Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Thermodynamically Consistent Fractional Visco-Elasto-Plastic Model
  with Memory-Dependent Damage for Anomalous Materials   We develop a thermodynamically consistent, fractional visco-elasto-plastic
model coupled with damage for anomalous materials. The model utilizes
Scott-Blair rheological elements for both visco-elastic/plastic parts. The
constitutive equations are obtained through Helmholtz free-energy potentials
for Scott-Blair elements, together with a memory-dependent fractional yield
function and dissipation inequalities. A memory-dependent Lemaitre-type damage
is introduced through fractional damage energy release rates. For
time-fractional integration of the resulting nonlinear system of equations, we
develop a first-order semi-implicit fractional return-mapping algorithm. We
also develop a finite-difference discretization for the fractional damage
energy release rate, which results into Hankel-type matrix-vector operations
for each time-step, allowing us to reduce the computational complexity from
$\mathcal{O}(N^3)$ to $\mathcal{O}(N^2)$ through the use of Fast Fourier
Transforms. Our numerical results demonstrate that the fractional orders for
visco-elasto-plasticity play a crucial role in damage evolution, due to the
competition between the anomalous plastic slip and bulk damage energy release
rates.

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The categories of this paper are: solv-int
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The categories of this paper are: econ
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol