Farid ABED-MERAIM, PhD

Professor

Arts et Métiers ParisTech

Metz, France


Biography

Farid Abed-Meraim received his Ph.D. degree in theoretical and applied mechanics from École Polytechnique, Paris, in 1999. From 1999 to 2000, he held a Postdoctoral position at the LMT laboratory, Ecole Normale Supérieure de Cachan. He then joined Arts et Métiers ParisTech, Metz Campus, in 2000, where he works currently as a Professor at the LEM3 laboratory. From 2006 to 2008, he worked as a CNRS full-time Research Associate at the LaMCoS laboratory of INSA, Lyon. He also was a Visiting Professor at Eindhoven Technical University (Department of Mechanical Engineering) from 2010 to 2011. His main current research interests include structural stability (bifurcation) analysis of dissipative systems (elastoplastic, viscoelastic, and viscoplastic), material instability modeling in relation to the prediction of formability of metal sheets, and multiscale approaches (micromechanics, crystal plasticity, scale-transition schemes) as well as finite element technology (solid-shell formulations).

Research Interest

Theoretical and Applied Mechanics, Mechanics of Materials, Computational Mechanics, Stability & Bifurcation, Sheet Metal Forming.

Scientific Activities

Publications

1) Tian, H., Potier-Ferry, M., Abed-Meraim, F.
A numerical method based on Taylor series for bifurcation analyses within Föppl–von Karman plate theory
(2018) Mechanics Research Communications, 93, pp. 154-158. Cited 3 times.
2) Kpeky, F., Abed-Meraim, F., Daya, E.M., Samah, O.-D. Modeling of hybrid vibration control for multilayer structures using solid-shell finite elements (2018) Mechanics of Advanced Materials and Structures, 25 (12), pp. 1033-1046.
3) Aouadi, M., Bettaieb, M.B., Abed-Meraim, F. Mathematical and numerical analysis in thermo-gradient-dependent theory of plasticity (2018) ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 98 (9), pp. 1603-1622.
4) Ben Bettaieb, M., Abed-Meraim, F. Influence of the non-schmid effects on the ductility limit of polycrystalline sheet metals (2018) Materials, 11 (8), art. no. 1386.
5) Ben Bettaieb, M., Abed-Meraim, F. Strain localization analysis for planar polycrystals based on bifurcation theory
(2018) Comptes Rendus - Mecanique, 346 (8), pp. 647-664.
6) Chalal, H., Abed-Meraim, F. Quadratic solid-shell finite elements for geometrically nonlinear analysis of functionally graded material plates (2018) Materials, 11 (6), art. no. 1046, .
7) Bouktir, Y., Chalal, H., Abed-Meraim, F. Prediction of necking in thin sheet metals using an elastic–plastic model coupled with ductile damage and bifurcation criteria (2018) International Journal of Damage Mechanics, 27 (6), pp. 801-839. Cited 2 times.
8) Kpeky, F., Abed-Meraim, F., Boudaoud, H., Daya, E.M. Linear and quadratic solid–shell finite elements SHB8PSE and SHB20E for the modeling of piezoelectric sandwich structures (2018) Mechanics of Advanced Materials and Structures, 25 (7), pp. 559-578. Cited 5 times.
9) Gupta, A., Ben Bettaieb, M., Abed-Meraim, F., Kalidindi, S.R. Computationally efficient predictions of crystal plasticity based forming limit diagrams using a spectral database (2018) International Journal of Plasticity, 103, pp. 168-187. Cited 1 time.
10) Kpeky, F., Abed-Meraim, F., Daya, E.M. New linear and quadratic prismatic piezoelectric solid–shell finite elements
(2018) Applied Mathematics and Computation, 319, pp. 355-368. Cited 3 times.
11) Bettaieb, M.B., Abed-Meraim, F. Ductility prediction of substrate-supported metal layers based on rate-independent crystal plasticity theory
(2018) International Journal of Material Forming, pp. 1-15. Article in Press.
12) Kpeky, F., Akoussan, K., Abed-Meraim, F., Daya, E.-M. Influence of geometric and material parameters on the damping properties of multilayer structures
