By Joseph E. Bowles
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Extra info for Analytical and Computer Methods in Foundation Engineering
24). 24) (cf. 6). 28. 30) a2 + ~c~51, - ~31E?. Electrorheological Fluids An incompressible fluid is only capable of isochoric motions. Such an internal constraint can be expressed by div v = tr D = 0. 31). 32) 0~4 = 0 ~ 0/5 = OL51 0/6:0~ where 0/ij are functions of ~ only. 46) in this 0/21 tr ( D E ® E) + (0/31 + 0/321EI2)IDI 2 + 2a51[DEI 2 ~ 0. Proceeding similarly as in the case of compressible fluids we can show 15Note, that all coefficients aij and ¢(IEI 2) are functions of 0 and p. 3. 34. 3 4 0/32 Jr ~O~51 ~_- 0.
Concerning the remaining material functions a2, a3 and a5 we assume that the material shows the following behaviour: in the absence and presence of an electric field the behaviour is that of a generalized Newtonian fluid with power p. The power p can depend on the magnitude of the electric field (cf. Halsey, Martin, Adolf , Bayer ) and all terms have the same growth behaviour. Moreover we restrict ourselves to the case when as, a3 and a5 are functions of the invariants 0, ID] z and IE[ 2 only, because we are merely interested in the growth of the material functions a2, or3 and as.
Halsey, Martin, Adolf , Bayer ) and all terms have the same growth behaviour. Moreover we restrict ourselves to the case when as, a3 and a5 are functions of the invariants 0, ID] z and IE[ 2 only, because we are merely interested in the growth of the material functions a2, or3 and as. The growth of the other invariants can be obtained as a combination of these considered. 9) + ~o, where aij are functions of 0, and in general p = p(lE[2). 11) where 1 < Poo _< p(IEI 2) <_ p0. 13) where f~ = p - 1 or p - 2.