Full-field stress computation from measured deformation fields: A hyperbolic formulation

Recent developments in imaging techniques and correlation algorithms enable measurement of strain fields on a deforming material at high spatial and temporal resolution. In such cases, the computation of the stress field from the known deformation field becomes an interesting possibility. This is kn...

Full description

Saved in:
Bibliographic Details
Published inJournal of the mechanics and physics of solids Vol. 147; p. 104186
Main Authors Cameron, Benjamin C., Tasan, C.Cem
Format Journal Article
LanguageEnglish
Published London Elsevier Ltd 01.02.2021
Elsevier BV
Subjects
Online AccessGet full text
ISSN0022-5096
1873-4782
DOI10.1016/j.jmps.2020.104186

Cover

Abstract Recent developments in imaging techniques and correlation algorithms enable measurement of strain fields on a deforming material at high spatial and temporal resolution. In such cases, the computation of the stress field from the known deformation field becomes an interesting possibility. This is known as an inverse problem. Current approaches to this problem, such as the finite element update method, are generally over-determined and must rely on statistical approaches to minimize error. This provides approximate solutions in some cases, however, implementation difficulties, computational requirements, and accuracy are still significant challenges. Here, we show how the inverse problem can be formulated deterministically and solved exactly in two or three dimensions for large classes of materials including isotropic elastic solids, Newtonian fluids, non-Newtonian fluids, granular materials, plastic solids subject to co-directionality, and some other plastic solids subject to associative or non-associative flow rules. This solution is based on a single assumption of the alignment of the principal directions of stress and strain or strain rate. No further assumptions regarding incompressibility, pressure independence, yield surface shape or the hardening law are necessary. This assumption leads to a closed, first order, linear system of hyperbolic partial differential equations with variable coefficients. The solution of this class of problems is well established and hence the equations can be solved to give the solution for any geometry and loading condition, enabling broad applicability to a variety of problems. We provide a numerical proof-of-principle study of the plastic deformation of a two-dimensional bar with spatially varying yield stress and strain hardening coefficient. The results are validated against the solution of the corresponding forward problem – solved with a commercial finite element solver – indicating the solution is exact up to numerical error (the normalized root mean square error of the stress is 1.63×10−4). No model calibration or material parameters are required. The sensitivity of the solution to error in the input data is also analyzed. Interestingly, this solution procedure lends itself to a simple physical interpretation of stress propagation through the material. Finally, we provide some examples showing how this approach may be analytically applied to both solid and fluid mechanics problems. [Display omitted] •An approach is developed to compute the full field stress from the strain.•Stress is obtained from a hyperbolic system of partial differential equations.•The equation is exact for isotropic materials that are elastic, plastic or viscous.•The approach is valid in two or three dimensions for any geometry and loading.•The approach is suitable for application to digital image correlation data.
AbstractList Recent developments in imaging techniques and correlation algorithms enable measurement of strain fields on a deforming material at high spatial and temporal resolution. In such cases, the computation of the stress field from the known deformation field becomes an interesting possibility. This is known as an inverse problem. Current approaches to this problem, such as the finite element update method, are generally over-determined and must rely on statistical approaches to minimize error. This provides approximate solutions in some cases, however, implementation difficulties, computational requirements, and accuracy are still significant challenges. Here, we show how the inverse problem can be formulated deterministically and solved exactly in two or three dimensions for large classes of materials including isotropic elastic solids, Newtonian fluids, non-Newtonian fluids, granular materials, plastic solids subject to co-directionality, and some other plastic solids subject to associative or non-associative flow rules. This solution is based on a single assumption of the alignment of the principal directions of stress and strain or strain rate. No further assumptions regarding incompressibility, pressure independence, yield surface shape or the hardening law are necessary. This assumption leads to a closed, first order, linear system of hyperbolic partial differential equations with variable coefficients. The solution of this class of problems is well established and hence the equations can be solved to give the solution for any geometry and loading condition, enabling broad applicability to a variety of problems. We provide a numerical proof-of-principle study of the plastic deformation of a two-dimensional bar with spatially varying yield stress and strain hardening coefficient. The results are validated against the solution of the corresponding forward problem – solved with a commercial finite element solver – indicating the solution is exact up to numerical error (the normalized root mean square error of the stress is 1.63×10−4). No model calibration or material parameters are required. The sensitivity of the solution to error in the input data is also analyzed. Interestingly, this solution procedure lends itself to a simple physical interpretation of stress propagation through the material. Finally, we provide some examples showing how this approach may be analytically applied to both solid and fluid mechanics problems. [Display omitted] •An approach is developed to compute the full field stress from the strain.•Stress is obtained from a hyperbolic system of partial differential equations.•The equation is exact for isotropic materials that are elastic, plastic or viscous.•The approach is valid in two or three dimensions for any geometry and loading.•The approach is suitable for application to digital image correlation data.
Recent developments in imaging techniques and correlation algorithms enable measurement of strain fields on a deforming material at high spatial and temporal resolution. In such cases, the computation of the stress field from the known deformation field becomes an interesting possibility. This is known as an inverse problem. Current approaches to this problem, such as the finite element update method, are generally over-determined and must rely on statistical approaches to minimize error. This provides approximate solutions in some cases, however, implementation difficulties, computational requirements, and accuracy are still significant challenges. Here, we show how the inverse problem can be formulated deterministically and solved exactly in two or three dimensions for large classes of materials including isotropic elastic solids, Newtonian fluids, non-Newtonian fluids, granular materials, plastic solids subject to co-directionality, and some other plastic solids subject to associative or non-associative flow rules. This solution is based on a single assumption of the alignment of the principal directions of stress and strain or strain rate. No further assumptions regarding incompressibility, pressure independence, yield surface shape or the hardening law are necessary. This assumption leads to a closed, first order, linear system of hyperbolic partial differential equations with variable coefficients. The solution of this class of problems is well established and hence the equations can be solved to give the solution for any geometry and loading condition, enabling broad applicability to a variety of problems. We provide a numerical proof-of-principle study of the plastic deformation of a two-dimensional bar with spatially varying yield stress and strain hardening coefficient. The results are validated against the solution of the corresponding forward problem – solved with a commercial finite element solver – indicating the solution is exact up to numerical error (the normalized root mean square error of the stress is 1.63×10−4). No model calibration or material parameters are required. The sensitivity of the solution to error in the input data is also analyzed. Interestingly, this solution procedure lends itself to a simple physical interpretation of stress propagation through the material. Finally, we provide some examples showing how this approach may be analytically applied to both solid and fluid mechanics problems.
ArticleNumber 104186
Author Cameron, Benjamin C.
