Strongly nonlinear pulse attenuation in microgranular chains with fractional contact dissipation

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.