Truesdell Noll

The notion of state was derived from the theory of mechanics and of thermodynamics and generalised by mathematical system theory. Following the tradition of the field theory of continua (Truesdell Noll, 1965) quantities of a theory can be classified into two categories state variables and constitutive quantities. State variables are functions such that their values... 

This is the hypoelastic constitutive equation considered by Truesdell (see Truesdell and Noll [20]). In large deformations, this equation should be independent of the motion of the observer, a property termed objectivity, i.e., it should be invariant under rigid rotation and translation of the coordinate frame. In order to investigate this property, a coordinate transformation (A.50) is applied. If the elastic stress rate relation is to be unchanged in the new coordinate system denoted x, then... 

Since elastic behavior is important for inelastic constitutive equations, it is instructive to examine the behavior of the hypoelastic constitutive equation (5.112) in some detail. This has been addressed variously by Truesdell and Noll [20], Eringen [16], Atluri [17], and others. 

Truesdell, C. and Noll, W., The Non-Linear Field Theories of Mechanics, in Encyclopedia of Physics, Vol. III/3 (edited by Fliigge, S.), Springer-Verlag, Berlin, 1965. 

Kinematical relations in large deformations are given here for reference. Most of the material is well known, and may be extracted or deduced from the comprehensive expositions of Truesdell and Toupin [19], Truesdell and Noll [20], or other texts in continuum mechanics, where further details may be found. 

C Truesdell, W Noll. The Non-Linear Field Theories of Mechanics. In S Fliige Ed. Handbuchder Physik Berlin/Heidelberg/New York Springer III/3, 1965. New York Springer-Verlag. 

Truesdell, C., Noll, W. The nonlinear field theories of mechanics. In Fliigge, S. (ed.) Hand-... 

Truesdell, C.A., Noll, W. (1965). The non-linear field theories of mechanics. Handbuch der Physik 3(3 1-602, S. Fltlgge, ed. Springer Berlin. 

To characterize the position and motion of a material point we will content ourselves with the use of Cartesian coordinates. This frees us from the various, mainly mathematical difficulties, involved in the use of more general coordinate systems. For cases where non-Cartesian coordinates are imavoidable the reader is referred to more comprehensive treatments or textbooks on continnttm mechanics (Becker and Burger 1975 Eringen 1967 Haupt 2000 Truesdell and Noll 1965 Truesdell and Toupin 1960). 

Truesdell C, Noll W (1965) The nonlinear field theories of mechanics. In FlOgge S (ed) Encyclopedia of physics, vol III/3. Springer, Heidelberg Truesdell C, Toupin RA (1960) The classical field theories. In Flugge S (ed) Encyclopedia of physics, vol III/l. Springer, Heidelberg... 

Truesdell C, Noll W (1965) The nonlinear field theory of mechanics. In Hugge S (ed) Encyclopedia of physics, III/3. Springer, Berlin... 

Moreover h i) is called obliviator of order r and it satisfies the following conditions (Truesdell and Noll 1965) ... 

Following the principles of continuum mechanics, the balance relations of mechanics and electrodynamics are presented. They follow general principles or the laws of nature. Based on the principles by Truesdell and Noll (2003), the balance equations... 

C.A. TRUESDELL W. NOLL The Non-linear Field Theories in Mechanics. Handbuch derPhysik III/3, edited by S. FLUGGE, Springer-Verlag, Berlin 1965... 

Note that since m(s) and a( i, 2) are functions only of time y, then t]q, y3, and v are constants. A material that can be represented by the constitutive equation given in Eq. (3.76) is called a Coleman-Noll second-order fluid (Coleman and Markovitz 1964 Truesdell and Noll 1965). For steady-state simple shear flow, Eq. (3.76) yields... 

Here, in the commonly accepted notation, we have set the scalar function Lagrange multiplier to be A = — A2. The stress vector t and generalised stress vector s take the forms (cf. Truesdell and Noll [270, p.40], Goodbody [115, p.207])... 

C. Truesdell and W. Noll in Handbuch der Physik, S. Fliigge (Ed.), Volume III/3, Springer-Verlag, Berlin, 1965. 

---