Inverse design of periodic microstructures with targeted nonlinear mechanical behaviour

Area of Science:

• Materials Science
• Mechanical Engineering
• Computational Mechanics

Background:

• Designing materials with specific nonlinear mechanical responses is crucial for advanced applications.
• Tailoring microstructure properties often involves complex optimization challenges.

Purpose of the Study:

• To introduce an inverse design framework for precisely controlling nonlinear mechanical responses in periodic microstructures.
• To achieve prescribed nonlinear stress-strain relationships through topology optimization.

Main Methods:

• Utilizing a deformation-driven homogenization framework.
• Implementing strongly enforced periodic boundary conditions and removing translational nullspace to simplify constraint handling.
• Leveraging automatic differentiation for efficient gradient calculation in optimization.
• Proposing an intermediate density penalty constraint for discrete design.

Main Results:

• Demonstrated the framework's efficacy through numerical examples.
• Showcased microstructures with targeted nonlinear behaviors, including softening, stiffening, and directional properties.
• Successfully minimized the error between target and realized material properties.

Conclusions:

• The proposed inverse design framework enables precise tailoring of nonlinear mechanical responses in microstructures.
• The methodology simplifies implementation and effectively guides the design of discrete microstructures with desired properties.
• This approach offers a powerful tool for developing advanced materials with customized mechanical performance.