Dynamics of chains with non-monotone stress–strain relations. I. Model and numerical experiments

Oscillatory behavior in a chain of masses connected by springs with continuous but non-monotonic spring forces can be induced under quasi-static loading. Insight into the birth of this behavior is obtained from a single mass system. A bifurcation study shows the potential for equilibrium jumps between multiple equilibria. As such, the transients occurring under quasi-static loading do not converge to the static loading case. Transients during dynamic loading show sensitivity to the loading parameters.

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“…The work is motivated by the work of Balk, Cherkaev and Slepyan in Refs. [1,2] and in related work in Refs. [3][4][5][6].…”

Section: Introductionmentioning

confidence: 86%

Twinkling Phenomena in Snap-Through Oscillators

Feeny

Diaz

2010

Journal of Vibration and Acoustics

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“…The concept of lattice structure with waiting links is researched by Cherkaev and Slepyan (1995), who analyzed the loading responses of lattice structures with waiting links and explained the failure of a lattice structure under dynamic loading. Balk et al (2001) further expand the waiting link concept and simulate the delocalization of damages in a lattice structure. Slepyan and Ayzenberg-Stepanenko (2004) include the effect of cracks into the lattice structure and conduct studies on dynamic fracture propagation.…”

Section: Lattice and Truss Structuresmentioning

confidence: 99%

Impact Mechanics and High-Energy Absorbing Materials: Review

2008

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“…Moreover, the dynamics of atomic-scale configurational changes as well as the mechanisms of damage and fracture have been analyzed by recourse to chains of elements with a nonmonotonic force-displacement (or stress-strain) response; see, e.g., Refs. [64][65][66][67][68][69][70][71].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

2014

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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.

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Dynamics of chains with non-monotone stress–strain relations. I. Model and numerical experiments

Cited by 77 publications

References 14 publications

Twinkling Phenomena in Snap-Through Oscillators

Twinkling Phenomena in Snap-Through Oscillators

Impact Mechanics and High-Energy Absorbing Materials: Review

Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

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