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Wave Propagation Analysis in 2D Nonlinear Periodic Structures Prone to Mechanical Instabilities

Abstract : This chapter analyzes wave propagation in periodic network materials, which shows higher-order gradient effects in the presence of a nonlinear response. For this purpose, second-order gradient nonlinear continua are evaluated as substitution media for the initially discrete networks. The chapter identifies the effective mechanical energy of pantographic extensible lattices in the nonlinear regime, considering extensible situations and following the heuristic homogenization procedure used by Piola. On the basis of the energy expression of the identified hyperelastic second-grade continuum, the chapter also analyzes the propagation of longitudinal waves in the homogenized nonlinear pantograph microstructure, which is incorporated into macroscopic one-dimensional (1D) beams. For both linear and nonlinear situations, an increase of the wavenumber entails an increase of the modulus and shape of the phase velocity, thus reflecting the dispersive behavior for the effective second-gradient medium.
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https://hal.univ-lorraine.fr/hal-03311834
Contributor : Jean-François GANGHOFFER Connect in order to contact the contributor
Submitted on : Monday, August 2, 2021 - 9:54:34 AM
Last modification on : Friday, August 5, 2022 - 2:54:00 PM

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Hilal Reda, Yosra Rahali, Jean-François Ganghoffer, Hassan Lakiss. Wave Propagation Analysis in 2D Nonlinear Periodic Structures Prone to Mechanical Instabilities. From Microstructure Investigations to Multiscale Modeling : bridging the Gap, John Wiley & Sons, Inc., pp.67-97, 2017, 978-1786302595. ⟨10.1002/9781119476757.ch3⟩. ⟨hal-03311834⟩

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