Shape-programming of hyperelastic plates through differential growth: an analytical approach

Area of Science:

• Solid Mechanics
• Materials Science
• Computational Engineering

Background:

• Hyperelastic plates undergo deformations due to internal growth.
• Controlling the 2D shape of these plates is crucial for advanced applications.
• Existing methods may lack analytical precision for complex shape programming.

Purpose of the Study:

• To derive analytical formulas for 2D shape-programming of hyperelastic plates.
• To establish a method for predicting plate configurations based on differential growth.
• To enable the design of arbitrary 2D shapes through controlled growth.

Main Methods:

• Developed a plate equation system incorporating growth functions from a 3D governing system.
• Employed a series expansion and truncation approach for simplification.
• Solved the plate equations explicitly using a novel analytical method.
• Utilized inverse problem-solving to derive formulas for growth function identification.

Main Results:

• Obtained explicit solutions revealing the relationship between plate configuration and differential growth fields.
• Derived analytical formulas for generating arbitrary 2D geometrical shapes.
• Demonstrated formula efficiency through examples consistent with numerical simulations.

Conclusions:

• The derived analytical formulas provide a powerful tool for precise 2D shape-programming of hyperelastic plates.
• This work offers a pathway for designing intelligent soft devices with tailored geometries.
• The findings have significant implications for the field of soft robotics and adaptive materials.