Tasan, C.Cem
Author_xml – sequence: 1
  givenname: Benjamin C.
  surname: Cameron
  fullname: Cameron, Benjamin C.
  email: bcam@mit.edu
  organization: Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, USA
– sequence: 2
  givenname: C.Cem
  surname: Tasan
  fullname: Tasan, C.Cem
  email: tasan@mit.edu
  organization: Department of Materials Science and Engineering, Massachusetts Institute of Technology, USA
BookMark eNp9kE9LxDAQxYOs4O7qF_AU8Nw1Sds0ES-L-A8WvCh4C9l0giltU5NW2G9va_fkYWFgYN77zTBvhRatbwGha0o2lFB-W22qposbRtg0yKjgZ2hJRZEmWSHYAi0JYSzJieQXaBVjRQjJSUGX6PNpqOvEOqhLHPsAMWLjm27ode98i23wDW5AxyFAiUuwPjRHZULiHd7ir0MHYe9rZ_AkD_Wf4RKdW11HuDr2Nfp4enx_eEl2b8-vD9tdYlIm-iS1qTB5Dqne77m1mjANxlpiOTeloVQSQWQmrREy50Wa6bFEZvKCcy5LK9M1upn3dsF_DxB7VfkhtONJxTJJZUFlWowuMbtM8DEGsMq4-cU-aFcrStSUo6rUlKOaclRzjiPK_qFdcI0Oh9PQ_QzB-PqPg6CicdAaKF0A06vSu1P4L3aDj5c
CitedBy_id crossref_primary_10_1038_s41524_022_00752_4
crossref_primary_10_1115_1_4065337
crossref_primary_10_1016_j_jmps_2022_105076
crossref_primary_10_1016_j_cma_2022_115225
crossref_primary_10_1016_j_jmps_2025_106122
crossref_primary_10_1115_1_4050535
crossref_primary_10_1016_j_ijsolstr_2022_111912
crossref_primary_10_1111_str_12410
crossref_primary_10_1016_j_finmec_2023_100201
crossref_primary_10_1016_j_ijimpeng_2024_105083
crossref_primary_10_1111_str_12434
crossref_primary_10_1016_j_ijplas_2022_103512
Cites_doi 10.1063/1.1712836
10.1016/S0022-5096(99)00066-6
10.1243/030932405X16151
10.1007/s11340-015-0009-1
10.1016/j.jmps.2004.12.008
10.1016/0956-7151(94)90502-9
10.1016/j.actamat.2015.05.038
10.1016/j.polymer.2014.10.010
10.1016/j.phpro.2015.07.072
10.1137/1024038
10.1088/0266-5611/21/2/R01
10.1016/j.compositesa.2009.08.016
10.1115/1.3167205
10.1061/(ASCE)HY.1943-7900.0000850
10.1016/j.jallcom.2017.11.020
10.1016/0167-1987(94)90100-7
10.1007/s11340-008-9148-y
10.1063/1.1721329
10.1111/j.1475-1305.2006.00258.x
10.1016/j.compositesa.2017.12.018
10.1007/s12008-011-0129-5
10.1016/j.compositesa.2007.11.011
10.1002/nme.914
10.1016/j.jmbbm.2016.03.014
10.1016/0924-0136(94)90378-6
10.1016/j.mechmat.2015.09.004
10.1007/s00348-006-0212-z
10.1007/s00466-010-0496-y
10.1016/S0022-5096(99)00022-8
10.1098/rsta.1932.0009
10.1016/j.actamat.2009.10.058
10.1007/s11340-017-0269-z
10.1016/j.cma.2007.06.019
10.1016/j.ijmecsci.2016.08.018
10.1111/j.1475-1305.2005.00227.x
10.1088/0957-0233/20/6/062001
10.1111/j.1475-1305.2007.00348.x
10.1002/zamm.19300100308
10.1016/j.ijplas.2008.04.003
10.1007/s00348-005-0991-7
10.1016/j.ijplas.2005.04.007
10.1016/j.matlet.2009.06.020
10.1103/PhysRevB.58.11258
10.1016/j.actamat.2017.09.026
ContentType Journal Article
Copyright 2020 Elsevier Ltd
Copyright Elsevier BV Feb 2021
Copyright_xml – notice: 2020 Elsevier Ltd
– notice: Copyright Elsevier BV Feb 2021
DBID AAYXX
CITATION
7SR
7TB
7U5
8BQ
8FD
FR3
JG9
KR7
L7M
DOI 10.1016/j.jmps.2020.104186
DatabaseName CrossRef
Engineered Materials Abstracts
Mechanical & Transportation Engineering Abstracts
Solid State and Superconductivity Abstracts
METADEX
Technology Research Database
Engineering Research Database
Materials Research Database
Civil Engineering Abstracts
Advanced Technologies Database with Aerospace
DatabaseTitle CrossRef
Materials Research Database
Civil Engineering Abstracts
Engineered Materials Abstracts
Technology Research Database
Mechanical & Transportation Engineering Abstracts
Solid State and Superconductivity Abstracts
Engineering Research Database
Advanced Technologies Database with Aerospace
METADEX
DatabaseTitleList
Materials Research Database
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1873-4782
ExternalDocumentID 10_1016_j_jmps_2020_104186
S0022509620304130
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
1B1
1RT
1~.
1~5
29L
4.4
457
4G.
5GY
5VS
6TJ
7-5
71M
8P~
9JN
AACTN
AAEDT
AAEDW
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
ABFNM
ABFSI
ABJNI
ABMAC
ABXDB
ABYKQ
ACDAQ
ACGFS
ACIWK
ACNNM
ACRLP
ADBBV
ADEZE
ADIYS
ADMUD
ADTZH
AEBSH
AECPX
AEKER
AENEX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHJVU
AI.
AIEXJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
ASPBG
AVWKF
AXJTR
AZFZN
BBWZM
BJAXD
BKOJK
BLXMC
CS3
DU5
E.L
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
GBLVA
HMV
HVGLF
HZ~
H~9
IHE
J1W
JJJVA
KOM
LY7
M24
M38
M41
MO0
N9A
NDZJH
O-L
O9-
OAUVE
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
RNS
ROL
RPZ
SDF
SDG
SDP
SES
SET
SEW
SMS
SPC
SPCBC
SPD
SPG
SST
SSZ
T5K
VH1
WUQ
XFK
XPP
YQT
ZMT
~02
~G-
AATTM
AAXKI
AAYWO
AAYXX
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
AEIPS
AEUPX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
CITATION
EFKBS
~HD
7SR
7TB
7U5
8BQ
8FD
AFXIZ
AGCQF
AGRNS
BNPGV
FR3
JG9
KR7
L7M
SSH
ID FETCH-LOGICAL-c328t-3f38c55e3abb6ffa02aecff0f66cdc119080949fc8956734a34a84c576669df93
IEDL.DBID .~1
ISSN 0022-5096
IngestDate Fri Jul 25 06:30:14 EDT 2025
Wed Oct 01 05:16:31 EDT 2025
Thu Apr 24 23:08:40 EDT 2025
Fri Feb 23 02:43:10 EST 2024
IsPeerReviewed true
IsScholarly true
Keywords Visco-plastic material
Elastic material
Finite differences
Inverse problem
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c328t-3f38c55e3abb6ffa02aecff0f66cdc119080949fc8956734a34a84c576669df93
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
PQID 2491971937
PQPubID 2045442
ParticipantIDs proquest_journals_2491971937
crossref_citationtrail_10_1016_j_jmps_2020_104186
crossref_primary_10_1016_j_jmps_2020_104186
elsevier_sciencedirect_doi_10_1016_j_jmps_2020_104186
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate February 2021
2021-02-00
20210201
PublicationDateYYYYMMDD 2021-02-01
PublicationDate_xml – month: 02
  year: 2021
  text: February 2021
PublicationDecade 2020
PublicationPlace London
PublicationPlace_xml – name: London
PublicationTitle Journal of the mechanics and physics of solids
PublicationYear 2021
Publisher Elsevier Ltd
Elsevier BV
Publisher_xml – name: Elsevier Ltd
– name: Elsevier BV
References Huang, Gao, Nix, Hutchinson (b30) 2000; 48
Tresca (b59) 1864
Crouzeix, Périé, Collombet, Douchin (b13) 2009; 40
Florentin, Lubineau (b19) 2011; 5
Gurtin, Anand (b24) 2005; 53
Martinez, Balandraud, Toussaint, Cam, Berghezan (b40) 2014; 55
Hill (b29) 1950
Von Mises (b62) 1913
Blaber, Adair, Antoniou (b6) 2015; 55
Gelin, Ghouati (b20) 1994; 45
Viala, Placet, Cogan (b61) 2018; 106
Gurtin, Fried, Anand (b25) 2010
Réthoré, Hild, Roux (b48) 2007; 196
Fleck, Willis (b17) 2009; 15
Heays, Friedrich, Melville, Nokes (b27) 2014; 140
Weir, Akella, Ruddle, Goodwin, Hsiung (b64) 1998; 58
Yan, Tasan, Raabe (b65) 2015; 96
Jones, Oliphant, Peterson (b31) 2001
Prandtl, Ludwig, 1924. Spannungsverteilung in plastischen Körpern. In: Proceedings of the 1st International Congress on Applied Mechanics, pp. 3–54.
