Abstract

In this paper, a data-driven approach for constructing elastoplastic constitutive law of microstructured materials is proposed by combining the insights from plasticity theory and the tools of artificial intelligence (i.e., constructing yielding function through ANN) to reduce the required amount of data for machine learning. Illustrative examples show that the constitutive laws constructed by the present approach can be used to solve the boundary value problems (BVPs) involving elastoplastic materials with microstructures under complex loading paths (e.g., cyclic/reverse loading) effectively. The limitation of the proposed approach is also discussed.

References

References
1.
Hill
,
R.
,
1998
,
The Mathematical Theory of Plasticity
,
Oxford University Press
,
New York
.
2.
Hill
,
R.
, and
Rice
,
J. R.
,
1972
, “
Constitutive Analysis of Elastic-Plastic Crystals at Arbitrary Strain
,”
J. Mech. Phys. Solids
,
20
(
6
), pp.
401
413
. 10.1016/0022-5096(72)90017-8
3.
Drucker
,
D. C.
, and
Prager
,
W3.
,
1952
, “
Soil Mechanics and Plastic Analysis or Limit Design
,”
Q. Appl. Math.
,
10
(
2
), pp.
157
165
. 10.1090/qam/48291
4.
Fung
,
Y. C.
, and
Drucker
,
D. C.
,
1966
, “
Foundation of Solid Mechanics
,”
ASME J. Appl. Mech.
,
33
(
1
), p.
238
. 10.1115/1.3625018
5.
Ghaboussi
,
J.
, and
Sidarta
,
D. E.
,
1998
, “
New Nested Adaptive Neural Networks (NANN) for Constitutive Modeling
,”
Comput. Geotech.
,
22
(
1
), pp.
29
52
. 10.1016/S0266-352X(97)00034-7
6.
Furukawa
,
T.
, and
Yagawa
,
G.
,
1998
, “
Implicit Constitutive Modelling for Viscoplasticity Using Neural Networks
,”
Int. J. Numer. Methods Eng.
,
43
(
2
), pp.
195
219
. 10.1002/(SICI)1097-0207(19980930)43:2<195::AID-NME418>3.0.CO;2-6
7.
Al-Haik
,
M.
,
Hussaini
,
M.
, and
Garmestani
,
H.
,
2006
, “
Prediction of Nonlinear Viscoelastic Behavior of Polymeric Composites Using an Artificial Neural Network
,”
Int. J. Plast.
,
22
(
7
), pp.
1367
1392
. 10.1016/j.ijplas.2005.09.002
8.
Yang
,
H.
,
Guo
,
X.
,
Tang
,
S.
, and
Liu
,
W. K.
,
2019
, “
Derivation of Heterogeneous Material Laws Via Data-Driven Principal Component Expansions
,”
Comput. Mech.
,
64
(
2
), pp.
365
379
. 10.1007/s00466-019-01728-w
9.
Zopf
,
C.
, and
Kaliske
,
M.
,
2017
, “
Numerical Characterisation of Uncured Elastomers by a Neural Network Based Approach
,”
Comput. Struct.
,
182
, pp.
504
525
. 10.1016/j.compstruc.2016.12.012
10.
Mozaffar
,
M.
,
Bostanabad
,
R.
,
Chen
,
W.
,
Ehmann
,
K.
,
Cao
,
J.
, and
Bessa
,
M.
,
2019
, “
Deep Learning Predicts Path-Dependent Plasticity
,”
Proc. Natl. Acad. Sci. U. S. A.
,
116
(
52
), pp.
26414
26420
. 10.1073/pnas.1911815116
11.
Wang
,
K.
, and
Sun
,
W.
,
2019
, “
Meta-Modeling Game for Deriving Theory-Consistent, Microstructure-Based Traction–Separation Laws Via Deep Reinforcement Learning
,”
Comput. Methods Appl. Mech. Eng.
,
346
, pp.
216
241
. 10.1016/j.cma.2018.11.026
12.
Wang
,
K.
, and
Sun
,
W.
,
2018
, “
A Multiscale Multi-Permeability Poroplasticity Model Linked by Recursive Homogenizations and Deep Learning
,”
Comput. Methods Appl. Mech. Eng.
,
334
, pp.
337
380
. 10.1016/j.cma.2018.01.036
13.
Liu
,
Z.
,
Bessa
,
M. A.
, and
Liu
,
W. K.
,
2016
, “
Self-Consistent Clustering Analysis: An Efficient Multi-Scale Scheme for Inelastic Heterogeneous Materials
,”
Comput. Methods Appl. Mech. Eng.
,
306
, pp.
319
341
. 10.1016/j.cma.2016.04.004
14.
Bessa
,
M. A.