(2018) Composite Structures, 183 (1), pp. 611-619.
13) Bettaieb, M.B., Abed-Meraim, F., Lemoine, X.
Numerical investigation of the combined effects of curvature and normal stress on sheet metal
formability
(2017) International Journal of Material Forming, pp. 1-11. Article in Press.
14) Chalal, H., Abed-Meraim, F.
Numerical predictions of the occurrence of necking in deep drawing processes
(2017) Metals, 7 (11), art. no. 455, . Cited 2 times.
15) Ben Bettaieb, M., Abed-Meraim, F.
Strain rate effects on localized necking in substrate-supported metal layers
(2017) International Journal of Advanced Manufacturing Technology, 92 (9-12), pp. 3461-3480. Cited
1 time.
16) Bettaieb, M.B., Abed-Meraim, F.
Theoretical and numerical investigation of the impact of out-of-plane compressive stress on sheet
metal formability
(2017) International Journal of Mechanical Sciences, 130, pp. 244-257. Cited 2 times.
17) Wang, P., Chalal, H., Abed-Meraim, F.
Quadratic prismatic and hexahedral solid–shell elements for geometric nonlinear analysis of
laminated composite structures
(2017) Composite Structures, 172, pp. 282-296. Cited 1 time.
18) Ben Bettaieb, M., Abed-Meraim, F.
Localized Necking in Elastomer-Supported Metal Layers: Impact of Kinematic Hardening
(2017) Journal of Manufacturing Science and Engineering, Transactions of the ASME, 139 (6), art.
no. 061008, . Cited 2 times.
19) Ben Bettaieb, M., Abed-Meraim, F.
Effect of kinematic hardening on localized necking in substrate-supported metal layers
(2017) International Journal of Mechanical Sciences, 123, pp. 177-197. Cited 4 times.
20) Akpama, H.K., Ben Bettaieb, M., Abed-Meraim, F.
Localized necking predictions based on rate-independent self-consistent polycrystal plasticity:
Bifurcation analysis versus imperfection approach
(2017) International Journal of Plasticity, 91, pp. 205-237. Cited 5 times.
21) Soho, K., Lemoine, X., Abed-Meraim, F., Zahrouni, H.
Investigation of the effect of temper rolling on the texture evolution and mechanical behavior of IF
steels using multiscale simulation
(2017) International Journal of Material Forming, 10 (1), pp. 29-42. Cited 2 times.
22) Chalal, H., Abed-Meraim, F.
Hardening effects on formability limit prediction based on gurson-type damage models and bifurcation
analysis
(2017) Proceedings of the 14th International Conference on Computational Plasticity - Fundamentals
and Applications, COMPLAS 2017, 2017-January, pp. 174-183.
23) Chalal, H., Abed-Meraim, F.
Determination of forming limit diagrams based on ductile damage models and necking criteria
(2017) Latin American Journal of Solids and Structures, 14 (10), pp. 1872-1892.
24) Kpeky, F., Abed-Meraim, F., Daya, E.M.
Analysis of primal and dual variables in structural shape control by piezoelectric patches using
solid-shell finite elements
(2017) 8th Conference on Smart Structures and Materials, SMART 2017 and 6th International
Conference on Smart Materials and Nanotechnology in Engineering, SMN 2017, 2017-January, pp.
188-199.
25) Akpama, H.K., Bettaieb, M.B., Abed-Meraim, F.
Prediction of plastic instability in sheet metals during forming processes using the loss of ellipticity
approach
(2017) Latin American Journal of Solids and Structures, 14 (10), pp. 1816-1836.
26) Wang, P., Chalal, H., Abed-Meraim, F.
Explicit dynamic analysis of sheet metal forming processes using linear prismatic and hexahedral
solid-shell elements
(2017) Engineering Computations (Swansea, Wales), 34 (5), pp. 1413-1445.
27) Wang, P., Chalal, H., Abed-Meraim, F.
Linear and quadratic solid-shell elements for quasi-static and dynamic simulations of thin 3D
structures: Application to a deep drawing process
(2017) Journal of Mechanical Engineering, 63 (1), pp. 25-34. Cited 1 time.
28) Wang, P., Chalal, H., Abed-Meraim, F.
