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research
Avalanches, thresholds, and diffusion in meso-scale amorphous plasticity
Authors
Craig E Maloney
Botond Tyukodi
Damien Vandembroucq
Publication date
17 May 2019
Publisher
'American Physical Society (APS)'
Doi
Cite
View
on
arXiv
Abstract
We present results on a meso-scale model for amorphous matter in athermal, quasi-static (a-AQS), steady state shear flow. In particular, we perform a careful analysis of the scaling with the lateral system size,
L
L
L
, of: i) statistics of individual relaxation events in terms of stress relaxation,
S
S
S
, and individual event mean-squared displacement,
M
M
M
, and the subsequent load increments,
Ξ
Ξ³
\Delta \gamma
Ξ
Ξ³
, required to initiate the next event; ii) static properties of the system encoded by
x
=
Ο
y
β
Ο
x=\sigma_y-\sigma
x
=
Ο
y
β
β
Ο
, the distance of local stress values from threshold; and iii) long-time correlations and the emergence of diffusive behavior. For the event statistics, we find that the distribution of
S
S
S
is similar to, but distinct from, the distribution of
M
M
M
. We find a strong correlation between
S
S
S
and
M
M
M
for any particular event, with
S
βΌ
M
q
S\sim M^{q}
S
βΌ
M
q
with
q
β
0.65
q\approx 0.65
q
β
0.65
.
q
q
q
completely determines the scaling exponents for
P
(
M
)
P(M)
P
(
M
)
given those for
P
(
S
)
P(S)
P
(
S
)
. For the distribution of local thresholds, we find
P
(
x
)
P(x)
P
(
x
)
is analytic at
x
=
0
x=0
x
=
0
, and has a value
P
(
x
)
β£
x
=
0
=
p
0
\left. P(x)\right|_{x=0}=p_0
P
(
x
)
β£
x
=
0
β
=
p
0
β
which scales with lateral system length as
p
0
βΌ
L
β
0.6
p_0\sim L^{-0.6}
p
0
β
βΌ
L
β
0.6
. Extreme value statistics arguments lead to a scaling relation between the exponents governing
P
(
x
)
P(x)
P
(
x
)
and those governing
P
(
S
)
P(S)
P
(
S
)
. Finally, we study the long-time correlations via single-particle tracer statistics. The value of the diffusion coefficient is completely determined by
β¨
Ξ
Ξ³
β©
\langle \Delta \gamma \rangle
β¨
Ξ
Ξ³
β©
and the scaling properties of
P
(
M
)
P(M)
P
(
M
)
(in particular from
β¨
M
β©
\langle M \rangle
β¨
M
β©
) rather than directly from
P
(
S
)
P(S)
P
(
S
)
as one might have naively guessed. Our results: i) further define the a-AQS universality class, ii) clarify the relation between avalanches of stress relaxation and diffusive behavior, iii) clarify the relation between local threshold distributions and event statistics
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Last time updated on 11/12/2019