Grédiac, Pierron (b21) 2004; 59
Zachmanoglou, Thoe (b66) 1986
Timoshenko (b56) 1983
Tong (b57) 2005; 41
Pan, Qian, Xie, Asundi (b42) 2009; 20
Zhu, Poh (b70) 2016; 117
Mooney (b41) 1940; 11
Zhu, Kang, Yu, Poh (b69) 2016; 61
Colliat-Dangus, Desrues, Foray (b11) 1988
Hild, Roux (b28) 2006; 42
Kang, Wilkinson, Embury, Jain (b32) 2005; 40
Réthoré (b47) 2010
Levy (b38) 1891; 32
Avril, Bonnet, Bretelle, Grédiac, Hild, Ienny, Latourte, Lemosse, Pagano, Pagnacco, Pierron (b5) 2008; 48
Anand, Gu (b2) 2000; 48
Grédiac, Pierron (b22) 2006; 22
Schroers, Johnson (b52) 2004; 255506
Asaro (b4) 1983
Tudisco, Hall, Charalampidou, Kardjilov, Hilger, Sone (b60) 2015; 69
Harris, Bakker (b26) 1994; 29
Taylor, Quinney (b55) 1931; 230
Trefethen (b58) 1982; 24
Bridgman (b9) 1953
Chakrabarty (b10) 2012
Siddiqui, Khan, Khan, Shahzad, Khan, Nisar, Noman (b53) 2017; 57
Feichter, Major, Lang (b15) 2007
Grédiac, Toussaint, Pierron (b23) 2002; 39
Lenoir, Bornert, Desrues, Bésuelle, Viggiani (b36) 2007; 43
Fleck, Muller, Ashby, Hutchinson (b16) 1994; 42
Boussinesq (b8) 1897
Coulomb (b12) 1773; 7
Kundu, Cohen, Dowling (b34) 2012
Zhao, Wang, Chang, Yan (b68) 2016; 92
Anon (b3) 2017
Strang (b54) 2007
Zhang, Raabe, Tasan (b67) 2017; 141
Plancher, Qu, Vonk, Gorji, Tancogne-Dejean, Tasan (b44) 2019
Lele, Anand (b35) 2009; 25
LeVeque (b37) 2002
Liu, Liu, Jiang, Wang, Yang, Zhang (b39) 2018; 735
Ramesh (b46) 2000
Adrian (b1) 2005; 39
Bonnet, Constantinescu (b7) 2005; 21
Florentin, Lubineau (b18) 2010; 46
Rivlin (b49) 1948; 241
von Reuss (b63) 1930; 10
Elsinga, Scarano, Wieneke, Van Oudheusden (b14) 2006; 41
Korsunsky, Sebastiani, Bemporad (b33) 2009; 63
Pierron, Grédiac (b43) 2012
Roters, Eisenlohr, Hantcherli, Tjahjanto, Bieler, Raabe (b50) 2010; 58
Roux, Hild, Viot, Bernard (b51) 2008; 39
Bridgman (10.1016/j.jmps.2020.104186_b9) 1953
Boussinesq (10.1016/j.jmps.2020.104186_b8) 1897
Florentin (10.1016/j.jmps.2020.104186_b18) 2010; 46
Rivlin (10.1016/j.jmps.2020.104186_b49) 1948; 241
Crouzeix (10.1016/j.jmps.2020.104186_b13) 2009; 40
Feichter (10.1016/j.jmps.2020.104186_b15) 2007
Tong (10.1016/j.jmps.2020.104186_b57) 2005; 41
Mooney (10.1016/j.jmps.2020.104186_b41) 1940; 11
Timoshenko (10.1016/j.jmps.2020.104186_b56) 1983
Zhao (10.1016/j.jmps.2020.104186_b68) 2016; 92
Asaro (10.1016/j.jmps.2020.104186_b4) 1983
Weir (10.1016/j.jmps.2020.104186_b64) 1998; 58
Réthoré (10.1016/j.jmps.2020.104186_b48) 2007; 196
Taylor (10.1016/j.jmps.2020.104186_b55) 1931; 230
Strang (10.1016/j.jmps.2020.104186_b54) 2007
Zhu (10.1016/j.jmps.2020.104186_b70) 2016; 117
Blaber (10.1016/j.jmps.2020.104186_b6) 2015; 55
Zachmanoglou (10.1016/j.jmps.2020.104186_b66) 1986
von Reuss (10.1016/j.jmps.2020.104186_b63) 1930; 10
Grédiac (10.1016/j.jmps.2020.104186_b21) 2004; 59
Anon (10.1016/j.jmps.2020.104186_b3) 2017
Trefethen (10.1016/j.jmps.2020.104186_b58) 1982; 24
Von Mises (10.1016/j.jmps.2020.104186_b62) 1913
Roux (10.1016/j.jmps.2020.104186_b51) 2008; 39
Yan (10.1016/j.jmps.2020.104186_b65) 2015; 96
Kundu (10.1016/j.jmps.2020.104186_b34) 2012
Harris (10.1016/j.jmps.2020.104186_b26) 1994; 29
Huang (10.1016/j.jmps.2020.104186_b30) 2000; 48
Martinez (10.1016/j.jmps.2020.104186_b40) 2014; 55
Coulomb (10.1016/j.jmps.2020.104186_b12) 1773; 7
Hill (10.1016/j.jmps.2020.104186_b29) 1950
Zhu (10.1016/j.jmps.2020.104186_b69) 2016; 61
Heays (10.1016/j.jmps.2020.104186_b27) 2014; 140
Liu (10.1016/j.jmps.2020.104186_b39) 2018; 735
Schroers (10.1016/j.jmps.2020.104186_b52) 2004; 255506
Siddiqui (10.1016/j.jmps.2020.104186_b53) 2017; 57
Ramesh (10.1016/j.jmps.2020.104186_b46) 2000
Tresca (10.1016/j.jmps.2020.104186_b59) 1864
Hild (10.1016/j.jmps.2020.104186_b28) 2006; 42
Colliat-Dangus (10.1016/j.jmps.2020.104186_b11) 1988
Korsunsky (10.1016/j.jmps.2020.104186_b33) 2009; 63
Fleck (10.1016/j.jmps.2020.104186_b16) 1994; 42
LeVeque (10.1016/j.jmps.2020.104186_b37) 2002
Levy (10.1016/j.jmps.2020.104186_b38) 1891; 32
Pierron (10.1016/j.jmps.2020.104186_b43) 2012
Gurtin (10.1016/j.jmps.2020.104186_b25) 2010
Adrian (10.1016/j.jmps.2020.104186_b1) 2005; 39
Avril (10.1016/j.jmps.2020.104186_b5) 2008; 48
Bonnet (10.1016/j.jmps.2020.104186_b7) 2005; 21
Grédiac (10.1016/j.jmps.2020.104186_b23) 2002; 39
Plancher (10.1016/j.jmps.2020.104186_b44) 2019
Anand (10.1016/j.jmps.2020.104186_b2) 2000; 48
Jones (10.1016/j.jmps.2020.104186_b31) 2001
Pan (10.1016/j.jmps.2020.104186_b42) 2009; 20
Kang (10.1016/j.jmps.2020.104186_b32) 2005; 40
Chakrabarty (10.1016/j.jmps.2020.104186_b10) 2012
Fleck (10.1016/j.jmps.2020.104186_b17) 2009; 15
Gelin (10.1016/j.jmps.2020.104186_b20) 1994; 45
Florentin (10.1016/j.jmps.2020.104186_b19) 2011; 5
10.1016/j.jmps.2020.104186_b45
Roters (10.1016/j.jmps.2020.104186_b50) 2010; 58
Zhang (10.1016/j.jmps.2020.104186_b67) 2017; 141
Lenoir (10.1016/j.jmps.2020.104186_b36) 2007; 43
Elsinga (10.1016/j.jmps.2020.104186_b14) 2006; 41
Viala (10.1016/j.jmps.2020.104186_b61) 2018; 106
Gurtin (10.1016/j.jmps.2020.104186_b24) 2005; 53
Lele (10.1016/j.jmps.2020.104186_b35) 2009; 25
Tudisco (10.1016/j.jmps.2020.104186_b60) 2015; 69
Grédiac (10.1016/j.jmps.2020.104186_b22) 2006; 22
Réthoré (10.1016/j.jmps.2020.104186_b47) 2010
References_xml – volume: 40
  start-page: 1732
