Abstract

Instabilities in solids and structures are ubiquitous across length and time scales, and our engineering design principles commonly aim to prevent those. In recent years, engineering mechanics has undergone a paradigm shift towards taking advantage of instabilities. At the core of all instabilities lies a non-convex energy landscape that is responsible, e.g., for phase transitions, localization, and structural buckling. Among others, such systems can give rise to strongly nonlinear transition waves that switch between stable configurations (e.g., between phases or between buckled shapes). Understanding the underlying dynamic phenomena enables us to understand the physics of various microscale phenomena as well as to create new interesting mechanical systems that exploit the effects of instability. Here, we will develop the underlying theory and discuss its application to selected examples including periodic snapping structures for mechanical logic and nonlinear diodes, domain switching in ferroelectric ceramics, and composites with metastable phase transitions.