Effect of directed aging on nonlinear elasticity and memory formation in a material

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Effect of directed aging on nonlinear elasticity and memory formation in a material

Daniel Hexner, Nidhi Pashine, Andrea J. Liu, and Sidney R. Nagel

Phys. Rev. Research 2, 043231 – Published 13 November 2020

Abstract

Disordered solids often change their elastic response as they slowly age. Using experiments and simulations, we study how aging disordered planar networks under an applied stress affects their nonlinear elastic response. We are able to modify dramatically the elastic properties of our systems in the nonlinear regime. Using simulations, we study two models for the microscopic evolution of properties of such a material; the first considers changes in the material strength, while the second considers distortions in the microscopic geometry. Both models capture different aspects of the experiments including the encoding of memories of the aging history of the system and the dramatic effects on the material's nonlinear elastic properties. Our results demonstrate how aging can be used to create complex elastic behavior in the nonlinear regime.

Received 15 August 2020
Accepted 22 October 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.043231

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Aging Elasticity Memory Poisson ratio

Amorphous materials

NetworksPolymers & Soft MatterCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Daniel Hexner ^1,2,*,†, Nidhi Pashine ^1,†, Andrea J. Liu ², and Sidney R. Nagel¹

¹Department of Physics and James Franck and Enrico Fermi Institutes, University of Chicago, Chicago, Illinois 60637, USA
²Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

^*Present address: Faculty of Mechanical Engineering, Technion, 320000 Haifa, Israel; danielhe@me.technion.ac.il
^†D.H. and N.P. contributed equally to this work.

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Vol. 2, Iss. 4 — November - December 2020

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Figure 1
Experiments of aging under isotropic compression. (a) Schematic of the experimental protocol. Our networks are aged under compression at an elevated temperature for a duration of one hour. Once aged, these networks are removed from its confining box and immediately brought back to room temperature. The aged networks are measured under extensional uniaxial strain; $ε^{0}$ is the strain measured with respect to the original unaged system, while $ε$ is the strain of the network measured with respect to its aged size. (b) Aged networks are measured under uniaxial extension along the $x$ axis. The gray vertical dashed line corresponds to the unaged size, $L_{initial}$ . Networks with data shown in blue (triangle), green (circle), and red (square) were aged at $ε_{Age}^{0} = - 0.1, - 0.2$ , and $- 0.3$ , respectively. (c) Poisson's ratio of aged networks vs strain for the same networks as in (b). Note that the strain $ε_{x}$ is with respect to the aged system. Vertical dashed lines in blue, green, and red mark $L_{initial}$ for data sets corresponding to $ε_{Age}^{0} = - 0.1, - 0.2$ , and $- 0.3$ , respectively.
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Figure 2
Left: the $k$ model at $Δ Z \approx 1.51$ . Right: $ℓ$ model at $Δ Z \approx 0.53$ . (a), (e) The compression energy versus strain for an unaged system and a system aged under $5 %$ compression (dashed line). In the $k$ model the global minimum remains at zero strain, since bond lengths do not change while in the $ℓ$ model the global minimum shifts. The difference in the unaged energy versus strain between the two models is caused by the two different values of $Δ Z$ (picked to allow comparison of the two models at the same range of strains). (b), (f) The Poisson's ratio within linear response versus time. In the $ℓ$ model the curve is nonmonotonic and has a minimum. (c), (g) The evolution of the Poisson's ratio as a function of strain. In the $k$ model, the local minimum occurs near the aging strain, $ε_{Age} = - 0.05$ (vertical dashed line). In the $ℓ$ model the minimum corresponds to the strain needed to undo the volume change that occurred during aging (dashed lines). (d), (h) The Poisson's ratio versus strain. For the $k$ model these are measured at a constant $ε_{Age}^{2} t$ . The aging strain is denoted by vertical dashed lines. In the $ℓ$ model, the curves are at a constant $t ε_{Age}$ and the dashed lines denote the strain corresponding to the unaged system at asymptotic times, $- ε_{Age} / (1 + ε_{Age})$ . Note that in (e) the strain is measured with respect to the unaged system, while for (g) and (h) it is measured with respect to the new global minimum, which depends on the aging time and $ε_{Age}$ .
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Figure 3
In the $k$ model, the Poisson's ratio at $ε = ε_{Age}$ as a function of scaled time approximately collapses.
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Figure 4
Aging under shear. Left: $k$ model. Right: $ℓ$ model. The system is aged by compressing along the $x$ axis and stretching along the $y$ axis. (a), (d) The shear stiffness versus measuring strain, $ε$ ; (b), (e) the Poisson's ratio versus strain. The full line denotes, $ν_{x}$ , the Poisson's ratio when the system is strained along the $x$ axis. The dashed line denotes, $ν_{y}$ , measured by straining along the $y$ axis. (c), (f) The stiffness to uniaxial deformation, $K_{x}$ and $K_{y}$ along the $x$ axis and $y$ axis. Note that after aging, $K_{x} > K_{y}$ in $k$ model while $K_{x} < K_{y}$ in the $ℓ$ model.
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Figure 5
Experiments of stiffness-dominated aging under isotropic compression. (a) A schematic of the experimental protocol. The networks are allowed to relax after aging under compression. The aged networks are then measured under compressive uniaxial strain. (b) Networks are compressed uniaxially along the $x$ axis, and their response is measured along the $y$ axis. $ε$ is the strain of the network measured with respect to its aged size. Purple (star) data correspond to unaged networks. Green (circle) and red (square) data are from networks aged at two different strains. Vertical dashed lines in red and green correspond to the physical size to which they were compressed during aging, $L_{box}$ . (c) The Poisson's ratio versus strain for the same set of experiments as (b).
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Figure 6
Correlation between the elastic response at different strains for the unaged system. (a) The Pearson correlation function of $B_{i} (ε)$ with $B_{i} (0)$ . Expansion is denoted by the full line, and compression is denoted by a dashed line. Correlations for compression decay more rapidly than for expansion. The different colors are for different values of $Δ Z$ as shown in the legend of (b). (b) Correlations of $G_{i} (ε)$ and $G_{i} (0)$ decay faster for lower coordination number, $Δ Z$ . Since the unaged system is on average isotropic $G_{i}$ correlations are equal for positive and negative strains.
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