Quadratic solid–shell elements for nonlinear structural analysis and sheet metal forming simulation
(2017) Computational Mechanics, 59 (1), pp. 161-186. Cited 6 times.
29) Akpama, H.K., Bettaieb, M.B., Abed-Meraim, F.
Numerical integration of rate-independent BCC single crystal plasticity models: comparative study of
two classes of numerical algorithms
(2016) International Journal for Numerical Methods in Engineering, 108 (5), pp. 363-422. Cited 8
times.
30) Akpama, H.K., Bettaieb, M.B., Abed-Meraim, F.
Ductility prediction of substrate-supported metal layers based on rate-independent crystal plasticity
theory
(2016) MATEC Web of Conferences, 80, art. no. 02007, .
31) Wang, P., Chalal, H., Abed-Meraim, F.
Simulation of nonlinear benchmarks and sheet metal forming processes using linear and quadratic
solid-shell elements combined with advanced anisotropic behavior models
(2016) MATEC Web of Conferences, 80, art. no. 07001, .
32) Bettaieb, M.B., Lagaza, H., Abed-Meraim, F., Lemoine, X.
Prediction of Forming Limit Diagrams under combined Bending-Stretching loadings
(2016) MATEC Web of Conferences, 80, art. no. 03003, .
33) Wang, P., Chalal, H., Abed-Meraim, F.
On the use of solid-shell elements for thin structures: Application to impact and sheet metal forming
simulations
(2016) AIP Conference Proceedings, 1769, art. no. 070007, .
34) Msolli, S., Bettaieb, M.B., Abed-Meraim, F.
Modeling of void coalescence initiation and its impact on the prediction of material failure
(2016) AIP Conference Proceedings, 1769, art. no. 160006, .
35) Akpama, H.K., Bettaieb, M.B., Abed-Meraim, F.
Prediction of localized necking based on crystal plasticity: Comparison of bifurcation and imperfection
approaches
(2016) Key Engineering Materials, 716, pp. 779-789.
36) Akpama, H.K., Ben Bettaieb, M., Abed-Meraim, F.
Influence of the yield surface curvature on the forming limit diagrams predicted by crystal plasticity
theory
(2016) Latin American Journal of Solids and Structures, 13 (12), pp. 2231-2250. Cited 2 times.
37) Bouktir, Y., Chalal, H., Haddad, M., Abed-Meraim, F.
Investigation of ductility limits based on bifurcation theory coupled with continuum damage mechanics
(2016) Materials and Design, 90, pp. 969-978. Cited 1 time.
38) Chalal, H., Abed-Meraim, F.
Hardening effects on strain localization predictions in porous ductile materials using the bifurcation
approach
(2015) Mechanics of Materials, 91 (P1), art. no. 2457, pp. 152-166. Cited 7 times.
39) Kpeky, F., Boudaoud, H., Abed-Meraim, F., Daya, E.M.
Modeling of viscoelastic sandwich beams using solid-shell finite elements
(2015) Composite Structures, 133, pp. 105-116. Cited 5 times.
40) Ben Bettaieb, M., Abed-Meraim, F.
Investigation of localized necking in substrate-supported metal layers: Comparison of bifurcation and
imperfection analyses
(2015) International Journal of Plasticity, 65, pp. 168-190. Cited 20 times.
41) Akpama, H.K., Ben Bettaieb, M., Abed-Meraim, F.
A comparative study of forming limit diagrams predicted by two different plasticity theories involving
vertex effects
(2015) Key Engineering Materials, 651-653, pp. 21-26. Cited 1 time.
42) Abed-Meraim, F., Peerlings, R.H.J., Geers, M.G.D.
Comparison of bifurcation analysis and maximum force criteria in the prediction of necking in
stretched metal sheets
(2015) Proceedings of the 8th International Conference on Computational Plasticity - Fundamentals
and Applications, COMPLAS 2015, pp. 182-193.
43) Wang, P., Chalal, H., Abed-Meraim, F.
Efficient solid-shell finite elements for quasi-static and dynamic analyses and their application to
sheet metal forming simulation
(2015) Key Engineering Materials, 651-653, pp. 344-349. Cited 2 times.
44) Abed-Meraim, F., Peerlings, R.H.J., Geers, M.G.D.
Bifurcation analysis versus maximum force criteria in formability limit assessment of stretched metal
sheets
