According to reference (see [2, 3]), the involute and evolute curves of the spacelike curve a in E1 with a spacelike binormal or a spacelike

principal normal in Minkowski 3-space have been investigated.

Since the curve [alpha](t) is also in space, there exists Frenet frame {T, N, B} at each points of the curve where T is unit tangent vector, N is

principal normal vector and B is binormal vector, respectively.

where [lambda] = g([alpha], N), [mu] = g(a, T), and v = g([alpha], [B.sub.2]) are the

principal normal, the tangential, and the second binormal component of the position vector of the curve, respectively.

They found parametrization of constant slope surfaces for the tangent, the

principal normal, the binormal and the Darboux indicatrices of a space curve.

The

principal normal stresses and maximum shear stress together with the angle of the principal axis can be determined from the applied stresses (fx, fy and fs) using the following equations [Bruhn, 1973], [Niu, 2005]:

The

principal normal stress differences, [[sigma].sub.E], is a measure of elastic component of a viscoelastic system undergoing deformation (for example, in a capillary rheometer) and is a function of filler loading, temperature, and the nature of the fluid.

Well-known partner curves are the Bertrand curves, which are defined by the property that at the corresponding points of two space curves the

principal normal vectors are common.

Let [alpha] : [a, b] [right arrow] [E.sup.3.sub.1] be a unit-speed spacelike curve with timelike

principal normal. A tubular surface of radius [lambda] > 0 about a is the surface with parametrization

The vectors T, N, B in (2.1) are called the vectors of the tangent,

principal normal and the binormal line of c, respectively.

On the basis the resultants of three papers earlier mentioned, the

principal normal stresses in the plastic and elastic region is calculated.

The

principal normal stress difference increases nonlinearly with shear stress.

Then T, N, [B.sub.1], [B.sub.2] are, respectively, the tangent, the

principal normal, the binormal (the first binormal), and the trinormal (the second binormal) vector fields.