By Zhi-He Jin (auth.), David Y. Gao, Ray W. Ogden (eds.)

As any human task wishes ambitions, mathematical examine wishes difficulties -David Hilbert Mechanics is the paradise of mathematical sciences -Leonardo da Vinci Mechanics and arithmetic were complementary companions when you consider that Newton's time and the historical past of technological know-how indicates a lot facts of the ben eficial impact of those disciplines on one another. pushed through more and more complex smooth technological functions the symbiotic dating among arithmetic and mechanics is constantly becoming. besides the fact that, the more and more huge variety of professional journals has generated a du ality hole among the 2 companions, and this hole is growing to be wider. Advances in Mechanics and arithmetic (AMMA) is meant to bridge the space by way of supplying multi-disciplinary courses which fall into the 2 following complementary different types: 1. An annual booklet devoted to the most recent advancements in mechanics and arithmetic; 2. Monographs, complicated textbooks, handbooks, edited vol umes and chosen convention complaints. The AMMA annual booklet publishes invited and contributed compre hensive experiences, examine and survey articles in the huge region of recent mechanics and utilized arithmetic. Mechanics is known right here within the so much basic experience of the be aware, and is taken to include appropriate actual and organic phenomena related to electromagnetic, thermal and quantum results and biomechanics, in addition to normal dy namical platforms. particularly inspired are articles on mathematical and computational types and techniques in accordance with mechanics and their interactions with different fields. All contributions should be reviewed in order to warrantly the top attainable medical standards.

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**Example text**

The surfaces x = 0 and x = b of the strip are subjected to sudden temperature drops Ta and Tb, respectively. The initial and boundary conditions for the temperature field are T=O, t = O. T = -Ta, x =0, T=-n, x = b. 16), a multi-layered material model is first employed. In the discrete model, the FGM strip is divided into N + 1 homogeneous layers in the thickness direction, as shown in Fig. 9. The thickness of the nth layer, hn , is n=O,l, ... ,N, 44 ADVANCES IN MECHANICS AND MATHEMATICS II, 2003 where Xn and Xn+1 denote the x-coordinates of the two boundaries of the nth layer with Xo = 0 and XN+1 = b, respectively.

1) ,~, where T is the temperature, qi the heat flux vector and k(x) the spacedependent thermal conductivity. 2) -qi,i = p(x)c(x)8t' where t is time, p(x) the mass density and c(x) the specific heat. Here no internal heat generation is considered. Substitution of Eq. 1) into Eq. 5) where the boundary on = anT U an q U ane, To, t, ij and Ta are the given initial temperature, boundary temperature, boundary heat flux, and ambient temperature, respectively, n the outward normal direction on on, and h the heat transfer coefficient.

The R-curve 30 ADVANCES IN MECHANICS AND MATHEMATICS II, 2003 and residual strength behavior of a ceramic/metal FGM are then studied based on a crack-bridging mechanism (Jin and Batra, 1996a). 1 Fracture toughness Based on a Rule of Mixtures A simple approach to estimate the fracture toughness of a ceramic/metal FGM is to use rules of mixtures. The rule of mixtures concept may be simplistic since the micro-damage processes are not considered. Neverthless, the rule of mixtures estimate admits simple expression for the fracture toughness.