(2014) International Journal of Applied Mechanics, 6 (6), art. no. 1450064, . Cited 1 time.
45) Abed-Meraim, F., Balan, T., Altmeyer, G.
Investigation and comparative analysis of plastic instability criteria: Application to forming limit
diagrams
(2014) International Journal of Advanced Manufacturing Technology, 71 (5-8), pp. 1247-1262. Cited
27 times.
46) Mansouri, L.Z., Chalal, H., Abed-Meraim, F.
Ductility limit prediction using a GTN damage model coupled with localization bifurcation analysis
(2014) Mechanics of Materials, 76, pp. 64-92. Cited 25 times.
47) Franz, G., Abed-Meraim, F., Berveiller, M.
Effect of microstructural and morphological parameters on the formability of BCC metal sheets
(2014) Steel Research International, 85 (6), pp. 980-987. Cited 2 times.
48) Soho, K., Abed-Meraim, F., Lemoine, X., Zahrouni, H.
Multiscale finite element simulation of forming processes based on crystal plasticity
(2014) Key Engineering Materials, 611-612, pp. 545-552.
49) Kpeky, F., Boudaoud, H., Chalal, H., Abed-Meraim, F., Daya, E.M.
Vibration modeling of sandwich structures using solid-shell finite elements
(2014) 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference
on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid
Dynamics, ECFD 2014, pp. 3650-3657.
50) Franz, G., Abed-Meraim, F., Berveiller, M.
Impact of intragranular substructure parameters on the forming limit diagrams of single-phase B.C.C.
steels
(2013) Materials, 6 (11), pp. 5217-5233.
51) Franz, G., Abed-Meraim, F., Berveiller, M.
Strain localization analysis for single crystals and polycrystals: Towards microstructure-ductility
linkage
(2013) International Journal of Plasticity, 48, pp. 1-33. Cited 36 times.
52) Pipard, J.-M., Balan, T., Abed-Meraim, F., Lemoine, X.
Elasto-visco-plastic modeling of mild steels for sheet forming applications over a large range of strain
rates
(2013) International Journal of Solids and Structures, 50 (16-17), pp. 2691-2700. Cited 3 times.
53) Carvalho Resende, T., Bouvier, S., Abed-Meraim, F., Balan, T., Sablin, S.-S.
Dislocation-based model for the prediction of the behavior of b.c.c. materials - Grain size and strain
path effects
(2013) International Journal of Plasticity, 47, pp. 29-48. Cited 29 times.
54) Pipard, J.-M., Balan, T., Abed-Meraim, F., Lemoine, X.
Physically-motivated elasto-visco-plastic model for the large strain-rate behavior of steels
(2013) Key Engineering Materials, 554-557, pp. 1164-1173.
55) Abed-Meraim, F., Trinh, V.-D., Combescure, A.
New quadratic solid-shell elements and their evaluation on linear benchmark problems
(2013) Computing, 95 (5), pp. 373-394. Cited 14 times.
56) Franz, G., Abed-Meraim, F., Zineb, T.B.
Effect of microstructural and physical mechanisms on mechanical properties of single-phase steels
(2013) Advanced Science Letters, 19 (1), pp. 346-350.
57) Carvalho-Resende, T., Balan, T., Bouvier, S., Abed-Meraim, F., Sablin, S.-S.
Numerical investigation and experimental validation of a plasticity model for sheet steel forming
(2013) Modelling and Simulation in Materials Science and Engineering, 21 (1), . Cited 5 times.
58) Salahouelhadj, A., Abed-Meraim, F., Chalal, H., Balan, T.
Application of the continuum shell finite element SHB8PS to sheet forming simulation using an
extended large strain anisotropic elastic-plastic formulation
(2012) Archive of Applied Mechanics, 82 (9), pp. 1269-1290. Cited 19 times.
59) Mansouri, L.Z., Chalal, H., Abed-Meraim, F., Balan, T.
Plastic instability based on bifurcation analysis: Effect of hardening and gurson damage parameters
on strain localization
(2012) Key Engineering Materials, 504-506, pp. 35-40.
60) Abed-Meraim, F., Trinh, V.-D., Combescure, A.
Assumed-strain solid-shell formulation for the six-node finite element SHB6: Evaluation on non-linear
benchmark problems
