Data-free physics-informed inverse programming of bistable kirigami energy landscapes

Area of Science:

• Mechanics of Materials
• Metamaterials Science
• Computational Physics

Background:

• Kirigami metamaterials leverage geometric patterns for tunable mechanical properties.
• Bistability in kirigami arises from complex energy landscapes, crucial for programmable functionality.
• Current design methods often lack efficiency and require extensive experimental data.

Purpose of the Study:

• To develop a unified framework for forward prediction and inverse programming of bistable kirigami energy landscapes.
• To enable the design of kirigami structures with prescribed energy barriers and deformation states.
• To establish an efficient, data-free approach for programming mechanical energy landscapes.

Main Methods:

• Implementation of a physics-informed neural network (PINN) framework.
• Embedding equilibrium conditions, energy formulations, and geometric compatibility into the learning objective.
• Utilizing forward and inverse prediction settings, including a minimally specified inverse problem.

Main Results:

• PINN achieved high accuracy (R² > 0.99, barrier errors < 0.1%) in forward energy landscape prediction.
• Inverse programming accurately identified kirigami geometries (barrier errors < 5%) and inferred landscapes in underdetermined cases (mean barrier error 0.4%).
• Experimental validation on 3D-printed prototypes confirmed programmed energy barrier ordering and demonstrated sequential actuation.

Conclusions:

• The developed PINN framework provides an efficient method for programming bistable energy landscapes in kirigami.
• This approach facilitates the design of kirigami metamaterials for applications requiring programmable mechanical responses.
• The findings pave the way for advancements in deployable structures, soft robotics, and impact mitigation devices.