Geometry of incompatible deformations: differential geometry in continuum mechanics
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2019]
|
| Series: | De Gruyter studies in mathematical physics
volume 50 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Enthält Literaturverzeichnis (Seite [380] - 386) und Index |
| Physical Description: | XX, 388 Seiten Illustrationen, Diagramme 24 cm x 17 cm |
| ISBN: | 9783110562019 3110562014 |
Staff View
MARC
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| 100 | 1 | |a Lychev, Sergey |d 1970- |e Verfasser |0 (DE-588)1171862539 |4 aut | |
| 245 | 1 | 0 | |a Geometry of incompatible deformations |b differential geometry in continuum mechanics |c Sergey Lychev and Konstantin Koifman |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2019] | |
| 264 | 4 | |c © 2019 | |
| 300 | |a XX, 388 Seiten |b Illustrationen, Diagramme |c 24 cm x 17 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematical physics |v volume 50 | |
| 500 | |a Enthält Literaturverzeichnis (Seite [380] - 386) und Index | ||
| 650 | 0 | 7 | |a Festkörpermechanik |0 (DE-588)4129367-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
| 653 | |a Deformation | ||
| 653 | |a Mechanische Spannung | ||
| 653 | |a Mannigfaltigkeit | ||
| 653 | |a Differentialgeometrie | ||
| 689 | 0 | 0 | |a Festkörpermechanik |0 (DE-588)4129367-8 |D s |
| 689 | 0 | 1 | |a Differentialgeometrie |0 (DE-588)4012248-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Koifman, Konstantin |e Verfasser |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-3-11-056321-4 |
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| 830 | 0 | |a De Gruyter studies in mathematical physics |v volume 50 |w (DE-604)BV040141722 |9 50 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-030686691 | ||
Record in the Search Index
| _version_ | 1804179083609767936 |
|---|---|
| adam_text | CONTENTS
PREFACE* VII
GENERAL SCHEME OF NOTATIONS * XIX
1 INTRODUCTION * 1
2 GEOMETRY OF PHYSICAL SPACE * 3
2.1 EUCLIDEAN AFFINE SPACE * 4
2.1.1 GENERAL DEFINITIONS * 4
2.1.2 TOPOLOGY ON 8*
-----
9
2.1.3 SMOOTH MAPPINGS ON
%
* 9
2.1.4 PARALLEL TRANSPORT * 13
2.1.5 TOTAL DERIVATIVES OF VECTOR AND TENSOR FIELDS *
2.1.6 INTEGRATION * 16
2.1.7 SYMMETRIZATION AND ANTISYMMETRIZATION * 17
2.1.8 DIVERGENCE * 17
2.1.9 CURL * 18
2.2 CURVILINEAR COORDINATES * 19
2.2.1 REPARAMETRIZATION * 19
2.2.2 COORDINATE CURVES * 21
2.2.3 LOCAL BASIS * 21
2.2.4 FROM POINTWISE TO THE WHOLE * 22
2.2.5 METRIC TENSORS * 23
2.2.6 PARALLEL TRANSPORT * 24
2.2.7 TOTAL DERIVATIVES * 24
2.2.8 INTEGRATION * 28
2.2.9 THE PHYSICAL BASIS * 28
