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Extra info for Advanced Mechanics of Materials 6th edition Solution Manual

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A" a2, and a3 describe nonlinear elastic behavior, and hI and h2 nonlinear electroelastic behavior. (16) includes all terms up to the third degree of the finite strain tensor, the reference electric potential gradient, and their products. This is enough for describing the basic effects of biasing fields in electrostrictive ceramics. Constitutive relations obtained from (16) were linearized in [8] for small, dynamic fields superposed on finite, static biasing fields. The linear equations were used to study plane waves propagating under various mechanical and/or electric biasing fields.

Stru. vol. 673-683. [S] A. E. Clark, M. L. Spano and H. T. 95 alloys. IEEE Trans. 1964-1966. [6] A. N. Abd-Alla and G. A. Maugin, Nonlinear phenomena in magnetostrictive elastic resonators, Int. J. Engng. 1613-1619,. [7] S. S. Antrnan, Synthesis of Nonlinear Constitutive Functions, Applications to the Electromagnetic Control of Snapping, Transactions of the ASME J. Appl. , vol. 66 (1999), pp. 280-283. [8] G. A. Maugin, Continuum Mechanics of Electromagnetic Solids. (North-Holland. ) [9] Y. H.

The magnetization saturation increases with the increase of the compressive stress. 3. MODELING CONSTITUTIVE RELATIONS The total strain syand magnetization M; can be decomposed into the linear and the remanent parts Sij =s/ +S/ ' M j =M/ +M/ (1) where the superscript ' e' represents recoverable (linear) part while the superscript'r ' represents the remanent (non-linear) part. The linear response of the ferromagnetic solids is given by means of the piezomagnetic equation: sij-Sy'=Syk,O"k/+rkijHk , Mj-M/=rjkjO"Iq+XijHj (2) where Sijk/ is elastic moduli, rijk the piezomagnetic coefficient, and Xij the susceptibility tensor.

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