To better understand the rheological response of PP/HNT nanocomposites prepared with and without water injection, especially the PP-HNTs interaction in P-H5 and P-H5-W samples, a truncated K-BKZ constitutive equation
There are tree constitutive restrictions of the third grade fluid with the constitutive equation
(13) (see V.
A constitutive equation
can represent the material's flow behavior and has been widely used as inputs for finite element analyses to simulate the response of materials under specific processing conditions .
The Weibull distribution  is further used to describe the damage evolution of microdefect, and then the material constitutive equation
and load displacement equation considering damage and fractal characteristics are deduced to obtain the modified acoustic emission statistical model.
The hard rock constitutive equation
considering the thermal-mechanical coupling is given by (17) after the damage threshold point.
Therefore the canopy is described by Kirchhoff material constitutive equation
in this paper.
During 1996, Gent publishes a short note  where he proposed a new constitutive equation
for the nonlinear elastic behavior of rubber like materials.
After substantial algebraic manipulations of Maxwell's equations, considering the constitutive equation
, we obtain the following set of coupled differential equations of the z-components of the electric and magnetic fields:
In the constitutive equation
(2), derivative order a is bounded 0 < [alpha] < 1, f stands for the force in the viscoelastic rod, and [E.sub.[alpha]], [A.sub.[alpha]], and [l.sub.[alpha]] are modulus of elasticity, cross-sectional area, and length of the viscoelastic rod.
Specifically, the constitutive equation
of nonlocal elasticity for homogenous and isotropic elastic solids read
With the help of inequality (10) by taking into account the constitutive equation
[(2).sub.6] and the Schwarz's inequality, we obtain:
Combining the measured stress growth coefficient and the BKZ constitutive equation
, the DF can be deduced indirectly.