2.3 NADIA OPERATOR FORMALISM IN 3D-SPACE * 28
2.3.1 DEFINITIONS OF NABLA * 29
2.3.2 OPERATIONS IN EUCLIDEAN SPACE * 29
2.3.3 NABLA AND MAPPINGS * 30
2.3.4 COORDINATE REPRESENTATIONS FOR DIVERGENCE *
2.3.5 COORDINATE REPRESENTATIONS FOR CURL * 33
2.4 RIEMANNIAN SPACE * 33
2.4.1 GENERAL DEFINITION * 33
2.4.2 SMOOTH MAPPINGS ON S6 * 35
2.4.3 GEOMETRIC MEASURES AND GEODESICS * 37
2.4.4 PARALLEL TRANSPORT * 38
2.4.5 INTEGRATION * 40
2.5 NEWTONIAN SPACE-TIME * 40
2.5.1 NEWTONIAN SPACE-TIME MANIFOLD * 41
2.5.2 NEWTON*S LAWS
-----
42
2.5.3 RIGID FRAME
-----
44
2.5.4 CHANGE OF FRAME * 44
2.6 RELATIVISTIC SPACE-TIME * 46
2.6.1 LORENTZIAN MANIFOLDS * 46
2.6.2 TIME ORIENTATION * 47
2.6.3 DEFINITION OF RELATIVISTIC SPACE-TIME * 48
2.6.4 OBSERVERS * 48
2.6.5 LORENTZ TRANSFORMATIONS * 49
2.6.6 MATTER * 49
2.6.7 THE EINSTEIN EQUATION * 51
2.7 CONCLUDING REMARKS * 57
3 ESSENTIALS OF NON-LINEAR ELASTICITY THEORY* 59
3.1 SHAPES AND DEFORMATION * 59
3.2 SHAPE COORDINATES AND BASIS * 61
3.3 DEFORMATION GRADIENT AND STRAIN MEASURES * 64
3.3.1 DEFORMATION GRADIENT * 64
3.3.2 STRAIN MEASURES * 66
3.3.3 DEFORMATION GRADIENT IN CURVILINEAR COORDINATES * 67
3.3.4 STRAIN MEASURES IN CURVILINEAR COORDINATES * 68
3.4 DISPLACEMENT FIELD * 69
3.5 MOTION
-----
70
3.6 COMPATIBILITY CONDITIONS * 70
3.6.1 REVIEW ON DE RHAM COHOMOLOGY * 70
3.6.2 NECESSARY AND SUFFICIENT CONDITIONS FOR COMPATIBILITY*
3.7 STRESSES * 75
3.8 NON-LINEAR ELASTICITY AS FIELD THEORY * 78
3.8.1 ACTION AND ITS LAGRANGIAN * 78
3.8.2 PARTIAL AND FULL VARIATIONS * 79
3.8.3 FIELD EQUATIONS * 84
3.8.4 ACTION INVARIANCE CONDITIONS * 84
3.9 CONSTITUTIVE RELATIONS * 87
3.9.1 PRINCIPLE OF MATERIAL-FRAME INDIFFERENCE * 87
3.9.2 THE CAUCHY POLAR DECOMPOSITION THEOREM * 89
3.9.3 SIMPLE MATERIAL * 90
3.9.4 REPRESENTATION THEOREMS * 92
3.10 HYPERELASTIC SOLIDS * 94
3.10.1 EXPRESSIONS FOR STRESSES * 94
3.10.2 UNIVERSAL DEFORMATIONS * 94
3.11
3.11.1
3.11.2
3.11.3
3.11.4
3.12
3.12.1
3.12.2
3.12.3
3.12.4
3.12.5
3.12.6
3.12.7
3.12.8
3.12.9
3.12.10
4
4.1
4.2
4.3
4.4
4.5
4.5.1
4.5.2
4.5.3
4.5.4
5
5.1
5.2
5.3
5.3.1
5.3.2
5.4
5.4.1
5.4.2
5.5
5.6
LINEARIZED ELASTICITY * 103
LINEARIZED KINEMATICS * 103
LINEARIZED CONSTITUTIVE RELATIONS * 105
LINEARIZED STRESSES * 106
THE GREEN-RIVLIN-SHIELD-TRUESDELL FORMULA * 107
DISTRIBUTED DEFECTS IN SOLIDS * 109
PRELIMINARY REMARKS * 109
TOTAL DISTORTION 1-FORMS * 110
FOUR-DIMENSIONAL SPACE AND THE HOMOTOPY OPERATOR * 111
DECOMPOSITION OF TOTAL DISTORTION INTO EXACT AND ANTIEXACT PARTS * 112
CONTINUITY EQUATIONS OF DEFECT DYNAMICS * 112
4D REPRESENTATION * 113
THE MOMENTUM EQUATION * 113
EQUATIONS IN MATRIX FORM * 114
