Sentence examples for material equations from inspiring English sources

In the case of linear material equations the electromagnetic volume force equals zero.

Numerical results corresponding to certain material combinations and interlayer material equations are presented and analysed.

The latter are derived from the conditions of stress finiteness at the ends of pre-fracture zones and the material equations.

We thereby derive new projection operators for the discrete tensor material equations and obtain a compact numerical scheme for the discrete differential operators.

They are called constitutive or material equations closing the governing equations leading to partial differential equations of the electric potential ϕ, the displacement u i, and the temperature T. The necessary connection for the charge potential is given by the so-called MAXWELL LORENTZ aether relation: D_{i} = varepsilon_{0} E_{i}, (14).

The heat capacity c, coefficients of thermal expansion α ij, components of stiffness tensor C ijkl are assumed to be constant, otherwise the above material equations are not valid, for a thermodynamical derivation of all aforementioned constitutive equations, see (Abali 2016, Sect. 3.3).

There is a well-known material equation for the couple stress with one parameter, see for example (Gao and Park 2007): begin{array}{*{20}l} mu_{ijk} = c S_{jk,i}, end{array} (32).

Normal and shear stresses are assumed to be constant in this zones and to satisfy some material equation, which can be taken from theory or derived experimentally.

First, strain rate dependent mechanical behavior of matrix and fibers are experimentally characterized and for each constituent a dynamic empirical material equation is presented.

The model is based on the pure material equation of state only (no mixture equation of state is used) for the computation of the reaction zone of detonation waves.

We fit Equations 1, 2, and 3 and Supplemental Material, Equation S1 with eight different options and chose the best fit based on the smallest DIC (see Supplemental Material, Table S4).