Mode Coarsening or Fracture: Energy Transfer Mechanisms in Dynamic Buckling of Rods

Abstract

© 2021 American Physical Society. We present results of a hybrid experimental, theoretical, and simulation-based investigation of the postbuckling behavior of thin elastic rods axially impacted by a projectile. We find a new postbuckling mechanism: mode coarsening. Much akin to inverse energy cascade phenomena in other nonlinear dynamic systems, energy is transferred during mode coarsening from higher to lower wave numbers - unless the rod breaks, abruptly dissipating in the course of fracture the rod's strain energy. We derive a model that provides a predictive means to capture mode coarsening in the form of a nondissipative, purely geometric force relaxation mechanism, and validate the model by means of molecular dynamics (MD) based structural dynamics simulations for rods of wood and pasta considering different thermodynamic ensembles. The scalability of theory and simulation for engineering applications opens new venues toward safe design of engineering structures subject to impact-induced risks of buckling, ranging from skyscrapers, to aerospace structures, to the crashworthiness of vehicles, for example.