“Viscosity is the most ubiquitous dissipative mechanical behavior” (Maugin, 1999). Despite its ubiquity, even for those systems where the mechanisms causing viscous and other forms of dissipation are known there are only a few quantitative models that extract the macroscopic rheological response from these microscopic mechanisms. One such mechanism is the stochastic breaking and forming of bonds which is present in polymer networks with transient cross-links, strong inter-layer bonding between graphene sheets, and sliding dry friction. In this paper we utilize a simple yet flexible model to show analytically how stochastic bonds can induce an array of rheological behaviors at the macroscale. We find that varying the bond interactions induces a Maxwell-type macroscopic material behavior with Newtonian viscosity, shear thinning, shear thickening, or solid like friction when subjected to shear at constant rates. When bond rupture is independent of the force applied, Newtonian viscosity is the predominant behavior. When bond breaking is accelerated by the applied force, a shear thinning response becomes most prevalent. Further connections of the macroscopic response to the interaction potential and rates of bonding and unbonding are illustrated through phase diagrams and analysis of limiting cases. Finally, we apply this model to polymer networks and to experimental data on “solid bridges” in polydisperse granular media. We imagine possible applications to material design through engineering bonds with specific interactions to bring about a desired macroscopic behavior.
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This content will become publicly available on August 21, 2024
Material-geometry interplay in damping of biomimetic scale beams
Biomimetic scale-covered substrates are architected meta-structures exhibiting fascinating emergent nonlinearities via the geometry of collective scales contacts. Despite much progress in understanding their elastic nonlinearity, their dissipative behavior arising from scales sliding is relatively uninvestigated in the dynamic regime. Recently discovered is the phenomena of viscous emergence, where dry Coulomb friction between scales can lead to apparent viscous damping behavior of the overall multi-material substrate. In contrast to this structural dissipation, material dissipation common in many polymers has never been considered, especially synergistically with geometrical factors. This aspect is addressed here, where material viscoelasticity is introduced via a simple Kelvin–Voigt model for brevity and clarity. The results contrast the two damping sources in these architectured systems: material viscoelasticity and geometrical frictional scales contact. It is discovered that although topically similar in effective damping, viscoelastic damping follows a different damping envelope than dry friction, including starkly different effects on damping symmetry and specific damping capacity.
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- Award ID(s):
- 2028338
- NSF-PAR ID:
- 10448594
- Date Published:
- Journal Name:
- Applied Physics Letters
- Volume:
- 123
- Issue:
- 8
- ISSN:
- 0003-6951
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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