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

Abstract

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 numbersunless 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.

Dynamics of Kirchhoff rods and rings from a minimal coupling quantum isomorphism

“…The isomorphism also gives a possible new perspective on the mode coarsening behavior recently observed in experiments on dynamically buckled rods [21]. The observed scaling behavior k ∼ t −1/1.9 is close to k ∼ t −1/2 , what one would expect from first order time-dependent perturbation theory when the potential (buckling force) is a step function at t = 0.…”

“…The case of Eqs. (7) with M = K = C = 0 and P > 0 is known as the dynamical buckling equation [19][20][21], yet the extra features described above are well-studied extensions of linear buckling [22][23][24], if not typically together and in a dynamical context. Counter-intuitively, even when a rod is everywhere in tension it can buckle given suitable boundary conditions [25].…”

“…A big caveat, however, is that the derivation of the rSSE from the rTDSE assumes adiabatically slow time dependence, and this assumption is almost certainly violated for impact forces such as those used in Ref. [21]. What happens to the isomorphism under more general time-dependent forces, including impact forces and longitudinal sound waves, is certainly an interesting direction for future work.…”

Implementing a non-local lattice particle method in the open-source large-scale atomic/molecular massively parallel simulator

“…Due to its advantages when analyzing discontinuity-related issues, discrete particle-based methods have been utilized to analyze bone fracture [15,16], diffusion in concrete [17,18], concrete failure [19][20][21], dynamic buckling of rods [22], fracture of fiber-reinforced laminated composites [23,24] and nanocomposites [25]. Nonetheless, continuous models, such as finite element analysis (FEM), are the most common framework employed to study the critical zones in structures vulnerable to cracks.…”