Definition Of Stress Tensor Research Articles

Formulations of nonlocal continuum mechanics based on a new definition of stress tensor

In this paper, attention is given to some basic problems in nonlocal continuum mechanics. Firstly, a surface-induced traction is introduced through nonlocal residuals of the surface. By it, a new measure of stress called the nonlocal stress is defined. The corresponding nonlocal stress formula and nonlocal balance equations distinguishing from the existing forms are established systematically. The existence of nonlocal residuals of body force, body moment and energy is investigated in detail based on the objectivity of the nonlocal balance equation of energy. Based on these results, the nonlocal hyperelastic constitutive equation is consistently deduced. Finally, the linear nonlocal elasticity is used to analyse the lattice contraction on a crystal surface induced by the surface-induced traction. The effects of the ``boundary layer'' are discussed. Some interesting results are given.

Can the definition of mechanical stress tensor be applied to a dielectric fluid in an electrostatic or magnetostatic field?

It is proved that, for an uncharged and linear dielectric fluid at rest and in local equilibrium in an electrostatic or magnetostatic field, the definition of stress tensor employed in continuum mechanics is inconsistent with the assumption that the stress tensor depends only on the local values of mass density, temperature, electric- or magnetic-field components and the derivatives of these quantities with respect to space and time.