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Volume 116
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Strongly nonlinear pulse attenuation in microgranular chains with fractional contact dissipation
Dong Feng, Kai Zheng *
RWTH Aachen University, Mies-van-der-Rohe-Straße 1, 52074, Aachen, Germany
10.1016/j.partic.2026.06.009
Volume 116, September 2026, Pages 202-213
Received 3 April 2026, Revised 4 June 2026, Accepted 8 June 2026, Available online 13 June 2026, Version of Record 4 July 2026.
E-mail: kai.zheng@rwth-aachen.de
Highlights

• Fractional contact dissipation captures coating-induced memory in microgranular contacts.

• Memory damping reshapes pulse decay from near-exponential behavior to anomalous power-law trends.

• A truncated Grünwald–Letnikov scheme enables efficient history-dependent simulations.

• The memory order and strength tune attenuation and pulse broadening in nonlinear lattices.


Abstract

Microgranular chains provide a useful platform for controlling impact pulses and wave transmission in microscale granular metamaterials, where interfacial coatings, adsorbed layers, and adhesive junctions can strongly affect contact dissipation. However, most existing granular-chain models still rely on local, memoryless damping laws and therefore cannot adequately describe broad relaxation spectra and long-tailed memory effects at microcontacts. This study aims to clarify how non-Markovian contact dissipation modifies strongly nonlinear pulse attenuation and waveform evolution. A one-dimensional precompressed chain of identical microspheres is formulated by combining Hertzian contact nonlinearity with a Caputo-type fractional contact dissipation law. The resulting history-dependent lattice is solved using an explicit time-stepping scheme coupled with a truncated Grünwald–Letnikov convolution, and its response is compared with that of a classical viscous reference model subjected to impact excitation. The results show that fractional dissipation produces nonuniform attenuation, persistent post-peak tails, and pronounced pulse broadening that cannot be reproduced by local viscous damping. Increasing the dissipation strength reduces transmitted peak velocities and contact forces while increasing cumulative energy loss. Overall, the main contributions of this study are the development of a fractional contact-dissipation model for microgranular chains, the implementation of an efficient truncated Grünwald–Letnikov scheme, and the demonstration that contact memory provides an effective mechanism for controlling pulse attenuation, broadening, and energy loss.

Graphical abstract
Keywords
Microgranular chains; Fractional dissipation; Memory effects; Grünwald–Letnikov convolution
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