  year: 2009
  end-page: 1740
  ident: b13
  article-title: An orthotropic variant of the equilibrium gap method applied to the analysis of a biaxial test on a composite material
  publication-title: Composites A
– volume: 53
  start-page: 1624
  year: 2005
  end-page: 1649
  ident: b24
  article-title: A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations
  publication-title: J. Mech. Phys. Solids
– volume: 39
  start-page: 1253
  year: 2008
  end-page: 1265
  ident: b51
  article-title: Three-dimensional image correlation from X-ray computed tomography of solid foam
  publication-title: Composites A
– start-page: 273
  year: 2007
  end-page: 274
  ident: b15
  article-title: Methods for measuring biaxial deformation on rubber and polypropylene specimens
  publication-title: Experimental Analysis of Nano and Engineering Materials and Structures
– volume: 40
  start-page: 559
  year: 2005
  end-page: 570
  ident: b32
  article-title: Microscopic strain mapping using scanning electron microscopy topography image correlation at large strain
  publication-title: J. Strain Anal. Eng. Des.
– volume: 42
  start-page: 475
  year: 1994
  end-page: 487
  ident: b16
  article-title: Strain gradient plasticity: theory and experiment
  publication-title: Acta Metall. Mater.
– year: 2012
  ident: b34
  article-title: Fluid Mechanics
– volume: 59
  start-page: 1287
  year: 2004
  end-page: 1312
  ident: b21
  article-title: Numerical issues in the virtual fields method
  publication-title: Internat. J. Numer. Methods Engrg.
– year: 2017
  ident: b3
  article-title: ABAQUS standard User’s Manual
– year: 2010
  ident: b25
  article-title: The Mechanics and Thermodynamics of Continua
– year: 2012
  ident: b43
  article-title: The Virtual Fields Method: Extracting Constitutive Mechanical Parameters from Full-Field Deformation Measurements
– year: 2012
  ident: b10
  article-title: Theory of Plasticity
– volume: 141
  start-page: 374
  year: 2017
  end-page: 387
  ident: b67
  article-title: Designing duplex, ultrafine-grained Fe-Mn-Al-C steels by tuning phase transformation and recrystallization kinetics
  publication-title: Acta Mater.
– volume: 61
  start-page: 397
  year: 2016
  end-page: 409
  ident: b69
  article-title: Logarithmic rate based elasto-viscoplastic cyclic constitutive model for soft biological tissues
  publication-title: J. Mech. Behav. Biomed. Mater.
– volume: 55
  start-page: 1105
  year: 2015
  end-page: 1122
  ident: b6
  article-title: Ncorr: open-source 2D digital image correlation matlab software
  publication-title: Exp. Mech.
– volume: 55
  start-page: 6345
  year: 2014
  end-page: 6353
  ident: b40
  article-title: Thermomechanical analysis of the crack tip zone in stretched crystallizable natural rubber by using infrared thermography and digital image correlation
  publication-title: Polymer
– year: 1913
  ident: b62
  article-title: Mechanics of solid bodies in the plastically-deformable state
– volume: 10
  start-page: 266
  year: 1930
  end-page: 274
  ident: b63
  article-title: Berücksichtigung der elastischen Formänderung in der Plastizitätstheorie
  publication-title: ZAMM Z. Angew. Math. Mech. ZAMM.
– volume: 42
  start-page: 69
  year: 2006
  end-page: 80
  ident: b28
  article-title: Digital image correlation: From displacement measurement to identification of elastic properties - A review
  publication-title: Strain
– year: 2001
  ident: b31
  article-title: Open source scientific tools for python
– volume: 241
  year: 1948
  ident: b49
  article-title: Large elastic deformations of isotropic materials IV. Furhter developments of the general theory
  publication-title: Philos. Trans. R. Soc. Lond. Ser. A
– volume: 15
  start-page: 161
  year: 2009
  end-page: 177
  ident: b17
  article-title: Journal of the Mechanics and Physics of Solids A mathematical basis for strain-gradient plasticity theory — Part I : Scalar plastic multiplier
  publication-title: Mater. Sci.
– volume: 41
  start-page: 933
  year: 2006
  end-page: 947
  ident: b14
  article-title: Tomographic particle image velocimetry
  publication-title: Exp. Fluids
– volume: 48
  start-page: 381
  year: 2008
  end-page: 402
  ident: b5
  article-title: Overview of identification methods of mechanical parameters based on full-field measurements
  publication-title: Exp. Mech.
– volume: 29
  start-page: 35
  year: 1994
  end-page: 48
  ident: b26
  article-title: A soil stress transducer for measuring in situ soil stresses
  publication-title: Soil Tillage Res.
– year: 1897
  ident: b8
  article-title: Théorie de l’écoulement tourbillonnant et tumultueux des liquides dans les lits rectilignes a grande section, vol. 1
– volume: 69
  start-page: 509
  year: 2015
  end-page: 515
  ident: b60
  article-title: Full-field measurements of strain localisation in sandstone by neutron tomography and 3D-volumetric digital image correlation
  publication-title: Physics Procedia
– volume: 117
  start-page: 265
  year: 2016
  end-page: 274
  ident: b70
  article-title: A finite deformation elasto-plastic cyclic constitutive model for ratchetting of metallic materials
  publication-title: Int. J. Mech. Sci.
