By Jiashi Yang

ISBN-10: 1441936394

ISBN-13: 9781441936394

This quantity is meant to supply researchers and graduate scholars with the elemental features of the continuum modeling of electroelastic interactions in solids. A concise therapy of linear, nonlinear, static and dynamic theories and difficulties is gifted. The emphasis is on formula and realizing of difficulties priceless in equipment functions instead of answer recommendations of mathematical difficulties. the math utilized in this publication is minimum. This quantity is appropriate for a one-semester graduate direction on electroelasticity. it may possibly even be used as a reference for graduate scholars and researchers in mechanics and acoustics.

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Therefore, within the linear theory, there is no need to distinguish capital and lowercase indices. Only lowercase indices will be used in the linear theory. The material time derivative of an infinitesimal field variable f(y,t) is simply the partial derivative with respect to t: 32 For the finite strain tensor In the linear theory, the infinitesimal strain tensor will be denoted by The material electric field becomes Similarly, Since the various stress tensors are either approximately zero (quadratic in the infinitesimal gradients) or about the same, we will use to denote the stress tensor that is linear in the infinitesimal gradients.

3-3. Show that 4. 1-49) has been used. Use the divergence theorem 19 which implies that where and (a scalar) defined by are the reference or material electric displacement and body free change per unit undeformed volume. From Equation which implies that where defined by is the reference electric field. From the total mass of the material body is a constant, which is the mass in the reference state where is the mass density in the reference state. 1-56) have been used. Hence 21 In summary, the balance laws in material form are CONSTITUTIVE RELATIONS 5.

INITIAL-BOUNDARY-VALUE PROBLEM Since the curl-free equation is automatically satisfied. The angular momentum equation is satisfied because is symmetric. The present mass density appears in the equation of conservation of mass only, and therefore can be calculated from the equation after the deformation and the electric field have been found. The energy equation is satisfied by the forms of the constitutive relations. 6-4) can be written as four equations for the four unknowns and 25 Consider an interface between medium 1 and medium 2.

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An introduction to the theory of piezoelectricity by Jiashi Yang

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