🧩 mems-ana_demo

d33-dominant MEMS piezoelectric hysteresis visualization

This directory contains a frozen demo snapshot 🧊 that visualizes the quasi-static
out-of-plane displacement of a MEMS piezoelectric structure dominated by the
piezoelectric coefficient d33, driven by a ferroelectric P–Ez hysteresis loop.

🎯 Purpose
This demo is not intended for quantitative device design.
Instead, it provides a clear, reproducible reference showing how:

⚡ Electrical hysteresis → 🛠 Mechanical displacement patterns

are mapped under a simplified, d33-dominant assumption.

🔗 Links

Language	GitHub Pages 🌐	GitHub 💻
🇺🇸 English

1️⃣ Electrical input: P–Ez hysteresis (V-only)

This figure shows the polarization–electric field (P–Ez) hysteresis loop
used as the electrical input to the model.

🔹 Key assumptions:

• 🔌 Voltage-driven only
• 🚫 Electrical current and dynamic switching effects are not modeled
• 🔁 Rising / falling voltage branches are explicitly defined

This hysteresis loop is imposed as a fixed, common input condition
for all subsequent mechanical results.

2️⃣ uₙ–V butterfly curve (d33-dominant, fixed scale)

This plot shows the resulting butterfly-shaped displacement–voltage response
derived from the P–Ez hysteresis under a d33-dominant assumption.

📐 Axes definition:

• Vertical axis: out-of-plane displacement $u_z$
• Horizontal axis: applied voltage

🎨 Visualization policy:

• Color / scale range is fixed to 0–500 nm
• Enables direct comparison across operating points

The butterfly shape directly reflects the underlying ferroelectric hysteresis.

3️⃣ Static uₙ(x, y) mid-plane maps

(absolute displacement)

These snapshots show the spatial distribution of $u_z(x,y)$ at the MEMS
mid-plane for selected voltage points along the butterfly curve.

🧭 Modeling notes:

• Displacement is treated as ABSOLUTE $u_z$
• A non-zero offset at 0 V is allowed
• Mechanical boundary conditions are schematic / conceptual

📊 All frames share the same color scale (0–500 nm)
to preserve visual consistency and comparability.

4️⃣ Dynamic response

uₙ(x, y) over voltage cycles

This animation illustrates the time evolution of $u_z(x,y)$
over multiple voltage cycles following the hysteresis loop.

⏱ Characteristics:

• Rising / falling branches follow the P–Ez loop explicitly
• Response is quasi-static (no inertia, no damping)
• Intended for intuitive understanding, not transient accuracy

▶️ How to run

python -m pip install -e .
python examples/animate_uz_midplane_typical_d33.py

📌 Scope and limitations

• 🔌 Voltage-driven analysis only (current not modeled)
• 📐 d33-dominant piezoelectric response
• 🚫 No losses, no nonlinear elasticity
• 🔩 No realistic anchors or packaging constraints
• 🧩 Boundary conditions are simplified for clarity

🧊 Status

• Stable
• Frozen demo snapshot
• All parameters are fixed for reproducibility

⚠️ Disclaimer

This demo is intended for conceptual understanding and visualization only.

Real device design and quantitative evaluation require additional physics, including:

• Electrical current and losses
• Nonlinear and rate-dependent mechanics
• Realistic boundary and anchoring conditions
• Full electromechanical coupling

Use this demo as a reference visualization, not a design authority.