RELATIONS OF DISLOCATION AND DISCLINATION FORMS WITH CONNECTION,
CURVATURE, AND TORSION FORMS * 114
APPLICATION OF YANG-MILLS COUPLING THEORY * 116
GEOMETRIC FORMALIZATION OF THE BODY AND ITS REPRESENTATION
IN PHYSICAL SPACE * 119
GEOMETRIC MOTIVATION * 119
COMPARISON BETWEEN CONVENTIONAL AND NON-EUCLIDEAN CONTINUUM
MECHANICS * 125
A BODY
-----
128
CONFIGURATIONS * 132
A SHAPE OF A BODY AS A SUBMANIFOLD OF THE PHYSICAL SPACE * 135
A SHAPE AS A SUBMANIFOLD * 135
THE LOCAL K-SLICE CONDITION * 136
THE INDUCED RIEMANNIAN SPACE STRUCTURE * 137
A SHAPE AND THE PHYSICAL SPACE. INTRINSIC VERSUS SPATIAL * 137
STRAIN MEASURES * 141
REVIEW ON CAUCHY THEORY * 141
CONFIGURATIONS AND DEFORMATIONS * 143
COORDINATE REPRESENTATIONS OF CONFIGURATIONS AND DEFORMATIONS * 144
THE GENERAL CASE * 144
THE EUCLIDEAN CASE * 146
TWO-POINT TENSORS * 149
TWO-POINT TENSOR BUNDLE * 149
THE TRANSPOSE AND ORTHOGONAL TENSORS * 151
CONFIGURATION GRADIENT * 153
LEFT AND RIGHT CAUCHY-GREEN STRAIN TENSORS * 156
5.6.1
5.6.2
5.6.3
6
6.1
6.2
6.3
6.4
6.4.1
6.4.2
6.4.3
6.4.4
6.5
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
8.2
8.3
8.4
8.5
8.5.1
8.5.2
8.5.3
9
9.1
9.2
9.2.1
9.2.2
SPATIAL MEASUREMENTS IN MATERIAL DESCRIPTION * 156
THE CAUCHY POLAR DECOMPOSITION THEOREM * 157
CAUCHY-GREEN STRAIN MEASURES AS PULLBACK AND PUSHFORWARD OF
METRICS * 158
MOTION * 161
MOTION AS A CURVE * 161
VELOCITY * 162
(M + L)-FORMALISM AND ACCELERATION * 164
FLOWS AND LIE DERIVATIVES * 165
VECTOR FIELDS AND INTEGRAL CURVES * 165
FLOW * 166
LIE DERIVATIVES * 168
TIME-DEPENDENT FLOW * 174
MOTION AS A TIME-DEPENDENT FLOW * 176
STRESS MEASURES
* 179
CONCENTRATED FORCES AND FORCE DENSITIES * 179
INCLINED HYPERPLANES * 181
PIOLA SECTION ON INCLINED HYPERPLANES * 183
THE CAUCHY SECTION * 185
CAUCHY AND PIOLA STRESSES * 186
TRANSFORMATION FROM SPATIAL DESCRIPTION TO MATERIAL * 188
EXAMPLE: NEO-HOOKEAN SOLIDS * 191
THE CASE DIM B = DIM
8FT
= 3 * 192
THE ESHELBY ENERGY-MOMENTUM TENSOR ON MANIFOLDS * 193
MATERIAL UNIFORMITY AND INHOMOGENEITY* 195
EQUIVALENCE RELATION BETWEEN SMOOTH EMBEDDINGS * 195
LOCAL CONFIGURATIONS AND SIMPLE BODIES * 195
MATERIAL UNIFORMITY * 196
A MATERIAL METRIC * 199
BODIES WITH VARIABLE MATERIAL COMPOSITION * 200
FORMALIZATION OF BODIES WITH VARIABLE MATERIAL COMPOSITION * 200
THE DISCRETE PROCESS * 203
THE CONTINUOUS PROCESS * 204
MATERIAL CONNECTIONS
* 209
CONNECTIONS ON VECTOR BUNDLES * 209
AFFINE CONNECTION * 212
THE TRANSFORMATION LAW * 213
TORSION, CURVATURE, AND NON-METRICITY * 214
9.2.3 A PARTICULAR CASE: EUCLIDEAN SPACE * 216
9.2.4 A PARTICULAR CASE: RIEMANNIAN SPACE * 218
9.2.5 CONNECTION ON THE PULLBACK BUNDLE * 220
