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Nonlinear, Nonequilibrium Elasticity in Diverse Materials

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Nonlinear mesoscopic elastic materials (NMEMs) exhibit unique and interesting properties related to nonlinear and nonequilibrium dynamics that are relevant to various natural and industrial processes ranging in scales and applications, e.g., the onset of earthquakes and avalanches in geophysics, the aging of infrastructures in civil engineering, the failure of mechanical parts in industrial settings, bone fragility in the medical field, or the design of novel materials, including nonlinear metamaterials, for shock absorption, acoustic focusing, and energy-harversting systems. These properties include the dependence of wave speed and damping parameters on strain amplitude, slow relaxation, and hysteresis with end-point memory.

In this publication, we evidence the tensorial nature of nonequilibrium dynamics in NMEMs by resonance experiments in a slender bar of Berea sandstone. We demonstrate that the parameters quantifying nonequilibrium dynamics vary substantially whether the sample is excited in a pure longitudinal mode or a pure torsional mode. This work represents a first step towards extending the theory of nonequilibrium dynamics in granular materials from 1D to 3D. Contact Marcel Remillieux for more information.

Remillieux, M. C., R. A. Guyer, C. Payan, and T. J. Ulrich Decoupling nonclassical nonlinear behavior of elastic wave types, Physical Review Letters 116 (11), 115501 (2016). (PDF File - 3.4 MB / doi:10.1103/PhysRevLett.116.115501)


Dynamic nonlinear elastic behavior, nonequilibrium dynamics, first observed as a curiosity in earth materials has now been observed in a great variety of solids. The primary manifestations of the behavior are characteristic wave distortion, and slow dynamics, a recovery process to equilibrium that takes place linearly with the logarithm of time, over hours to days after a wave disturbance. The link between the diverse materials that exhibit nonequilibrium dynamics appears to be the presence of soft regions, thought to be primarily 'damage' at many scales, ranging from order 10-9 m to 10-1 m at least. The regions of soft matter may be distributed as in a rock sample, or isolated, as in a sample with a single crack. The precise physical origin of the behavior is clear in some cases such as granular media where the source of the nonequilibrium dynamics, grain-to-grain interaction, is well understood. In other materials, it appears that the origin must be due fundamentally to shear sliding, related to crack and possibly dislocation dynamics, as well as less clear origins. Because the physical origins of the behavior are related to damage, damage diagnostics in solids, Nonlinear NonDestructive Evaluation, follows naturally. Nonequilibrium dynamics also plays a significant role in other areas such as earthquake strong ground motion and potentially to earthquake dynamics.

For more information, please contact Paul Johnson.

Book Published - Nonlinear Mesoscopic Elasticity

Authors Robert A. Guyer and Paul A. Johnson have published Nonlinear Mescopic Elasticity. This book is available from both Amazon and the publisher, Wiley VCH. (Sample Chapter)

  • Print ISBN: 9783527407033
  • Online ISBN: 9783527628261
  • DOI: 10.1002/9783527628261
  • Copyright © 2009 Wiley-VCH Verlag GmbH & Co. KGaA

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