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Dissipative Finite Element Formulation Applied to Piezoelectric Materials With the Debye Memory

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Figure

Fig. 1. A piezoelectric of domain Ω and boundary Γ with outward normal n and with randomly oriented electric dipoles p i .
Fig. 2. A continuum domain Ω with boundary Γ is discretized with n three- three-dimensional eight-node brick elements of domain Ω e and boundary Γ e .
Fig. 3. Front view of the piezoelectric plate and sketches of both mode operations: actuator with time-dependent voltage (left) and sensor with vertical displacement (right).
Fig. 6. Top: Prescribed electric field vs. time. Middle: polarization gener- gener-ated vs
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