9.2.6 THE MOVING FRAME METHOD
-----
222
9.2.7 THE WEITZENBOECK CONNECTION AS A MATERIAL CONNECTION * 225
9.2.8 THE WEITZENBOECK CONNECTION: EXAMPLE * 226
10 BALANCE EQUATIONS * 231
10.1 DIVERGENCE * 231
10.1.1 THE CASE OF A VECTOR FIELD * 231
10.1.2 THE CASE OF A COVECTOR-VALUED FORM * 234
10.2 THE REYNOLDS TRANSPORT THEOREM * 239
10.3 BALANCE EQUATIONS IN INTEGRAL FORM * 240
10.3.1 POWER BALANCE * 240
10.3.2 MASS CONSERVATION * 242
10.3.3 TRANSFORMATION OF THE SPATIAL POWER BALANCE EQUATION * 243
10.4 DERIVATION OF DIFFERENTIAL BALANCE EQUATIONS USING THE COVARIANCE
PRINCIPLE * 244
10.4.1 THE PRINCIPLE OF COVARIANCE * 244
10.4.2 CHANGE OF FRAME AND OBJECTIVE TRANSFORMATIONS * 245
10.4.3 DERIVATION OF SPATIAL CONSERVATION LAWS * 246
11 THE EVOLUTIONARY PROBLEM - EXAMPLES * 249
11.1 EXAMPLE: THE CYLINDRICAL PROBLEM * 249
11.1.1 HOLLOW CYLINDERS WITH DISCRETE INHOMOGENEITY * 249
11.1.2 HOLLOW CYLINDERS WITH CONTINUOUS INHOMOGENEITY * 255
11.1.3 RESULTS AND DISCUSSION * 263
11.2 UNIFORM INFLATION OF A SPHERICAL MULTILAYERED STRUCTURE * 267
11.2.1 LAYERS AND ASSEMBLIES * 267
11.2.2 COORDINATES AND VECTOR BASES * 268
11.2.3 STRAIN MEASURES * 271
11.2.4 INCOMPRESSIBLE MATERIAL * 271
11.2.5 COMPRESSIBLE MATERIAL * 273
11.2.6 CONTINUOUS NON-EUCLIDEAN STRUCTURES * 277
11.2.7 SMALL PERTURBATIONS OF THE SELF-STRESSED SHAPE * 280
11.3 BENDING OF RECTANGULAR BLOCKS * 281
11.3.1 DEFORMATIONS OF A SINGLE BLOCK * 281
11.3.2 STRESSES * 286
11.3.3 FORCES ON BOUNDARY SURFACES * 287
11.3.4 THIN LAYERS
-----
289
11.3.5 DISCRETE ACCRETION * 290
11.3.6 CONTINUOUS ACCRETION * 292
12 ALGEBRAIC STRUCTURES * 297
12.1 PRELIMINARY COMMENTS ON THE USE OF SETS * 297
12.2 ORDERED PAIRS. CARTESIAN PRODUCTS. RELATIONS * 297
12.3 FUNCTIONS * 298
12.4 SOME ALGEBRAIC STRUCTURES * 300
12.4.1 GROUPS
-----
300
12.4.2 RING
-----
300
12.4.3 MODULE * 301
12.5 LINEAR SPACES AND MAPPINGS * 301
12.5.1 VECTOR SPACE OVER R * 301
12.5.2 LINEAR AND K-LINEAR MAPPINGS * 303
12.5.3 TENSOR PRODUCTS OF VECTOR SPACES * 305
12.5.4 VECTORS AND LINEAR MAPPINGS IN EUCLIDEAN SPACE * 308
12.6 LINEAR GROUPS * 311
12.7 AFFINE SPACE * 312
13 REVIEW OF SMOOTH MANIFOLDS AND VECTOR BUNDLES * 315
13.1 SMOOTH MANIFOLDS * 315
13.1.1 TOPOLOGICAL SPACES * 315
13.1.2 SMOOTH STRUCTURE * 321
13.1.3 SMOOTH MAPPINGS
-----
322
13.1.4 EMBEDDED SUBMANIFOLDS * 325
13.2 THE * TOWER* OF TENSOR SPACES * 326
13.2.1 TANGENT SPACE TO A SMOOTH MANIFOLD * 326
13.2.2 THE TANGENT MAP AT A POINT * 332
13.2.3 COTANGENT SPACE TO A SMOOTH MANIFOLD * 333
13.2.4 REMARKS ON THE TANGENT SPACES * 334
13.2.5 THE * TOWER * 336
13.2.6 EXTERIOR FORMS * 337
