By Tribikram Kundu

So much books on nondestructive overview (NDE) concentration both at the theoretical historical past or on complicated purposes. Bridging the distance among the 2, Ultrasonic and Electromagnetic NDE for constitution and fabric Characterization: Engineering and Biomedical purposes brings jointly the foundations, equations, and purposes of ultrasonic and electromagnetic NDE in one, authoritative source. this is often additionally one of many first books to include a couple of renowned NDE equipment in line with electromagnetic suggestions. The e-book starts off with the suitable basics of mechanics and electromagnetic concept, derives the fundamental equations, after which, step-by-step, covers cutting-edge subject matters and functions of ultrasonic and electromagnetic NDE which are on the leading edge of analysis. those comprise engineering, organic, and medical functions resembling structural overall healthiness tracking, acoustic microscopy, the characterization of organic cells, and terahertz imaging. Written in undeniable language via a number of the world’s major specialists, the e-book comprises worked-out examples and routines that make this a superb source for coursework. The assurance of conventional and complicated NDE purposes additionally appeals to practising engineers and researchers.

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**Example text**

However, if the material response is symmetric about a plane or an axis, then the number of independent material constants is reduced. 1 One Plane of Symmetry Let the material have only one plane of symmetry, and this plane is the x1-plane; in other words, the x2 x3-plane whose normal is in the x1-direction is the plane of symmetry. For this material, if the stress states σ(ij1) and σ(ij2 ) are mirror images of each other with respect to the x1-plane, then the 24 Ultrasonic and Electromagnetic NDE for Structure and Material Characterization corresponding strain states ε (ij1) and ε (ij2 ) should be the mirror images of each other with respect to the same plane.

96 represents two waves propagating in the n direction with the velocity of cP and cS, respectively. Note that n is the unit vector in any direction. 97, the prime indicates derivative with respect to the argument. Clearly, here the direction of the displacement vector u and the wave propagation direction n are same. 99) is zero; hence, the direction of the displacement vector u is perpendicular to the wave propagation direction n. 98 correspond to P- and S-waves, respectively. 3 Two-Dimensional In-Plane Problems If the problem geometry is such that u1(x1, x2) and u2(x1, x2) are nonzero while u3 is equal to zero, then the problem is called an in-plane problem.

13, identical numerical values of strain components (εi′j′) are applied in two different directions. For isotropic material, equal strain values applied in two different directions should not make any difference in computing the strain energy density. For U0(εij) and U0(εi′j′) to be identical, U0 must be a function of strain invariants because strain invariants are the only parameters that do not change when the numerical values of the strain components are changed from εij to εi′j′. 39. 66) I2 = Note that I1, I2, and I3 are linear, quadratic, and cubic functions of strain components, respectively.