(2012) European Journal of Computational Mechanics, 21 (1-2), pp. 52-71. Cited 3 times.
61) Chalal, H., Salahouelhadj, A., Abed-Meraim, F.
Evaluation of a new solid-shell finite element on the simulation of sheet metal forming processes
(2012) Steel Research International, SPL. ISSUE, pp. 315-318.
62) Salahouelhadj, A., Abed-Meraim, F., Chalal, H., Balan, T.
On the implementation of the continuum shell finite element SHB8PS and application to sheet forming
simulation
(2011) AIP Conference Proceedings, 1353, pp. 1203-1208.
63) Mansouri, L.Z., Chalal, H., Abed-Meraim, F., Balan, T.
Prediction of strain localization during sheet metal forming using bifurcation analysis and gurson-type
damage - Complas XI
(2011) Computational Plasticity XI - Fundamentals and Applications, COMPLAS XI, pp. 1061-1070.
Cited 1 time.
64) Salahouelhadj, A., Chalal, H., Abed-Meraim, F., Balan, T.
Elastic-plastic analyses using the solid-shell finite element SHB8PS and evaluation on sheet forming
applications - COMPLAS XI
(2011) Computational Plasticity XI - Fundamentals and Applications, COMPLAS XI, pp. 1369-1379.
65) Trinh, V.-D., Abed-Meraim, F., Combescure, A.
A new assumed strain solid-shell formulation "SHB6" for the six-node prismatic finite element
(2011) Journal of Mechanical Science and Technology, 25 (9), pp. 2345-2364. Cited 21 times.
66) Leahu-Aluas, I., Abed-Meraim, F.
A proposed set of popular limit-point buckling benchmark problems
(2011) Structural Engineering and Mechanics, 38 (6), pp. 767-802. Cited 5 times.
67) Killpack, M., Abed-Meraim, F.
Limit-point buckling analyses using solid, shell and solid-shell elements
(2011) Journal of Mechanical Science and Technology, 25 (5), pp. 1105-1117. Cited 5 times.
68) Franz, G., Abed-Meraim, F., Zineb, T.B., Lemoine, X., Berveiller, M.
Impact of intragranular microstructure development on ductility limits of multiphase steels
(2011) Materials Science and Engineering A, 528 (10-11), pp. 3777-3785. Cited 4 times.
69) Abed-Meraim, F., Combescure, A.
New prismatic solid-shell element: Assumed strain formulation and hourglass mode analysis
(2011) Structural Engineering and Mechanics, 37 (2), pp. 253-256. Cited 2 times.
70) Racz, S.-G., Khan, S., Chalal, H., Abed-Meraim, F., Balan, T.
Prediction of springback after draw-bending test using different material models
(2010) AIP Conference Proceedings, 1315, pp. 419-424. Cited 2 times.
71) Carvalho Resende, T., Balan, T., Abed-Meraim, F., Bouvier, S., Sablin, S.-S.
Application of a dislocation based model for Interstitial Free (IF) steels to typical stamping simulations
(2010) AIP Conference Proceedings, 1252, pp. 1339-1346. Cited 3 times.
72) Altmeyer, G., Abed-Meraim, F., Balan, T.
Investigation of some localization criteria and their relevance to prediction of forming limit diagrams
(2010) Steel Research International, 81 (9), pp. 1364-1367.
73) Abed-Meraim, F., Combescure, A.
An improved assumed strain solid-shell element formulation with physical stabilization for geometric
non-linear applications and elastic-plastic stability analysis
(2009) International Journal for Numerical Methods in Engineering, 80 (13), pp. 1640-1686. Cited 54
times.
74) Altmeyer, G., Abed-Meraim, F., Balan, T.
Formability prediction of thin metal sheets using various localization criteria
(2009) International Journal of Material Forming, 2 (SUPPL. 1), pp. 423-426. Cited 2 times.
75) Franz, G., Abed-Meraim, F., Ben Zineb, T., Lemoine, X., Berveiller, M.
Strain localization analysis deduced from a large strain elastic-plastic self-consistent model for
multiphase steels
(2009) 12th International Conference on Fracture 2009, ICF-12, 7, pp. 5004-5013.
76) Haddag, B., Abed-Meraim, F., Balan, T.
Strain localization analysis using a large deformation anisotropic elastic-plastic model coupled with
damage
(2009) International Journal of Plasticity, 25 (10), pp. 1970-1996. Cited 74 times.
