Customizable wave tailoring nonlinear materials enabled by bilevel inverse design

Area of Science:

• Nonlinear dynamics
• Materials science
• Wave propagation

Background:

• Nonlinearities significantly alter wave propagation in diverse fields.
• Selecting the optimal nonlinearity for specific wave tailoring applications remains a challenge.

Purpose of the Study:

• To introduce a bilevel inverse design method for tailoring nonlinear mechanical wave responses.
• To identify optimal nonlinearities for impact mitigation and pulse shaping.

Main Methods:

• Developed a bilevel inverse design approach coupling structural shape optimization with reduced-order nonlinear dynamical inverse design.
• Applied the method to a 1D polynomial spring-mass chain (Fermi-Pasta-Ulam-Tsingou variant).
• Investigated two distinct problems: minimizing impact energy and transforming pulse shapes.

Main Results:

• Demonstrated that minor nonlinearity variations drastically alter system dynamics, outperforming linear systems.
• Showcased that the optimal nonlinearity significantly surpasses "energy locking" bistability for impact mitigation.
• Validated impact mitigation findings through experimental comparison, showing excellent agreement.

Conclusions:

• The developed framework enables passive nonlinear mechanical wave tailoring for materials.
• Potential applications include computing, signal processing, shock mitigation, and autonomous materials.