Contents
1 Material Models for Structural Analysis 3
1.1 Elastic materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Isotropic linear elastic material - IsoLE . . . . . . . . . . 3
1.1.2 Orthotropic linear elastic material - OrthoLE . . . . . . . 3
1.1.3 General anisotropic linear elastic material - AnisoLE . . . 4
1.1.4 Hyperelastic material - HyperMat . . . . . . . . . . . . . 4
1.1.5 Hyperelastic material - Compressible Mooney-Rivlin . . . 5
1.2 Winkler-Pasternak model . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Large-strain master material . . . . . . . . . . . . . . . . . . . . 7
1.4 Plasticity-based material models . . . . . . . . . . . . . . . . . . 7
1.4.1 Drucker-Prager model - DruckerPrager . . . . . . . . . . . 7
1.4.2 Drucker-Prager model with tension cut-off and isotropic
damage - DruckerPragerCut . . . . . . . . . . . . . . . . . 9
1.4.3 Mises plasticity model with isotropic damage - MisesMat 12
1.4.4 Mises plasticity model with isotropic damage, nonlocal -
MisesMatNl, MisesMatGrad . . . . . . . . . . . . . . . . . 13
1.4.5 Rankine plasticity model with isotropic damage and its
nonlocal formulations - RankMat, RankMatNl, RankMat-
Grad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.6 Perfectly plastic material with Mises yield condition - Steel1 16
1.4.7 Composite plasticity model for masonry - Masonry02 . . . 16
1.4.8 Nonlinear elasto-plastic material model for concrete plates
and shells - Concrete2 . . . . . . . . . . . . . . . . . . . . 23
1.5 Material models for tensile failure . . . . . . . . . . . . . . . . . . 23
1.5.1 Nonlinear elasto-plastic material model for concrete plates
and shells - Concrete2 . . . . . . . . . . . . . . . . . . . . 23
1.5.2 Smeared rotating crack model - Concrete3 . . . . . . . . . 23
1.5.3 Smeared rotating crack model with transition to scalar
damage - linear softening - RCSD . . . . . . . . . . . . . 25
1.5.4 Smeared rotating crack model with transition to scalar
damage - exponential softening - RCSDE . . . . . . . . . 25
1.5.5 Nonlocal smeared rotating crack model with transition to
scalar damage - RCSDNL . . . . . . . . . . . . . . . . . . 26
1.5.6 Isotropic damage model for tensile failure - Idm1 . . . . . 27
1.5.7 Nonlocal isotropic damage model for tensile failure - Idmnl1 34
1.5.8 Anisotropic damage model - Mdm . . . . . . . . . . . . . 39
1.5.9 Isotropic damage model for interfaces . . . . . . . . . . . 43
1.5.10 Isotropic damage model for interfaces using tabulated data
for damage . . . . . . . . . . . . . . . . . . . . . . . . . . 43
1.6 Material models specific to concrete . . . . . . . . . . . . . . . . 44
1.6.1 Mazars damage model for concrete - MazarsModel . . . . 44
1.6.2 Nonlocal Mazars damage model for concrete - MazarsMod-
elnl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
1.6.3 CebFip78 model for concrete creep with aging - CebFip78 45
1.6.4 Double-power law model for concrete creep with aging -
DoublePowerLaw . . . . . . . . . . . . . . . . . . . . . . . 45
1.6.5 B3 and MPS models for concrete creep with aging . . . . 45
1.6.6 MPS damage model . . . . . . . . . . . . . . . . . . . . . 54
2
1.6.7 Microplane model M4 - Microplane M4 . . . . . . . . . . 63
1.6.8 Damage-plastic model for concrete - ConcreteDPM . . . . 63
1.6.9 CDPM2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
1.7 Orthotropic damage model with fixed crack orientations for com-
posites - CompDamMat . . . . . . . . . . . . . . . . . . . . . . . 72
1.8 Orthotropic elastoplastic model with isotropic damage - Trab-
Bone3d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
