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

As any human job wishes pursuits, mathematical learn wishes difficulties -David Hilbert Mechanics is the paradise of mathematical sciences -Leonardo da Vinci Mechanics and arithmetic were complementary companions given that Newton's time and the background of technological know-how exhibits a lot facts of the ben eficial impression of those disciplines on one another. pushed by way of more and more difficult sleek technological functions the symbiotic courting among arithmetic and mechanics is consistently starting to be. in spite of 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 starting to be wider. Advances in Mechanics and arithmetic (AMMA) is meant to bridge the distance by means of offering multi-disciplinary courses which fall into the 2 following complementary different types: 1. An annual publication devoted to the most recent advancements in mechanics and arithmetic; 2. Monographs, complicated textbooks, handbooks, edited vol umes and chosen convention lawsuits. The AMMA annual e-book publishes invited and contributed compre hensive reports, learn and survey articles in the vast zone of recent mechanics and utilized arithmetic. Mechanics is known right here within the such a lot basic experience of the observe, and is taken to embody proper actual and organic phenomena related to electromagnetic, thermal and quantum results and biomechanics, in addition to common dy namical platforms. particularly inspired are articles on mathematical and computational types and strategies in response to mechanics and their interactions with different fields. All contributions may be reviewed on the way to warrantly the top attainable medical standards.

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1988; Bao and Hui, 1990). When a ceramic/metal FGM is fabricated with the ceramicrich region consisting of the metal particles dispersed in the continuous ceramic phase (Rabin and Heaps, 1993), the ceramic-rich region in the FGM may be regarded as a metal particulate reinforced ceramic matrix composite with graded composition and volume fractions. In this case, metal particle bridging may be a major toughening mechanism and the crack-bridging concept may be used to study the R-curve behavior of the FGM.

4) leads to the following system of Cauchy singular integral equations for 4>1 (r) and 4>2 (r) 1 1 ~ 1 [4>I(S) 47r Pl(r), - - + ~ L 1j (r, s)4>j(S) ds = --E -1 S - r . 1 )= 1ds = --E P2(r), 1 -- +~ 1 [4>2(S) -1 S - r 0 ~L2j(r,s)4>j(S) . 10) where the nondimensional coordinate r = x/a and the Fredholm kernels Lij(r, s) (i,j = 1, 2) can be found in Delale and Erdogan (1988). , 1973; Erdogan, 1978), Eqs. 11) have the following form of solution A. '1'1 A. 12) where 'l/Ji(r) (i = 1, 2) are continuous in the interval [-1, IJ.

3) holds (K -dominance zone). A simple estimate of the effect of material gradation on the size of the K -dominance zone may be made on the basis 18 ADVANCES IN MECHANICS AND MATHEMATICS II, 2003 of Eq. 3). The first term in Eq. E!. ) t/2 F v v + 8x E 8x + 8y E 8y + E v . 5) For a model I crack, at a radial distance r from the crack tip, 82 F 8x a 8xf3 rv KJ v'27rr to within an angular multiplier of order unity. This singularity is due to the first term in Eq. 5). Neglecting gradients of Poisson's ratio, the dominance of this first term over other terms involving modulus gradients in Eqs.