13.3 VECTOR BUNDLES AND THEIR SECTIONS * 340
13.3.1 SMOOTH VECTOR BUNDLES OF RANK
K
* 340
13.3.2 TANGENT AND COTANGENT BUNDLES * 341
13.3.3 OPERATIONS ON VECTOR BUNDLES * 343
13.3.4 VECTOR BUNDLES OF HIGHER RANK * 344
13.3.5 SECTIONS OF VECTOR BUNDLES * 345
13.3.6 VECTOR BUNDLE HOMOMORPHISMS * 347
13.3.7 PULLBACK AND PUSHFORWARD * 348
13.3.8 SMOOTH FRAMES * 350
13.3.9 EXTERIOR DIFFERENTIATION * 351
13.3.10 THE RIEMANNIAN METRIC AND MUSICAL ISOMORPHISMS * 352
13.4 ORIENTATION AND INTEGRATION ON MANIFOLDS * 354
13.4.1 THE VOLUME FORM AND ORIENTATION OF SMOOTH MANIFOLDS * 354
13.4.2 THE HODGE STAR OPERATOR * 355
13.4.3 INTEGRATION OF DIFFERENTIAL FORMS AND STOKES* THEOREM * 356
14 CONNECTIONS ON PRINCIPAL BUNDLES * 359
14.1 LIE GROUPS AND LIE ALGEBRAS * 359
14.1.1 LIE GROUPS AND HOMOMORPHISMS * 359
14.1.2 GROUP ACTION
-----
359
14.1.3 LIE ALGEBRA OF THE LIE GROUP * 361
14.1.4 ADJOINT REPRESENTATION * 363
14.1.5 EXPONENTIAL MAPPING* 363
14.2 PRINCIPAL BUNDLES * 364
14.2.1 BUNDLES * 364
14.2.2 PRINCIPAL BUNDLES * 365
14.2.3 FRAME BUNDLES * 366
14.2.4 ASSOCIATED BUNDLES * 367
14.3 CONNECTIONS
------
368
14.3.1 CONNECTIONS ON THE PRINCIPAL BUNDLE * 368
14.3.2 LOCAL REPRESENTATION OF CONNECTIONS * 369
14.3.3 LOCAL REPRESENTATION ON FRAME BUNDLES * 369
14.3.4 GAUGE MAPS * 370
14.3.5 PARALLEL TRANSPORT * 371
14.3.6 CURVATURE * 374
14.3.7 TORSION
-----
375
14.3.8 BIANCHI IDENTITIES * 376
14.3.9 COVARIANT DERIVATIVES ON ASSOCIATED VECTOR BUNDLES * 376
14.3.10 DIRECT CONSTRUCTION OF COVARIANT DERIVATIVES ON PRINCIPAL
BUNDLES * 377
BIBLIOGRAPHY * 381
INDEX * 387
|
| any_adam_object | 1 |
| author | Lychev, Sergey 1970- Koifman, Konstantin |
| author_GND | (DE-588)1171862539 |
| author_facet | Lychev, Sergey 1970- Koifman, Konstantin |
| author_role | aut aut |
| author_sort | Lychev, Sergey 1970- |
| author_variant | s l sl k k kk |
| building | Verbundindex |
| bvnumber | BV045299525 |
| classification_rvk | UF 3000 SK 370 UF 2000 |
| ctrlnum | (OCoLC)1074441708 (DE-599)DNB1162907878 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV045299525 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:14:14Z |
| institution | BVB |
| isbn | 9783110562019 3110562014 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030686691 |
| oclc_num | 1074441708 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-83 DE-11 |
| owner_facet | DE-19 DE-BY-UBM DE-83 DE-11 |
| physical | XX, 388 Seiten Illustrationen, Diagramme 24 cm x 17 cm |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematical physics |
| series2 | De Gruyter studies in mathematical physics |
