By Benoit Cushman-Roisin

This is often the 1st and in basic terms introductory point textual content to be had on geophysical fluid dynamics. Emphasis is put on physics, no longer arithmetic and easy and complicated laboratory demonstrations are featured in so much chapters. distinct modern issues, of weather dynamics and equatorial dynamics, together with the greenhouse impact, worldwide warming and southern oscillation are coated.

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**Example text**

4. Stress-strain curve for aluminium for various strain rates (Hauser et aI. 1960). 2) = G is the shear modulus of elasticity, E is Young's modulus and v is Poisson's ratio. 3) or 8ij = Eijkl(Jkl, where efjkl, E ijkl denote the material coefficients. g. E, vary with temperature and strain rate i. Although the relationship between (Jij and 8 kl is nonlinear in the global sense, linearity can still be considered to be valid for small strains. 4) where ifj are components of the strain rate tensor due to elastic deformation, ie, T are components of the strain rate tensor due to temperature dependent material properties, i'f/ are components of the strain rate tensor due to strain rate dependent material properties, and i& are components of the thermal strain rate tensors.

Ij are linear thermal expansion tensor components, the above expression becomes . = Eijkl(Jkl . ijT. 1 Idealization of Tension Test Linear idealizations of tension tests most often used in the literature are illustrated in Fig. 1. They show the following materials (a) rigid ideal-plastic, (b) ideal elasto-plastic, (c) linear hardening rigid-plastic, (d) linear hardening elasto-plastic. 1 c) {Et: Et:[1-w(e)] (e :::;; (J 0/ E), (e ~ (Jo/E). 1 d) Et: . where w(e) = E -E E1 ( 1 - (Jo) Nonlinear idealizations of work-hardening materials are presented in Fig.

Besides the deformation rate tensor d(x, t) we introduce also the Green-Lagrange strain rate tensor E( X, t), calculated as the material derivative of the Green-Lagrange finite strain. 56) Dt (ds) = 2 Dt [EKM(X, t)]dXKdXM· The tensors d(x, t) and E( X, t) are different measures of strain rate in Euler and Lagrange formulation, respectively: They are connected by the relationship . DEKM EKM(X,t) = ~ = [OX; oX :lX :lX u K U j M d;/x,t) ] x = x(X,t) . 60) m=O (a = 1,2,3), where AIX are principal stretches, and the scalar function f(AIX) satisfies the relations f(1) = 0, /,(1) = 1.