,
Bostanabad
,
R.
,
Liu
,
Z.
,
Hu
,
A.
,
Apley
,
D. W.
,
Brinson
,
C.
,
Chen
,
W.
, and
Liu
,
W. K.
,
2017
, “
A Framework for Data-Driven Analysis of Materials Under Uncertainty: Countering the Curse of Dimensionality
,”
Comput. Methods Appl. Mech. Eng.
,
320
, pp.
633
667
. 10.1016/j.cma.2017.03.037
15.
Kafka
,
O. L.
,
Cheng
,
Y.
,
Shakoor
,
M.
,
Liu
,
Z.
,
Wagner
,
G. J.
, and
Liu
,
W. K.
,
2018
, “
Data-Driven Mechanistic Modeling of Influence of Microstructure on High-Cycle Fatigue Life of Nickel Titanium
,”
J. Metals
,
70
(
7
), pp.
1
5
. 10.1007/s11837-018-2868-2
16.
Liu
,
Z.
,
Fleming
,
M.
, and
Liu
,
W. K.
,
2018
, “
Microstructural Material Database for Self-Consistent Clustering Analysis of Elastoplastic Strain Softening Materials
,”
Comput. Methods Appl. Mech. Eng.
,
330
, pp.
547
577
. 10.1016/j.cma.2017.11.005
17.
Shakoor
,
M.
,
Kafka
,
O. L.
, and
Liu
,
W. K.
,
2019
, “
Data Science for Finite Strain Mechanical Science of Ductile Materials
,”
Comput. Mech.
,
64
(
1
), pp.
33
45
. 10.1007/s00466-018-1655-9
18.
Cheng
,
G.
,
Li
,
X.
,
Nie
,
Y.
, and
Li
,
H.
,
2019
, “
FEM-Cluster Based Reduction Method for Efficient Numerical Prediction of Effective Properties of Heterogeneous Material in Nonlinear Range
,”
Comput. Methods Appl. Mech. Eng.
,
348
, pp.
157
184
. 10.1016/j.cma.2019.01.019
19.
Nie
,
Y.
,
Cheng
,
G.
,
Li
,
X.
,
Xu
,
L.
, and
Li
,
K.
,
2019
, “
Principle of Cluster Minimum Complementary Energy of FEM-Cluster-Based Reduced Order Method: Fast Updating the Interaction Matrix and Predicting Effective Nonlinear Properties of Heterogeneous Material
,”
Comput. Mech.
,
64
(
2
), pp.
323
349
. 10.1007/s00466-019-01710-6
20.
Tang
,
S.
,
Zhang
,
L.
, and
Liu
,
W. K.
,
2018
, “
From Virtual Clustering Analysis to Self-Consistent Clustering Analysis: a Mathematical Study
,”
Comput. Mech.
,
62
(
6
), pp.
1443
1460
. 10.1007/s00466-018-1573-x
21.
Kirchdoerfer
,
T.
, and
Ortiz
,
M.
,
2016
, “
Data Driven Computational Mechanics
,”
Comput. Methods Appl. Mech. Eng.
,
304
, pp.
81
101
. 10.1016/j.cma.2016.02.001
22.
Eggersmann
,
R.
,
Kirchdoerfer
,
T.
,
Reese
,
S.
,
Stainier
,
L.
, and
Ortiz
,
M.
,
2019
, “
Model-Free Data-Driven Inelasticity
,”
Comput. Methods Appl. Mech. Eng.
,
350
, pp.
81
99
. 10.1016/j.cma.2019.02.016
23.
Hill
,
R.
,
1985
, “
On the Micro-to-Macro Transition in Constitutive Analyses of Elastoplastic Response at Finite Strain
,”
Math. Proc. Camb. Philos. Soc.
,
98
(
3
), pp.
579
590
. 10.1017/S0305004100063787
24.
Nemat-Nasser
,
S.
, and
Hori
,
M.
,
1993
,
Micromechanics: Overall Properties of Heterogeneous Materials
,
Elsevier
,
Amsterdam
.
25.
Suquet
,
P. M.
,
1985
, “
Local and Global Aspects in the Mathematical Theory of Plasticity
,”
Plasticity Today: Modelling, Methods and Applications
,
A.
Sawczuk
and
G.
Bianchi
, eds.,
Elsevier Applied Science Publishers
, pp.
279
310
.
26.
Hill
,
R.
,
1965
, “
Continuum Micro-Mechanics of Elastoplastic Polycrystals
,”
J. Mech. Phys. Solids
,
13
(
2
), pp.
89
101
. 10.1016/0022-5096(65)90023-2
27.
Hill
,
R.
,
1972
, “
On Constitutive Macro-Variables for Heterogeneous Solids at Finite Strain
,”
Proc. R. Soc. Lond. A: Math. Phys. Sci.
,
326
(
1565
), pp.
131
147
. 0.1098/rspa.1972.0001
28.
Simo
,
J. C.
, and
Hughes
,
T. J.
,
2006
,
Computational Inelasticity
, Vol.
7
,
Springer Science & Business Media
.
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