Summary The stress-energy tensor for the perfect magnetofluid is considered to show that i) the energy variation is affected by the magnetic field, and ii) the energy density and the matter density conserve along the flow vector if and only if the magnitude of the magnetic field conserves ...
A perfect fluid, which was discussed in a previous post, will always have an isotropic pressure by definition. Note that we have not considered all possible casses of the stress energy tensor, such as those containing radiation and not matter. I am not sure why you are trying to consider...
The description of the constitutive behavior of this type of material relies on the identification of an appropriate strain-energy function (SEF) from which the stress-strain relation and its derivative, the elasticity tensor, can be derived (for more information on nonlinear continuum mechanics, ...
Here, μ, KB are the shear modulus and bulk modulus, respectively, and are in general functions of temperature, while I¯¯, I are fourth- and second-order identity tensors and ‘⊗’ is the notation for outer tensor product. Inelastic strain includes both strain rate-independent plastic...
As I'm sure I've mentioned before, I've heard people say that stress and pressure terms in the energy tensor act as a gravitational source, but I don't understand how this could be, given that these terms can simply appear or disappear (in a non-stationary situation), unlike energy an...
The work done to evolve the shear stress from σ s to σ d is σ s − σ d D c , referred to as the fracture energy. The crack half-length is L , of which F = L − R is the half-length of the developed part of the crack on which the shear stress is equal to σ d...
In the theory of elasticity, stress is usually defined 123 Journal of Nonlinear Science (2023) 33:31 Page 3 of 32 31 as the variational derivative of the energy with respect to a deformation tensor; it then naturally is a rank-2 tensor, twice contravariant in the case of the Cauchy ...
where i is a free index (i = 1, 2, 3), x is the Cartesian coordinate, σij are the components of the stress tensor and D/Dt is the Lagrangian (material) derivative. Einstein summation rules on repeated indices are applied. The acceleration of gravity in the ith direction is gi,...
Large strain formulation is more complex than small strain formulation because of geometric effects. Cauchy stress tensorσcan be calculated as the instantaneous stressσ0minus viscous stress relaxation termsσi: $${\varvec{\sigma}}\left(t\right)={{\varvec{\sigma}}}_{0}\left(t\right)-\sum...
where the terms Cm, Dm, Pm, Gm, ∏m, Ωm and εm consist, respectively, of the rate of advection of Rm, the rate of diffusion of Rm, the rate of shear stress production tensor of Rm, the rate of buoyancy production tensor of Rm, the transport of Rm due to turbulent pressure–str...