– volume: 41
  start-page: 167
  year: 2005
  end-page: 175
  ident: b57
  article-title: An evaluation of digital image correlation criteria for strain mapping applications
  publication-title: Strain
– volume: 106
  start-page: 91
  year: 2018
  end-page: 103
  ident: b61
  article-title: Identification of the anisotropic elastic and damping properties of complex shape composite parts using an inverse method based on finite element model updating and 3D velocity fields measurements (FEMU-3DVF): Application to bio-based composite violin sou
  publication-title: Composites A
– volume: 43
  start-page: 193
  year: 2007
  end-page: 205
  ident: b36
  article-title: Volumetric digital image correlation applied to x-ray microtomography images from triaxial compression tests on argillaceous rock
  publication-title: Strain
– volume: 58
  start-page: 11258
  year: 1998
  end-page: 11265
  ident: b64
  article-title: Static strengths of Ta and U under ultrahigh pressures
  publication-title: Phys. Rev. B
– volume: 22
  start-page: 602
  year: 2006
  end-page: 627
  ident: b22
  article-title: Applying the virtual fields method to the identification of elasto-plastic constitutive parameters
  publication-title: Int. J. Plast.
– volume: 5
  start-page: 227
  year: 2011
  end-page: 234
  ident: b19
  article-title: Using constitutive equation gap method for identification of elastic material parameters: technical insights and illustrations
  publication-title: Int. J. Interact. Des. Manuf.
– volume: 255506
  start-page: 20
  year: 2004
  end-page: 23
  ident: b52
  article-title: Ductile bulk metallic glass
  publication-title: Phys. Rev. Lett.
– volume: 96
  start-page: 399
  year: 2015
  end-page: 409
  ident: b65
  article-title: High resolution in situ mapping of microstrain and microstructure evolution reveals damage resistance criteria in dual phase steels
  publication-title: Acta Mater.
– year: 2007
  ident: b54
  article-title: Computational Science and Engineering
– start-page: 921
  year: 1983
  end-page: 934
  ident: b4
  article-title: Crystal plasticity
  publication-title: J. Appl. Mech.
– year: 1983
  ident: b56
  article-title: History of Strength of Materials, 1953
– volume: 25
  start-page: 420
  year: 2009
  end-page: 453
  ident: b35
  article-title: A large-deformation strain-gradient theory for isotropic viscoplastic materials
  publication-title: Int. J. Plast.
– year: 2000
  ident: b46
  article-title: Digital Photoelasticity
– year: 1986
  ident: b66
  article-title: Introduction to Partial Differential Equations with Applications
– volume: 140
  start-page: 2
  year: 2014
  end-page: 10
  ident: b27
  article-title: Quantifying the dynamic evolution of graded gravel beds using particle tracking velocimetry
  publication-title: J. Hydraul. Eng.
– volume: 32
  start-page: 248
  year: 1891
  end-page: 251
  ident: b38
  article-title: Ueber einen Fall von Gasabscess
  publication-title: Langenbeck’s Arch. Surg.
– volume: 48
  start-page: 1701
  year: 2000
  end-page: 1733
  ident: b2
  article-title: Granular materials: constitutive equations and strain localization
  publication-title: J. Mech. Phys. Solids
– year: 1988
  ident: b11
  article-title: Triaxial testing of granular soil under elevated cell pressure
  publication-title: Advanced Triaxial Testing of Soil and Rock
– start-page: 183
  year: 1950
  ident: b29
  article-title: Mathematical Theory of Plasticity
– volume: 735
  start-page: 1414
  year: 2018
  end-page: 1421
  ident: b39
  article-title: Gradient in microstructure and mechanical property of selective laser melted alsi10mg
  publication-title: J. Alloys Compd.
– volume: 48
  start-page: 99
  year: 2000
  end-page: 128
  ident: b30
  article-title: Mechanism-based strain gradient plasticity - II. Analysis
  publication-title: J. Mech. Phys. Solids
– volume: 92
  start-page: 107
  year: 2016
  end-page: 118
  ident: b68
  article-title: Mechanics of materials identification of post-necking stress – strain curve for sheet metals by inverse method
  publication-title: Mech. Mater.
– year: 2019
  ident: b44
  article-title: Tracking microstructure evolution in complex biaxial strain paths: A bulge test methodology for the scanning electron microscope
  publication-title: Exp. Mech.
– volume: 45
  start-page: 435
  year: 1994
  end-page: 440
  ident: b20
  article-title: An inverse method for determining viscoplastic properties of aluminium alloys
  publication-title: J. Mater. Process. Technol.
– volume: 63
  start-page: 1961
  year: 2009
  end-page: 1963
  ident: b33
  article-title: Focused ion beam ring drilling for residual stress evaluation
  publication-title: Mater. Lett.
– volume: 24
  start-page: 113
  year: 1982
  end-page: 136
  ident: b58
  article-title: Group velocity in finite difference schemes
  publication-title: SIAM Rev.
– start-page: 1885
  year: 2010
  end-page: 1891
  ident: b47
  article-title: A fully integrated noise robust strategy for the identification of constitutive laws from digital images
  publication-title: Internat. J. Numer. Methods Engrg.
– year: 1864
  ident: b59
  article-title: Sur l’ecoulement des corps solides soumis a de fortes pressions
– volume: 58
  start-page: 1152
  year: 2010
  end-page: 1211
  ident: b50
  article-title: Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications
  publication-title: Acta Mater.
– year: 2002
  ident: b37
  article-title: Finite Volume Methods for Hyperbolic Problems, vol. 31
– year: 1953
  ident: b9
  article-title: The effect of pressure on the tensile properties of several metals and other materials
  publication-title: J. Appl. Phys.
– volume: 57
  start-page: 755
  year: 2017
  end-page: 772
  ident: b53
  article-title: A projected finite element update method for inverse identification of material constitutive parameters in transversely isotropic laminates
  publication-title: Exp. Mech.
– volume: 46
  start-page: 521
  year: 2010
  end-page: 531
  ident: b18
  article-title: Identification of the parameters of an elastic material model using the constitutive equation gap method
  publication-title: Comput. Mech.
– volume: 21
  year: 2005
  ident: b7
  article-title: Inverse problems in elasticity
  publication-title: Inverse Problems
– volume: 20
  year: 2009
  ident: b42
  article-title: Two-dimensional digital image correlation for in-plane displacement and strain measurement: A review
  publication-title: Meas. Sci. Technol.
– reference: Prandtl, Ludwig, 1924. Spannungsverteilung in plastischen Körpern. In: Proceedings of the 1st International Congress on Applied Mechanics, pp. 3–54.
– volume: 39
  start-page: 15
  year: 2002
  ident: b23
  article-title: Special virtual fields for the direct determination of material parameters with the virtual fields method. 1-principle and definition
  publication-title: Int. J. Solids Struct.
– volume: 196
  start-page: 5016
  year: 2007
  end-page: 5030
  ident: b48
  article-title: Shear-band capturing using a multiscale extended digital image correlation technique
  publication-title: Comput. Methods Appl. Mech. Eng.
– volume: 39
  start-page: 159
  year: 2005
  end-page: 169
  ident: b1
  article-title: Twenty years of particle image velocimetry
  publication-title: Exp. Fluids
– volume: 11
  start-page: 582
  year: 1940
  end-page: 592
  ident: b41
  article-title: A theory of large elastic deformation
  publication-title: J. Appl. Phys.
– volume: 7
  start-page: 343
  year: 1773
  end-page: 382
  ident: b12
  article-title: Essay on the rules of maximis and minimis applied to some problems of equilibrium related to architecture
  publication-title: Acad. R. Sci. Meml. Phys.
– volume: 230
  start-page: 323
  year: 1931
  end-page: 362
  ident: b55
  article-title: The plastic distortion of metals
  publication-title: Philos. Trans. R. Soc. Lond.
