Odd elasticity realized by piezoelectric material with linear feedback

The systems exhibiting sustainable external energy exchange are abundant, e.g., biological organisms' reaction to external stimuli while maintaining a constant energy exchange with the surrounding. In a linear mechanical system exhibiting an external energy gain or release, the recently proposed odd elasticity theory can characterize the overall stress and strain response. However, realizing the required odd elasticity is still challenging. In this work, we discovered that the smart materials with designed feedbacks can achieve this odd elasticity, thereby providing a practical platform to analyze the phenomenon related to this novel elasticity theory. We also demonstrated this idea by designing a non-reciprocal Rayleigh wave via odd elasticity and the equivalent piezoelectricity with linear feedback. The underpinned electric energy scenario was also examined. Our work establishes a method to easily realize the materials with odd elastic behaviors and explore the rich phenomena related to non-Hermitian systems.