Mean field theory of yielding under oscillatory shear

Parley, Jack T.; Sastry, Srikanth; Sollich, Peter

doi:10.48550/arxiv.2112.11578

Cited by 4 publications

(7 citation statements)

References 33 publications

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“…Recent years have witnessed significant activity in developing a statistical mechanical description of these phenomena [2][3][4][5]. Yielding behaviour in model amorphous solids has been investigated experimentally [6][7][8], through computer simulations [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], and theoretical investigations including the study of elastoplastic models and corresponding mean field theories [4,13,[27][28][29][30][31][32][33]. These investigations have largely focused on the response to uniform shear, but several investigations have explored yielding behaviour under cyclic deformation [11, 12, 19, 21, 23-26, 29, 31-35].…”

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confidence: 99%

Yielding behavior of glasses under asymmetric cyclic deformation

Adhikari¹,

Mungan²,

Sastry³

2022

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We consider the yielding behaviour of a model glass subjected to asymmetric cyclic shear deformation, wherein the applied strain varies between 0 and a maximum value γmax, and study its dependence on the degree of annealing of the glass and system size. The yielding behaviour of well annealed glasses (unlike poorly annealed glasses) display striking differences from the symmetric case, with the emergence of an intermediate strain regime with substantial plasticity but no yielding. The observed behaviour is satisfactorily captured by a recently proposed model. For larger system sizes, the intermediate strain regime narrows, leading to a remarkable reversal of yield strain with annealing.

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confidence: 99%

Yielding behavior of glasses under asymmetric cyclic deformation

Adhikari¹,

Mungan²,

Sastry³

2022

Preprint

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“…Thanks to the normalisation of δP (σ, t w ), we then have from Eq. ( 10) that (16) which corresponds to the amount of stress that has been relaxed up to time t, due to plastic events. We will denote the total (asymptotic) amount of stress the system is able to relax as…”

Section: Overview Of Analytical Resultsmentioning

confidence: 99%

“…given by the Hurst exponent H = 1/µ, and the corresponding form of the yield rate Γ(t). From (16), this means that (assuming δP (σ, t) has decayed enough, see also App. C) the amount of stress relaxed up to time t is essentially given by the integral of the initial condition δP (σ, t w ) over the range of stress ∆σ below the yield threshold (note that σ ≈ 1 in this range).…”

Section: Overview Of Analytical Resultsmentioning

confidence: 99%

“…An obvious direction for extending the model would be to study the effect of disorder on the aging described here and in [25]. This could be done by introducing a distribution ρ(σ c ) of yield barriers as in [16,28]; in this way there would be aging not only in stress, but also as a result of mesoscopic regions transitioning to deeper energy minima with higher yield barriers. rate as ∆ t = ∆t Γ, we find…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…Elastoplastic models accordingly describe the dynamics of mesoscopic stress elements as consisting of periods of elastic loading interrupted by plastic relaxation events. This elastoplastic approach has been very successful in studying the yielding of amorphous solids under mechanical deformation [8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

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Mean field description of aging linear response in athermal amorphous solids

Parley¹,

Mandal²,

Sollich³

2022

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We study the linear response to strain in a mean field elastoplastic model for athermal amorphous solids, incorporating the power-law mechanical noise spectrum arising from plastic events. In the "jammed" regime of the model, where the plastic activity exhibits a non-trivial slow relaxation referred to as aging, we find that the stress relaxes incompletely to an age-dependent plateau, on a timescale which grows with material age. We determine the scaling behaviour of this aging linear response analytically, finding that key scaling exponents are universal and independent of the noise exponent µ. For µ > 1, we find simple aging, where the stress relaxation timescale scales linearly with the age tw of the material. At µ = 1, which corresponds to interactions mediated by the physical elastic propagator, we find instead a t 1/2 w scaling arising from the stretched exponential decay of the plastic activity. We compare these predictions with measurements of the linear response in computer simulations of a model jammed system of repulsive soft athermal particles, during its slow dissipative relaxation towards mechanical equilibrium, and find good agreement with the theory.

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Mapping out the glassy landscape of a mesoscopic elastoplastic model

Kumar

Patinet

Maloney

et al. 2022

The Journal of Chemical Physics

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We develop a mesoscopic model to study plastic behavior of amorphous materials under cyclic loading. The model is depinning-like and driven by a disordered thresholds dynamics coupled by long-range elastic interactions. We propose a simple protocol of ``glass preparation' which allows to mimic thermalisation at high temperature and aging at vanishing temperature. Various levels of glass stabilities (from brittle to ductile) can be achieved by tuning the aging duration. The aged glasses are immersed into a quenched disorder landscape, serving as initial configurations for various protocols of mechanical loading by shearing. The dependence of the plastic behavior upon monotonous loading is recovered. The behavior under cyclic loading is studied for different ages and system sizes. The size and age dependence of the irreversibility transition is discussed. A thorough characterization of the disorder-landscape is achieved through analysis of transition graphs, which describe plastic deformation pathways under athermal quasi-static shear. The analysis of the stability ranges of the strongly connected components of the transition graphs reveals the emergence of a phase-separation like process associated with the aging of the glass. Increasing the age and hence stability of the initial glass, results in a gradual break-up of the landscape of dynamically accessible stable states into three distinct regions: one region centered around the initially prepared glass phase, and two additional regions, characterized by well-separated ranges of positive and negative plastic strains, which are accessible only from the initial glass phase by passing through the stress peak in the forward, respectively, backward shearing directions.

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Mean field theory of yielding under oscillatory shear

Cited by 4 publications

References 33 publications

Yielding behavior of glasses under asymmetric cyclic deformation

Yielding behavior of glasses under asymmetric cyclic deformation

Mean field description of aging linear response in athermal amorphous solids

Mapping out the glassy landscape of a mesoscopic elastoplastic model

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