– volume: 11
  start-page: 582
  issue: 9
  year: 1940
  ident: 10.1016/j.jmps.2020.104186_b41
  article-title: A theory of large elastic deformation
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.1712836
– volume: 48
  start-page: 1701
  issue: 8
  year: 2000
  ident: 10.1016/j.jmps.2020.104186_b2
  article-title: Granular materials: constitutive equations and strain localization
  publication-title: J. Mech. Phys. Solids
  doi: 10.1016/S0022-5096(99)00066-6
– volume: 40
  start-page: 559
  issue: 6
  year: 2005
  ident: 10.1016/j.jmps.2020.104186_b32
  article-title: Microscopic strain mapping using scanning electron microscopy topography image correlation at large strain
  publication-title: J. Strain Anal. Eng. Des.
  doi: 10.1243/030932405X16151
– volume: 55
  start-page: 1105
  issue: 6
  year: 2015
  ident: 10.1016/j.jmps.2020.104186_b6
  article-title: Ncorr: open-source 2D digital image correlation matlab software
  publication-title: Exp. Mech.
  doi: 10.1007/s11340-015-0009-1
– ident: 10.1016/j.jmps.2020.104186_b45
– volume: 53
  start-page: 1624
  issue: 7
  year: 2005
  ident: 10.1016/j.jmps.2020.104186_b24
  article-title: A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations
  publication-title: J. Mech. Phys. Solids
  doi: 10.1016/j.jmps.2004.12.008
– volume: 42
  start-page: 475
  issue: 2
  year: 1994
  ident: 10.1016/j.jmps.2020.104186_b16
  article-title: Strain gradient plasticity: theory and experiment
  publication-title: Acta Metall. Mater.
  doi: 10.1016/0956-7151(94)90502-9
– volume: 255506
  start-page: 20
  issue: December
  year: 2004
  ident: 10.1016/j.jmps.2020.104186_b52
  article-title: Ductile bulk metallic glass
  publication-title: Phys. Rev. Lett.
– volume: 96
  start-page: 399
  issue: August
  year: 2015
  ident: 10.1016/j.jmps.2020.104186_b65
  article-title: High resolution in situ mapping of microstrain and microstructure evolution reveals damage resistance criteria in dual phase steels
  publication-title: Acta Mater.
  doi: 10.1016/j.actamat.2015.05.038
– volume: 55
  start-page: 6345
  issue: 24
  year: 2014
  ident: 10.1016/j.jmps.2020.104186_b40
  article-title: Thermomechanical analysis of the crack tip zone in stretched crystallizable natural rubber by using infrared thermography and digital image correlation
  publication-title: Polymer
  doi: 10.1016/j.polymer.2014.10.010
– volume: 69
  start-page: 509
  issue: October 2014
  year: 2015
  ident: 10.1016/j.jmps.2020.104186_b60
  article-title: Full-field measurements of strain localisation in sandstone by neutron tomography and 3D-volumetric digital image correlation
  publication-title: Physics Procedia
  doi: 10.1016/j.phpro.2015.07.072
– volume: 24
  start-page: 113
  issue: 2
  year: 1982
  ident: 10.1016/j.jmps.2020.104186_b58
  article-title: Group velocity in finite difference schemes
  publication-title: SIAM Rev.
  doi: 10.1137/1024038
– volume: 21
  issue: 2
  year: 2005
  ident: 10.1016/j.jmps.2020.104186_b7
  article-title: Inverse problems in elasticity
  publication-title: Inverse Problems
  doi: 10.1088/0266-5611/21/2/R01
– volume: 40
  start-page: 1732
  issue: 11
  year: 2009
  ident: 10.1016/j.jmps.2020.104186_b13
  article-title: An orthotropic variant of the equilibrium gap method applied to the analysis of a biaxial test on a composite material
  publication-title: Composites A
  doi: 10.1016/j.compositesa.2009.08.016
– year: 2002
  ident: 10.1016/j.jmps.2020.104186_b37
– start-page: 921
  year: 1983
  ident: 10.1016/j.jmps.2020.104186_b4
  article-title: Crystal plasticity
  publication-title: J. Appl. Mech.
  doi: 10.1115/1.3167205
– year: 2017
  ident: 10.1016/j.jmps.2020.104186_b3
– volume: 140
  start-page: 2
  issue: 7
  year: 2014
  ident: 10.1016/j.jmps.2020.104186_b27
  article-title: Quantifying the dynamic evolution of graded gravel beds using particle tracking velocimetry
  publication-title: J. Hydraul. Eng.
  doi: 10.1061/(ASCE)HY.1943-7900.0000850
– start-page: 273
  year: 2007
  ident: 10.1016/j.jmps.2020.104186_b15
  article-title: Methods for measuring biaxial deformation on rubber and polypropylene specimens
– volume: 39
  start-page: 15
  year: 2002
  ident: 10.1016/j.jmps.2020.104186_b23
  article-title: Special virtual fields for the direct determination of material parameters with the virtual fields method. 1-principle and definition
  publication-title: Int. J. Solids Struct.
– volume: 32
  start-page: 248
  issue: 3
  year: 1891
  ident: 10.1016/j.jmps.2020.104186_b38
  article-title: Ueber einen Fall von Gasabscess
  publication-title: Langenbeck’s Arch. Surg.
– volume: 735
  start-page: 1414
  year: 2018
  ident: 10.1016/j.jmps.2020.104186_b39
  article-title: Gradient in microstructure and mechanical property of selective laser melted alsi10mg
  publication-title: J. Alloys Compd.
  doi: 10.1016/j.jallcom.2017.11.020
– volume: 29
  start-page: 35
  issue: 1
  year: 1994
  ident: 10.1016/j.jmps.2020.104186_b26
  article-title: A soil stress transducer for measuring in situ soil stresses
  publication-title: Soil Tillage Res.
  doi: 10.1016/0167-1987(94)90100-7
– volume: 48
  start-page: 381
  issue: 4
  year: 2008
  ident: 10.1016/j.jmps.2020.104186_b5
  article-title: Overview of identification methods of mechanical parameters based on full-field measurements
  publication-title: Exp. Mech.
  doi: 10.1007/s11340-008-9148-y
– year: 2012
  ident: 10.1016/j.jmps.2020.104186_b10
– start-page: 1885
  issue: April
  year: 2010
  ident: 10.1016/j.jmps.2020.104186_b47
  article-title: A fully integrated noise robust strategy for the identification of constitutive laws from digital images
  publication-title: Internat. J. Numer. Methods Engrg.
– year: 1983
  ident: 10.1016/j.jmps.2020.104186_b56
– year: 1953
  ident: 10.1016/j.jmps.2020.104186_b9
  article-title: The effect of pressure on the tensile properties of several metals and other materials
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.1721329
– volume: 42
  start-page: 69
  issue: 2
  year: 2006
  ident: 10.1016/j.jmps.2020.104186_b28
  article-title: Digital image correlation: From displacement measurement to identification of elastic properties - A review
  publication-title: Strain
  doi: 10.1111/j.1475-1305.2006.00258.x
– volume: 106
  start-page: 91
  year: 2018
  ident: 10.1016/j.jmps.2020.104186_b61
  article-title: Identification of the anisotropic elastic and damping properties of complex shape composite parts using an inverse method based on finite element model updating and 3D velocity fields measurements (FEMU-3DVF): Application to bio-based composite violin sou
  publication-title: Composites A
  doi: 10.1016/j.compositesa.2017.12.018
– volume: 15
  start-page: 161
  issue: 1
  year: 2009
  ident: 10.1016/j.jmps.2020.104186_b17
  article-title: Journal of the Mechanics and Physics of Solids A mathematical basis for strain-gradient plasticity theory — Part I : Scalar plastic multiplier
  publication-title: Mater. Sci.
