Aging and linear response in the Hébraud-Lequeux model for amorphous rheology

Peter Sollich; Julien Olivier; Didier Bresch

doi:10.1088/1751-8121/aa6261

Aging and linear response in the Hébraud-Lequeux model for amorphous rheology

Peter Sollich, Julien Olivier, Didier Bresch

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Abstract

We analyse the aging dynamics of the Hébraud-Lequeux model, a self-consistent stochastic model for the evolution of local stress in an amorphous material. We show that the model exhibits initial-condition dependent freezing: the stress diffusion constant decays with time as D 1/t² during aging so that the cumulative amount of memory that can be erased, which is given by the time integral of D(t), is finite. Accordingly the shear stress relaxation function, which we determine in the long-time regime, only decays to a plateau and becomes progressively elastic as the system ages. The frequency-dependent shear modulus exhibits a corresponding overall decay of the dissipative part with system age, while the characteristic relaxation times scale linearly with age as expected.

Original language	English
Article number	165002
Journal	Journal of Physics A
Volume	50
Issue number	16
Early online date	23 Feb 2017
DOIs	https://doi.org/10.1088/1751-8121/aa6261
Publication status	Published - 17 Mar 2017

Keywords

aging rheology
asymptotic analysis
glassy dynamics

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10.1088/1751-8121/aa6261

Aging and linear response_SOLLICH_Accepted2_GREEN AAMAccepted author manuscript, 2.37 MB

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abstract = "We analyse the aging dynamics of the H{\'e}braud-Lequeux model, a self-consistent stochastic model for the evolution of local stress in an amorphous material. We show that the model exhibits initial-condition dependent freezing: the stress diffusion constant decays with time as D 1/t2 during aging so that the cumulative amount of memory that can be erased, which is given by the time integral of D(t), is finite. Accordingly the shear stress relaxation function, which we determine in the long-time regime, only decays to a plateau and becomes progressively elastic as the system ages. The frequency-dependent shear modulus exhibits a corresponding overall decay of the dissipative part with system age, while the characteristic relaxation times scale linearly with age as expected.",

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AU - Sollich, Peter

AU - Olivier, Julien

AU - Bresch, Didier

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Y1 - 2017/3/17

N2 - We analyse the aging dynamics of the Hébraud-Lequeux model, a self-consistent stochastic model for the evolution of local stress in an amorphous material. We show that the model exhibits initial-condition dependent freezing: the stress diffusion constant decays with time as D 1/t2 during aging so that the cumulative amount of memory that can be erased, which is given by the time integral of D(t), is finite. Accordingly the shear stress relaxation function, which we determine in the long-time regime, only decays to a plateau and becomes progressively elastic as the system ages. The frequency-dependent shear modulus exhibits a corresponding overall decay of the dissipative part with system age, while the characteristic relaxation times scale linearly with age as expected.

AB - We analyse the aging dynamics of the Hébraud-Lequeux model, a self-consistent stochastic model for the evolution of local stress in an amorphous material. We show that the model exhibits initial-condition dependent freezing: the stress diffusion constant decays with time as D 1/t2 during aging so that the cumulative amount of memory that can be erased, which is given by the time integral of D(t), is finite. Accordingly the shear stress relaxation function, which we determine in the long-time regime, only decays to a plateau and becomes progressively elastic as the system ages. The frequency-dependent shear modulus exhibits a corresponding overall decay of the dissipative part with system age, while the characteristic relaxation times scale linearly with age as expected.

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KW - asymptotic analysis

KW - glassy dynamics

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JO - Journal of Physics A

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ER -

Aging and linear response in the Hébraud-Lequeux model for amorphous rheology

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