A Scaling Framework for Mechanical Memristance: Dimensionless Metrics and Material Design Maps
Abstract
Mechanical memristors are systems whose dissipative response depends on the history of previous loading through an evolving internal state. History-dependent forces and dissipation occur in a wide range of materials and devices, including viscoelastic polymers, shape-memory materials, piezoelectrics, granular media and field-responsive fluids. Determining which of these responses admits a mechanical-memristor representation requires a constitutive test, as well as a comparison of scales. In this work, a fractional-order mechanical memristor model is developed and cast into a nondimensional form to identify the governing parameters controlling memory-dependent dissipation. The formulation leads to a set of dimensionless groups that characterise dissipation magnitude, memory-state scale and memory transfer. These quantities are combined into an effective mechanical memristance screening index Mh = βγ|ℋα(Ω)|, which provides a conditional measure of local damping modulation at matched response amplitude, constitutive slope and reference scales. Illustrative parameter scenarios are then constructed for material classes including shape-memory polymers, shape-memory alloys, hydrogels, nanocellulose, lignin-rich materials, natural fibres, piezoelectric polymers, piezoelectric ceramics, electrorheological fluids, magnetorheological fluids and granular dampers. The framework establishes a common basis for comparing memory-dependent damping within the adopted constitutive description and identifies the calibration required for its application to candidate materials and devices
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BibTeX
@misc{alhembar2026scaling,
title = {{A Scaling Framework for Mechanical Memristance: Dimensionless Metrics and Material Design Maps}},
author = {Abdulla Alhembar and Fabrizio Scarpa and Chrystel D. L. Remillat and Rodrigo J. da Silva and Ross Anderson and Ludovico Cademartiri and Abderrezak Bezazi and James P. K. Armstrong and Adam W. Perriman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18364},
eprint = {2609.18364},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18364},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - A Scaling Framework for Mechanical Memristance: Dimensionless Metrics and Material Design Maps
AU - Abdulla Alhembar
AU - Fabrizio Scarpa
AU - Chrystel D. L. Remillat
AU - Rodrigo J. da Silva
AU - Ross Anderson
AU - Ludovico Cademartiri
AU - Abderrezak Bezazi
AU - James P. K. Armstrong
AU - Adam W. Perriman
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18364
UR - https://arxiv.org/abs/2609.18364
AB - Mechanical memristors are systems whose dissipative response depends on the history of previous loading through an evolving internal state. History-dependent forces and dissipation occur in a wide range of materials and devices, including viscoelastic polymers, shape-memory materials, piezoelectrics, granular media and field-responsive fluids. Determining which of these responses admits a mechanical-memristor representation requires a constitutive test, as well as a comparison of scales. In this work, a fractional-order mechanical memristor model is developed and cast into a nondimensional form to identify the governing parameters controlling memory-dependent dissipation. The formulation leads to a set of dimensionless groups that characterise dissipation magnitude, memory-state scale and memory transfer. These quantities are combined into an effective mechanical memristance screening index Mh = βγ|ℋ_α(Ω)|, which provides a conditional measure of local damping modulation at matched response amplitude, constitutive slope and reference scales. Illustrative parameter scenarios are then constructed for material classes including shape-memory polymers, shape-memory alloys, hydrogels, nanocellulose, lignin-rich materials, natural fibres, piezoelectric polymers, piezoelectric ceramics, electrorheological fluids, magnetorheological fluids and granular dampers. The framework establishes a common basis for comparing memory-dependent damping within the adopted constitutive description and identifies the calibration required for its application to candidate materials and devices
ER -