| spelling | Lychev, Sergey 1970- Verfasser (DE-588)1171862539 aut Geometry of incompatible deformations differential geometry in continuum mechanics Sergey Lychev and Konstantin Koifman Berlin ; Boston De Gruyter [2019] © 2019 XX, 388 Seiten Illustrationen, Diagramme 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematical physics volume 50 Enthält Literaturverzeichnis (Seite [380] - 386) und Index Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Deformation Mechanische Spannung Mannigfaltigkeit Differentialgeometrie Festkörpermechanik (DE-588)4129367-8 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Koifman, Konstantin Verfasser aut Erscheint auch als Online-Ausgabe, PDF 978-3-11-056321-4 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-056227-9 De Gruyter studies in mathematical physics volume 50 (DE-604)BV040141722 50 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030686691&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lychev, Sergey 1970- Koifman, Konstantin Geometry of incompatible deformations differential geometry in continuum mechanics De Gruyter studies in mathematical physics Festkörpermechanik (DE-588)4129367-8 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4129367-8 (DE-588)4012248-7 |
| title | Geometry of incompatible deformations differential geometry in continuum mechanics |
| title_auth | Geometry of incompatible deformations differential geometry in continuum mechanics |
| title_exact_search | Geometry of incompatible deformations differential geometry in continuum mechanics |
| title_full | Geometry of incompatible deformations differential geometry in continuum mechanics Sergey Lychev and Konstantin Koifman |
| title_fullStr | Geometry of incompatible deformations differential geometry in continuum mechanics Sergey Lychev and Konstantin Koifman |
| title_full_unstemmed | Geometry of incompatible deformations differential geometry in continuum mechanics Sergey Lychev and Konstantin Koifman |
| title_short | Geometry of incompatible deformations |
| title_sort | geometry of incompatible deformations differential geometry in continuum mechanics |
| title_sub | differential geometry in continuum mechanics |
| topic | Festkörpermechanik (DE-588)4129367-8 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Festkörpermechanik Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030686691&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV040141722 |
| work_keys_str_mv | AT lychevsergey geometryofincompatibledeformationsdifferentialgeometryincontinuummechanics AT koifmankonstantin geometryofincompatibledeformationsdifferentialgeometryincontinuummechanics |