stress compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to the boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usual...

Since a classical charged point particle radiates energy and momentum it is argued that there must be radiation reaction force. Here we present an action for the Maxwell-Lorentz without self interactions model, where each only responds to fields of other particles. The corresponding stress-energy tensor automatically conserves in Minkowski appropriate spacetimes.

Abstract The paper presents analytical approach to electrostatic field for dielectric spheroids problem. For both oblate and prolate fields distributions are derived. variable separation method is applied. Electrostatic force evaluated with the help of Maxwell stress tensor generalized method, material density, coenergy equivalent dipole. Levitation forces versus axis permittivities height pres...

Typically, the force between paramagnetic particles in a uniform magnetic field is calculated using either dipole-based models or the Maxwell stress tensor combined with Laplace's equation for magnetostatics. Dipole-based models are fast but involve many assumptions, leading to inaccuracies in determining forces for clusters of particles. The Maxwell stress tensor yields an exact force calculat...

We describe local shearing box simulations of turbulence driven by the magnetorotational instability (MRI) in a collisionless plasma. Collisionless effects may be important in radiatively inefficient accretion flows, such as near the black hole in the Galactic Center. The MHD version of ZEUS is modified to evolve an anisotropic pressure tensor. A fluid closure approximation is used to calculate...

In this thesis we investigate the superenergy tensor that was introduced by Chevreton in 1964 as an electromagnetic counterpart to the Bel–Robinson tensor for the gravitational field. We show that in Einstein–Maxwell spacetimes with a source-free electromagnetic field, the Chevreton superenergy tensor has many interesting properties. It is a completely symmetric rank-4 tensor and it gives rise ...

A direct numerical simulation method based on the Maxwell stress tensor and a fictitious domain method has been developed to solve flows with suspended paramagnetic particles. The numerical scheme enables us to take into account both hydrodynamic and magnetic interactions between particles in a fully coupled manner. Particles are assumed to be non-Brownian with negligible inertia. Rigid body mo...