Neel Nadkarni | California Institute of Technology (original) (raw)
Supervisors: Chiara Daraio and Dennis Kochmann
less
Related Authors
Kwame Nkrumah University of Science and Technology
Uploads
Papers by Neel Nadkarni
We present a scaling law for the energy and speed of transition waves in dissipative and diffusiv... more We present a scaling law for the energy and speed of transition waves in dissipative and diffusive media. By considering uniform discrete lattices and continuous solids, we show that—for arbitrary highly nonlinear many-body interactions and multistable on-site potentials—the kinetic energy per density transported by a planar transition wave front always exhibits linear scaling with wave speed and the ratio of energy difference to interface mobility between the two phases. We confirm that the resulting linear superposition applies to highly nonlinear examples from particle to continuum mechanics.
We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of mass... more We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.
We present a scaling law for the energy and speed of transition waves in dissipative and diffusiv... more We present a scaling law for the energy and speed of transition waves in dissipative and diffusive media. By considering uniform discrete lattices and continuous solids, we show that—for arbitrary highly nonlinear many-body interactions and multistable on-site potentials—the kinetic energy per density transported by a planar transition wave front always exhibits linear scaling with wave speed and the ratio of energy difference to interface mobility between the two phases. We confirm that the resulting linear superposition applies to highly nonlinear examples from particle to continuum mechanics.
We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of mass... more We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.