1.8.1 Local formulation . . . . . . . . . . . . . . . . . . . . . . . 74
1.8.2 Nonlocal formulation - TrabBoneNL3d . . . . . . . . . . . 76
1.9 Material models for interfaces . . . . . . . . . . . . . . . . . . . . 76
1.9.1 Isotropic damage model for interfaces . . . . . . . . . . . 77
1.9.2 Simple interface material . . . . . . . . . . . . . . . . . . 77
1.10 Material models for lattice elements . . . . . . . . . . . . . . . . 78
1.10.1 Latticedamage2d . . . . . . . . . . . . . . . . . . . . . . . 78
2 Material Models for Transport Problems 84
2.1 Isotropic linear material for heat transport – IsoHeat . . . . . . . 84
2.2 Isotropic linear material for moisture transport – IsoLinMoisture 84
2.3 Isotropic material for moisture transport based on Baˇzant and
Najjar – BazantNajjarMoisture . . . . . . . . . . . . . . . . . . . 84
2.4 Nonlinear isotropic material for moisture transport – NlIsoMoisture 86
2.5 Material for cement hydration - CemhydMat . . . . . . . . . . . 87
2.6 Material for cement hydration - HydratingConcreteMat . . . . . 91
2.7 Coupled heat and mass transport material model - HeMotk . . . 93
2.8 Coupled heat and mass transport material model - HeMoKunzel 95
2.9 Material for unsaturated flow in lattice models – LatticeTransMat 97
2.9.1 One-dimensional transport element . . . . . . . . . . . . . 97
2.9.2 Constitutive laws . . . . . . . . . . . . . . . . . . . . . . . 98
3 Material Models for Fluid Dynamic 100
3.1 Newtonian fluid - NewtonianFluid . . . . . . . . . . . . . . . . . 100
3.2 Bingham fluid - BinghamFluid . . . . . . . . . . . . . . . . . . . 100
3.3 Two-fluid material - TwoFluidMat . . . . . . . . . . . . . . . . . 101
3.4 FE
2
fluid - FE2FluidMaterial . . . . . . . . . . . . . . . . . . . . 101
4 Material Drivers - Theory & Application 103
4.1 Multisurface plasticity driver - MPlasticMaterial class . . . . . . 103
4.1.1 Plasticity overview . . . . . . . . . . . . . . . . . . . . . . 103
4.1.2 Closest-point return algorithm . . . . . . . . . . . . . . . 104
4.1.3 Algorithmic stiffness . . . . . . . . . . . . . . . . . . . . . 106
4.1.4 Implementation of particular models . . . . . . . . . . . . 107
4.2 Isotropic damage model – IsotropicDamageMaterial class . . . . 108
4.3 Nonstationary linear transport model . . . . . . . . . . . . . . . . 109
4.4 Nonstationary nonlinear transport model . . . . . . . . . . . . . 110
4.5 Heat flux from radiation . . . . . . . . . . . . . . . . . . . . . . . 111
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List of Tables
1 Linear Isotropic Material - summary. . . . . . . . . . . . . . . . . 3
2 Orthotropic, linear elastic material – summary. . . . . . . . . . . 5
3 Anisotropic, linear elastic material – summary. . . . . . . . . . . 5
4 Hyperelastic material - summary. . . . . . . . . . . . . . . . . . . 6
5 Compressible Mooney-Rivlin - summary. . . . . . . . . . . . . . . 7
6 Winkler Pasternak material - summary. . . . . . . . . . . . . . . 7
7 Large-strain master material material - summary. . . . . . . . . . 8
8 DP material - summary. . . . . . . . . . . . . . . . . . . . . . . . 10
9 Drucker Prager material with tension cut-off - summary. . . . . . 11
10 Mises plasticity – summary. . . . . . . . . . . . . . . . . . . . . . 13
11 Nonlocal integral Mises plasticity – summary. . . . . . . . . . . . 15
12 Gradient-enhanced Mises plasticity – summary. . . . . . . . . . . 16
13 Rankine plasticity – summary. . . . . . . . . . . . . . . . . . . . 17
14 Nonlocal integral Rankine plasticity – summary. . . . . . . . . . 18