77) Franz, G., Abed-Meraim, F., Ben Zineb, T., Lemoine, X., Berveiller, M.
Role of intragranular microstructure development in the macroscopic behavior of multiphase steels in
the context of changing strain paths
(2009) Materials Science and Engineering A, 517 (1-2), pp. 300-311. Cited 17 times.
78) Franz, G., Abed-Meraim, F., Zineb, T.B., Lemoine, X., Berveiller, M.
Strain localization analysis using a multiscale model
(2009) Computational Materials Science, 45 (3), pp. 768-773. Cited 15 times.
79) Franz, G., Abed-Meraim, F., Lorrain, J.-P., Ben Zineb, T., Lemoine, X., Berveiller, M.
Ellipticity loss analysis for tangent moduli deduced from a large strain elastic-plastic self-consistent
model
(2009) International Journal of Plasticity, 25 (2), pp. 205-238. Cited 41 times.
80) Haddag, B., Abed-Meraim, F., Balan, T.
Strain localization and damage prediction during sheet metal forming
(2008) International Journal of Material Forming, 1 (SUPPL. 1), pp. 229-232. Cited 4 times.
81) Balan, T., Abed-Meraim, F.
Numerical investigation of the limit strains in sheet forming involving bending
(2008) 9th International Conference on Technology of Plasticity, ICTP 2008, pp. 690-695.
82) Altmeyer, G., Abed-Meraim, F., Balan, T.
Comparison of forming limit diagrams predicted with different localization criteria
(2008) Steel Research International, 79 (1), pp. 24-31.
83) Haddag, B., Abed-Meraim, F., Balan, T.
Finite element prediction of sheet forming defects using elastic-plastic, damage and localization
models
(2007) AIP Conference Proceedings, 908, pp. 227-232.
84) Franz, G., Abed-Meraim, F., Zineb, T.B., Lemoine, X., Berveiller, M.
A multiscale model based on intragranular microstructure: Influence of grain-scale substructure on
macroscopic behaviour of an if-steel during complex load paths
(2007) AIP Conference Proceedings, 908, pp. 1345-1350. Cited 1 time.
85) Haddag, B., Balan, T., Abed-Meraim, F.
Investigation of advanced strain-path dependent material models for sheet metal forming simulations
(2007) International Journal of Plasticity, 23 (6), pp. 951-979. Cited 56 times.
86) Franz, G., Abed-Meraim, F., Zineb, T.B., Lemoine, X., Berveiller, M.
A multiscale model based on intragranular microstructure - Prediction of dislocation patterns at the
microscopic scale
(2007) AIP Conference Proceedings, 907, pp. 47-52. Cited 1 time.
87) Abed-Meraim, F., Combescure, A.
A physically stabilized and locking-free formulation of the (SHB8PS) solid-shell element
(2007) European Journal of Computational Mechanics, 16 (8), pp. 1037-1072. Cited 2 times.
88) Abed-Meraim, F., Nguyen, Q.-S.
A quasi-static stability analysis for Biot's equation and standard dissipative systems
(2007) European Journal of Mechanics, A/Solids, 26 (3), pp. 383-393. Cited 6 times.
89) Haddag, B., Balan, T., Abed-Meraim, F.
Springback simulation: Impact of some advanced constitutive models and numerical parameters
(2005) AIP Conference Proceedings, 778 A, pp. 286-294. Cited 3 times.
90) Haddag, B., Balan, T., Abed-Meraim, F.
Springback prediction of sheet metal in the deep drawing process using elastoplastic
phenomenological models
(2005) Advanced Technology of Plasticity 2005 - Proceedings of the 8th International Conference on
Technology of Plasticity, ICTP 2005, .
91) Abed-Meraim, F., Combescure, A.
SHB8PS - A new adaptative, assumed-strain continuum mechanics shell element for impact analysis
(2002) Computers and Structures, 80 (9-10), pp. 791-803. Cited 38 times.
92) Abed Meraim, F.
Sufficient conditions for stability of viscous solids [Article@Conditions suffisantes de stabilite pour les
solides visqueux]
(1999) Comptes Rendus de l'Academie de Sciences - Serie IIb: Mecanique, Physique, Chimie,
Astronomie, 327 (1), pp. 25-31. Cited 5 times.

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