– volume: 5
  start-page: 227
  issue: 4
  year: 2011
  ident: 10.1016/j.jmps.2020.104186_b19
  article-title: Using constitutive equation gap method for identification of elastic material parameters: technical insights and illustrations
  publication-title: Int. J. Interact. Des. Manuf.
  doi: 10.1007/s12008-011-0129-5
– volume: 39
  start-page: 1253
  issue: 8
  year: 2008
  ident: 10.1016/j.jmps.2020.104186_b51
  article-title: Three-dimensional image correlation from X-ray computed tomography of solid foam
  publication-title: Composites A
  doi: 10.1016/j.compositesa.2007.11.011
– start-page: 183
  year: 1950
  ident: 10.1016/j.jmps.2020.104186_b29
– year: 2007
  ident: 10.1016/j.jmps.2020.104186_b54
– volume: 59
  start-page: 1287
  issue: 10
  year: 2004
  ident: 10.1016/j.jmps.2020.104186_b21
  article-title: Numerical issues in the virtual fields method
  publication-title: Internat. J. Numer. Methods Engrg.
  doi: 10.1002/nme.914
– volume: 61
  start-page: 397
  year: 2016
  ident: 10.1016/j.jmps.2020.104186_b69
  article-title: Logarithmic rate based elasto-viscoplastic cyclic constitutive model for soft biological tissues
  publication-title: J. Mech. Behav. Biomed. Mater.
  doi: 10.1016/j.jmbbm.2016.03.014
– year: 2012
  ident: 10.1016/j.jmps.2020.104186_b34
– volume: 45
  start-page: 435
  issue: 1–4
  year: 1994
  ident: 10.1016/j.jmps.2020.104186_b20
  article-title: An inverse method for determining viscoplastic properties of aluminium alloys
  publication-title: J. Mater. Process. Technol.
  doi: 10.1016/0924-0136(94)90378-6
– year: 1986
  ident: 10.1016/j.jmps.2020.104186_b66
– volume: 92
  start-page: 107
  year: 2016
  ident: 10.1016/j.jmps.2020.104186_b68
  article-title: Mechanics of materials identification of post-necking stress – strain curve for sheet metals by inverse method
  publication-title: Mech. Mater.
  doi: 10.1016/j.mechmat.2015.09.004
– volume: 41
  start-page: 933
  issue: 6
  year: 2006
  ident: 10.1016/j.jmps.2020.104186_b14
  article-title: Tomographic particle image velocimetry
  publication-title: Exp. Fluids
  doi: 10.1007/s00348-006-0212-z
– year: 1864
  ident: 10.1016/j.jmps.2020.104186_b59
– volume: 46
  start-page: 521
  issue: 4
  year: 2010
  ident: 10.1016/j.jmps.2020.104186_b18
  article-title: Identification of the parameters of an elastic material model using the constitutive equation gap method
  publication-title: Comput. Mech.
  doi: 10.1007/s00466-010-0496-y
– volume: 48
  start-page: 99
  issue: 1
  year: 2000
  ident: 10.1016/j.jmps.2020.104186_b30
  article-title: Mechanism-based strain gradient plasticity - II. Analysis
  publication-title: J. Mech. Phys. Solids
  doi: 10.1016/S0022-5096(99)00022-8
– year: 2000
  ident: 10.1016/j.jmps.2020.104186_b46
– volume: 7
  start-page: 343
  year: 1773
  ident: 10.1016/j.jmps.2020.104186_b12
  article-title: Essay on the rules of maximis and minimis applied to some problems of equilibrium related to architecture
  publication-title: Acad. R. Sci. Meml. Phys.
– volume: 230
  start-page: 323
  year: 1931
  ident: 10.1016/j.jmps.2020.104186_b55
  article-title: The plastic distortion of metals
  publication-title: Philos. Trans. R. Soc. Lond.
  doi: 10.1098/rsta.1932.0009
– year: 1988
  ident: 10.1016/j.jmps.2020.104186_b11
  article-title: Triaxial testing of granular soil under elevated cell pressure
– volume: 58
  start-page: 1152
  issue: 4
  year: 2010
  ident: 10.1016/j.jmps.2020.104186_b50
  article-title: Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications
  publication-title: Acta Mater.
  doi: 10.1016/j.actamat.2009.10.058
– volume: 57
  start-page: 755
  issue: 5
  year: 2017
  ident: 10.1016/j.jmps.2020.104186_b53
  article-title: A projected finite element update method for inverse identification of material constitutive parameters in transversely isotropic laminates
  publication-title: Exp. Mech.
  doi: 10.1007/s11340-017-0269-z
– volume: 196
  start-page: 5016
  year: 2007
  ident: 10.1016/j.jmps.2020.104186_b48
  article-title: Shear-band capturing using a multiscale extended digital image correlation technique
  publication-title: Comput. Methods Appl. Mech. Eng.
  doi: 10.1016/j.cma.2007.06.019
– volume: 117
  start-page: 265
  year: 2016
  ident: 10.1016/j.jmps.2020.104186_b70
  article-title: A finite deformation elasto-plastic cyclic constitutive model for ratchetting of metallic materials
  publication-title: Int. J. Mech. Sci.
  doi: 10.1016/j.ijmecsci.2016.08.018
– volume: 41
  start-page: 167
  issue: 4
  year: 2005
  ident: 10.1016/j.jmps.2020.104186_b57
  article-title: An evaluation of digital image correlation criteria for strain mapping applications
  publication-title: Strain
  doi: 10.1111/j.1475-1305.2005.00227.x
– year: 2001
  ident: 10.1016/j.jmps.2020.104186_b31
– year: 2012
  ident: 10.1016/j.jmps.2020.104186_b43
– volume: 241
  issue: 835
  year: 1948
  ident: 10.1016/j.jmps.2020.104186_b49
  article-title: Large elastic deformations of isotropic materials IV. Furhter developments of the general theory
  publication-title: Philos. Trans. R. Soc. Lond. Ser. A
– year: 1897
  ident: 10.1016/j.jmps.2020.104186_b8
– volume: 20
  issue: 6
  year: 2009
  ident: 10.1016/j.jmps.2020.104186_b42
  article-title: Two-dimensional digital image correlation for in-plane displacement and strain measurement: A review
  publication-title: Meas. Sci. Technol.
  doi: 10.1088/0957-0233/20/6/062001
– volume: 43
  start-page: 193
  issue: 3
  year: 2007
  ident: 10.1016/j.jmps.2020.104186_b36
  article-title: Volumetric digital image correlation applied to x-ray microtomography images from triaxial compression tests on argillaceous rock
  publication-title: Strain
  doi: 10.1111/j.1475-1305.2007.00348.x
– volume: 10
  start-page: 266
  issue: 3
  year: 1930
  ident: 10.1016/j.jmps.2020.104186_b63
  article-title: Berücksichtigung der elastischen Formänderung in der Plastizitätstheorie
  publication-title: ZAMM Z. Angew. Math. Mech. ZAMM.
  doi: 10.1002/zamm.19300100308
– volume: 25
  start-page: 420
  issue: 3
  year: 2009
  ident: 10.1016/j.jmps.2020.104186_b35
  article-title: A large-deformation strain-gradient theory for isotropic viscoplastic materials
  publication-title: Int. J. Plast.
  doi: 10.1016/j.ijplas.2008.04.003
– issue: i
  year: 2019
  ident: 10.1016/j.jmps.2020.104186_b44
  article-title: Tracking microstructure evolution in complex biaxial strain paths: A bulge test methodology for the scanning electron microscope
  publication-title: Exp. Mech.