15 Gradient-enhanced Rankine plasticity – summary. . . . . . . . . 19
16 Perfectly plastic material with Mises condition – summary. . . . 19
17 Composite model for masonry - summary. . . . . . . . . . . . . . 23
18 Nonlinear elasto-plastic material model for concrete - summary. . 24
19 Rotating crack model for concrete - summary. . . . . . . . . . . . 25
20 RC-SD model for concrete - summary. . . . . . . . . . . . . . . . 26
21 RC-SD model for concrete - summary. . . . . . . . . . . . . . . . 26
22 RC-SD-NL model for concrete - summary. . . . . . . . . . . . . . 27
23 Isotropic damage model for tensile failure – summary. . . . . . . 34
24 Nonlocal isotropic damage model for tensile failure – summary. . 37
25 Nonlocal isotropic damage model for tensile failure – continued. . 38
26 Basic equations of microplane-based anisotropic damage model . 39
27 MDM model - summary. . . . . . . . . . . . . . . . . . . . . . . . 42
28 Isotropic damage model for interface elements – summary. . . . . 44
29 Isotropic damage model for interface elements using tabulated
data for damage – summary. . . . . . . . . . . . . . . . . . . . . 45
30 Mazars damage model – summary. . . . . . . . . . . . . . . . . . 46
31 Nonlocal Mazars damage model – summary. . . . . . . . . . . . . 47
32 CebFip78 material model – summary. . . . . . . . . . . . . . . . 47
33 Double-power law model – summary. . . . . . . . . . . . . . . . . 48
34 B3 creep and shrinkage model – summary. . . . . . . . . . . . . . 57
35 B3solid creep and shrinkage model – summary. . . . . . . . . . . 59
36 MPS theory—summary. . . . . . . . . . . . . . . . . . . . . . . . 61
37 MPS damage–summary. . . . . . . . . . . . . . . . . . . . . . . . 62
38 Microplane model M4 – summary. . . . . . . . . . . . . . . . . . 63
39 Damage-plastic model for concrete – summary. . . . . . . . . . . 67
40 CDPM2 – summary. . . . . . . . . . . . . . . . . . . . . . . . . . 79
41 Orthotropic damage model with fixed crack orientations for com-
posites – summary. . . . . . . . . . . . . . . . . . . . . . . . . . . 80
42 Anisotropic elastoplastic model with isotropic damage - summary. 81
43 Nonlocal formulation of anisotropic elastoplastic model with isotropic
damage – summary. . . . . . . . . . . . . . . . . . . . . . . . . . 82
44 Simple interface material – summary. . . . . . . . . . . . . . . . . 82
45 Scalar damage model for 2d lattice elements – summary. . . . . . 83
4
46 Linear isotropic material for heat transport - summary. . . . . . 84
47 Linear isotropic material for moisture transport - summary. . . . 85
48 Nonlinear isotropic material for moisture transport - summary. . 85
49 Nonlinear isotropic material for moisture transport - summary. . 88
50 Cemhydmat - summary. . . . . . . . . . . . . . . . . . . . . . . . 89
51 HydratingConcreteMat - summary of affinity hydration models. . 92
52 Coupled heat and mass transfer material model - summary. . . . 94
53 Parameters from Kunzel’s model. . . . . . . . . . . . . . . . . . . 95
54 Coupled heat and mass transfer material model Kunzel - summary. 96
55 Material for unsaturated flow in lattice models - summary. . . . . 99
56 Newtonian Fluid material - summary. . . . . . . . . . . . . . . . 100
57 Bingham Fluid material - summary. . . . . . . . . . . . . . . . . 101
58 Two-Fluid material - summary. . . . . . . . . . . . . . . . . . . . 101
59 FE
2
fluid material - summary. . . . . . . . . . . . . . . . . . . . . 102
60 General multisurface closest point algorithm . . . . . . . . . . . . 106
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