Piezo stacks: Physics

Actuators & Sensors


Designing an actuator that utilizes a piezo stack as actuation principles is not trivial. To aid in this, this sheet elaborates on the parameters that are of interest for such a design. The behavior of a piezo stack can be summarized with the following properties:

  • Geometrical
  • Material
  • Mechanical
  • Electrical

Geometric properties

$A=H\cdot B\left[m^2\right]$

Cross section area


Layer thickness (typical 60-500 µm)

$n=\frac{L}{d_s} [-]$

Number of layers

Material properties




Young’s modulus


Poisson ratio


Damping constant


Operating temperature


Dielectric constant (typical value = 1750)


Charge constant

$HC=350\frac{J}{kg\cdot K}$ 

Spec. heat capacity


Spec. thermal conductivity


Typical voltage


$\Delta L_{max}=\frac{L}{1000}$

Maximum displacement


Axial stiffness




Resonance frequency


Minimum rise time


Phase lag

$F_{blocking}=\Delta l_{max}\cdot C_{axial}$

Blocking force

$\sigma_{dynamic}=15\ MPa$

Preload for dynamic use

$\sigma_{static}=30\ MPa$

Preload for static use

$4-20 \%$


$\Delta x_{creep}\left(t\right)=x\cdot0.01\cdot\log{\left(\frac{t}{0.1}\right)}$ 

Creep @ t [s]

$F_{pre\ tension}=\frac{1}{2}F_{blocking}$

Pre tension force (matching push-pull force)

Piezo stacks
Geometric characteristics of a Piezo stack


$x=d_{33}\cdot L\cdot\frac{U}{d_s}$

Displacement @ U [V]


Permittivity of free space


Small signal capacitance (typical for U < 100 V)

$C_L=1.7\cdot C_S$

Large signal capacitance (typical for U > 100 V)

$P=\frac{1}{2}\cdot f\cdot C\cdot U^2$

Average Polarization Power

$E=\frac{1}{2}\cdot C\cdot U^2$

Polarization energy


Not generic for all frequency ranges, just for indication:


Loss factor @ U [V]


Loss factor @ T [K]


Heat generation


Heat generation

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