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Piezoic

Live

Electromechanical analysis with constitutive bookkeeping

d₃₃* is not d₃₃. keff is a privilege, not a formula. Geometry is live.

Displacement and voltage come off a ferroelectric tester as two columns. Thickness is applied later, if at all. The butterfly is drawn in Origin. Resonance is fitted in a second program. Direct d₃₃ lives in a third file. d₃₃* = Smax / Emax is then published as d₃₃. keff is reported on an overdamped resonator because the formula still returns a number. None of this is malice. It is what happens when the analysis tool has no constitutive model.

Piezoic inverts that order. Geometry is a first-class object. Every derived quantity carries its definition: d₃₃* is labelled large-signal; the high-field slope of a unipolar S–E loop is the only S–E number allowed to stand next to a Berlincourt reading; keff is withheld when the resonator is overdamped, sparse, or non-resonant. A 15 % disagreement between d₃₃* and constitutive d₃₃ raises a flag. High d·g, high k² and high Qm are three different optima.

Soft PZT-5H analogue. Bipolar S–E family, 300–450 K. Remnant strain is a substantial fraction of Smax and the wings dip: ferroelastic switching, not a linear dielectric.
Unipolar S–E with the d₃₃* construction (Smax / Emax). The high-field slope differs by more than 15%. Piezoic refuses to let d₃₃* silently become the constitutive d₃₃.
IEEE 176 / EN 50324 thickness resonator: |Z| and phase against frequency. keff is reported only when the resonator is actually resonant.

What it does

  • S–E and P–E families sharing specimen geometry, so S(P) and electrostriction tests are rearrangements, not a second experiment
  • IEEE 176 / EN 50324 resonance with keff withheld when the resonator is not actually resonant
  • Berlincourt d₃₃(T) with heat/cool Td and hysteresis called out rather than hidden
  • Rayleigh dinit + α E₀ on subcoercive minors as a quantitative signature of domain-wall mobility
  • Constitutive FOMs sourced: g₃₃, e₃₃, k², d·g name their d₃₃ origin; giant d₃₃* is not allowed to inflate d·g