Till now, different constitutive models have been applied to model the hot deformation flow curves of different materials. In this research, the hot deformation flow stress of API X65 pipeline steel was modeled using the power law equation with strain dependent constants. The results was compared with the results of the other previously examined constitutive equations including the Arrhenius eq...

In this paper we discuss some thermoelastic and thermoviscoelastic models obtained from the Gurtin theory, based on invariance of entropy under time reversal. We derive differential systems where temperature velocity are ruled by generalized versions Moore-Gibson-Thompson equation. one-dimensional case, provide a complete analysis evolution, establishing an existence uniqueness result valid for...

In this paper, we are concerned with stable solutions to the fractional elliptic equation $$\begin{aligned} (-\Delta )^s u=e^u \text{ in } {\mathbb {R}}^{N}, \end{aligned}$$ where $$(-\Delta )^s$$ is Laplacian $$0<s<1$$ . By developing a new technique non-compactly supported test functions, establish nonexistence of provided that $$N<10s$$ This result optimal when $$s\uparrow 1$$ On other hand,...

Abstract. We consider here a discrete system of spheres interacting through a lubrication force. This force is dissipative, and singular near contact: it behaves like the reciprocal of interparticle distance. We propose a macroscopic constitutive equation which is built as the natural continuous counterpart of this microscopic lubrication model. This model, which is of the newtonian type, relie...

Gauss’ law and the equation of continuity must be satisfied in all materials be they solids, liquids or gases. Most materials are classified as simple materials; i.e., their electrical properties are linear, isotropic and homogeneous. Charge transport in these simple materials should be described by a constitutive equation known as Ohm’s law. When Ohm’s law is combined with Gauss’ law and the e...

We present a constitutive model capturing some of the experimentally observed features of soft biological tissues: nonlinear viscoelasticity, nonlinear elastic anisotropy, and nonlinear viscous anisotropy. For this model we derive the equation governing rectilinear shear motion in the plane of the fiber reinforcement; it is a nonlinear partial differential equation for the shear strain. Special...