– year: 1913
  ident: 10.1016/j.jmps.2020.104186_b62
– volume: 39
  start-page: 159
  issue: 2
  year: 2005
  ident: 10.1016/j.jmps.2020.104186_b1
  article-title: Twenty years of particle image velocimetry
  publication-title: Exp. Fluids
  doi: 10.1007/s00348-005-0991-7
– volume: 22
  start-page: 602
  issue: 4
  year: 2006
  ident: 10.1016/j.jmps.2020.104186_b22
  article-title: Applying the virtual fields method to the identification of elasto-plastic constitutive parameters
  publication-title: Int. J. Plast.
  doi: 10.1016/j.ijplas.2005.04.007
– volume: 63
  start-page: 1961
  issue: 22
  year: 2009
  ident: 10.1016/j.jmps.2020.104186_b33
  article-title: Focused ion beam ring drilling for residual stress evaluation
  publication-title: Mater. Lett.
  doi: 10.1016/j.matlet.2009.06.020
– volume: 58
  start-page: 11258
  issue: 17
  year: 1998
  ident: 10.1016/j.jmps.2020.104186_b64
  article-title: Static strengths of Ta and U under ultrahigh pressures
  publication-title: Phys. Rev. B
  doi: 10.1103/PhysRevB.58.11258
– volume: 141
  start-page: 374
  year: 2017
  ident: 10.1016/j.jmps.2020.104186_b67
  article-title: Designing duplex, ultrafine-grained Fe-Mn-Al-C steels by tuning phase transformation and recrystallization kinetics
  publication-title: Acta Mater.
  doi: 10.1016/j.actamat.2017.09.026
– year: 2010
  ident: 10.1016/j.jmps.2020.104186_b25
SSID ssj0005071
Score 2.427497
Snippet Recent developments in imaging techniques and correlation algorithms enable measurement of strain fields on a deforming material at high spatial and temporal...
SourceID proquest
crossref
elsevier
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 104186
SubjectTerms Algorithms
Computational fluid dynamics
Correlation analysis
Elastic material
Finite differences
Finite element method
Fluid flow
Fluid mechanics
Forward problem
Granular materials
Imaging techniques
Incompressibility
Inverse problem
Inverse problems
Newtonian fluids
Non Newtonian fluids
Parameter sensitivity
Partial differential equations
Plastic deformation
Strain hardening
Strain rate
Stress distribution
Stress propagation
Temporal resolution
Visco-plastic material
Yield stress
Title Full-field stress computation from measured deformation fields: A hyperbolic formulation
URI https://dx.doi.org/10.1016/j.jmps.2020.104186
https://www.proquest.com/docview/2491971937
Volume 147
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVESC
  databaseName: Baden-Württemberg Complete Freedom Collection (Elsevier)
  customDbUrl:
  eissn: 1873-4782
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0005071
  issn: 0022-5096
  databaseCode: GBLVA
  dateStart: 20110101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVESC
  databaseName: Elsevier ScienceDirect
  customDbUrl:
  eissn: 1873-4782
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0005071
  issn: 0022-5096
  databaseCode: .~1
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVESC
  databaseName: Elsevier ScienceDirect Freedom Collection Journals
  customDbUrl:
  eissn: 1873-4782
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0005071
  issn: 0022-5096
  databaseCode: ACRLP
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVESC
  databaseName: Elsevier SD Freedom Collection Journals [SCFCJ]
  customDbUrl:
  eissn: 1873-4782
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0005071
  issn: 0022-5096
  databaseCode: AIKHN
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVLSH
  databaseName: Elsevier Journals
  customDbUrl:
  mediaType: online
  eissn: 1873-4782
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0005071
  issn: 0022-5096
  databaseCode: AKRWK
  dateStart: 19521001
  isFulltext: true
  providerName: Library Specific Holdings
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3NS8MwFA9DL3oQP3E6Rw7epK5t0rTxNoZjKu7kYLeQpAluuDnmvPq3m5emY4rsIPTUJKW8JO8j-f3eQ-iaq5SoxMrIFNxGNDduSzlLFJVcm5jBxZIvBvM8ZIMRfRxn4wbq1VwYgFUG3V_pdK-tw5tOkGZnMZkAx9etReeBp3C751QxMNgpA1jf7dcGzCPOkzpjOPQOxJkK4zWdLSBld-qvOhPgU_9tnH6paW97-ofoIDiNuFv91xFqmPkx2t9IJXiCxhBLRh6Phiv-B9a-YIOXPAYWCZ5V54ElLs2as4j9kI873MWvLiRdKsgTjKE51PU6RaP-_UtvEIWqCZEmabGKiCWFzjJDpFLMWhmn0mhrY8uYLnXiHIDChXTc6sKFRjmh0j0F1S7uYIyXlpMztDN_n5tzhHVqSaKysshsRlVMZcxLRbhkytk7LfMmSmpxCR1SikNlizdRY8emAkQsQMSiEnET3azHLKqEGlt7Z_UsiB_LQjiNv3Vcq54yETala6c84bnzWPOLf372Eu2lgGnxqO0W2lktP82Vc0pWqu1XXRvtdh-eBsNvvtnhNg
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV07T8MwED6VMgAD4inK0wMbikjivMxWVaAW2k6t1M2yHVuAaKlK-f-cHac8hBiQMkRxLorOzj3i77sDuGQypjIyItAFM0GSa_yk0BMFJVM6zOzGkmsGMxhm3XFyP0knDejUXBgLq_S2v7Lpzlr7K9dem9fzpyfL8cW1iBF4bHf30BSvwXqS4kkT1tu9h-7wE-kR5lFdNNwKeO5MBfN6ns5t1e7Y7XZGllL9u3_6Yamd-7nbgW0fN5J29Wq70NCzPdj6Uk1wHyY2nQwcJI1UFBCiXM8Gp3xiiSRkWv0SLEmpV7RF4kTebkibPGJWupC2VDCxw7611wGM725HnW7gGycEisbFMqCGFipNNRVSZsaIMBZaGROaLFOlijAGKDCrY0YVmB3lNBF4FInC1CPLWGkYPYTm7HWmj4Co2NBIpmWRmjSRYSJCVkrKRCbR5SmRtyCq1cWVrypum1u88Bo-9sytirlVMa9U3IKrlcy8qqnx591pPQv828rgaPT_lDutp4z77xLHExaxHIPW_Pifj72Aje5o0Of93vDhBDZjC3FxIO5TaC4X7_oMY5SlPPdr8ANvWePh
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Full-field+stress+computation+from+measured+deformation+fields%3A+A+hyperbolic+formulation&rft.jtitle=Journal+of+the+mechanics+and+physics+of+solids&rft.au=Cameron%2C+Benjamin+C.&rft.au=Tasan%2C+C.Cem&rft.date=2021-02-01&rft.pub=Elsevier+Ltd&rft.issn=0022-5096&rft.volume=147&rft_id=info:doi/10.1016%2Fj.jmps.2020.104186&rft.externalDocID=S0022509620304130
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0022-5096&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0022-5096&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0022-5096&client=summon