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Contents

Preface
Glossary of Symbols
1. Introduction
1.1 Material Properties Input
1.2 Ambient Time Dependency
1.2.1 Temperature in Time
1.2.2 Concentration in Time
1.2.3 Maturity in Time
1.2.4 Pressure in Time
1.2.5 Time Dependency for Elements
1.2.6 Time Dependency for Nodes


I. Structural Analysis

2. Overview of Material Models for Structural Analysis
2.1 Structural Modeling
2.1.1 Concrete and Brittle Materials
2.1.2 Reinforcement
2.1.3 Soil and Rock
2.1.4 Masonry
2.1.5 Metals
2.1.6 Composites
2.1.7 Rubbers
2.1.8 Fabrics
2.2 Availability for Elements
3. Mass and Damping
3.1 Mass
3.1.1 Mass Density
3.1.2 Concentrated Mass
3.2 Damping
3.2.1 Viscous Damping
3.2.2 Structural Damping
3.2.3 Continuous Damping
3.2.4 Strain Energy Based Element Damping
4. Elasticity
4.1 Linear Elasticity
4.1.1 Isotropic Elasticity
4.1.2 Orthotropic Elasticity
4.1.3 Ambient Influence
4.2 Nonlinear Elasticity
4.2.1 Granular Materials
4.2.2 Uniaxial
4.2.3 User-supplied
4.3 Modified Elasticity
4.4 Hyperelasticity
4.4.1 Deviatoric Strain Energy
4.4.2 Hydrostatic Strain Energy
4.4.3 User-supplied
5. Plasticity
5.1 Isotropic Plasticity
5.1.1 Tresca or Von Mises
5.1.2 Mohr-Coulomb or Drucker-Prager
5.1.3 Rankine Principal Stress
5.1.4 Egg Cam-clay
5.1.5 Modified Mohr-Coulomb
5.1.6 Hoek-Brown Rock Plasticity
5.1.7 Fraction Model
5.2 Orthotropic Plasticity
5.2.1 Hill
5.2.2 Hoffmann
5.2.3 Rankine-Hill - Anisotropic
5.3 Viscoplasticity
5.3.1 Duvaut-Lions
5.3.2 Perzyna
6. Cracking
6.1 Smeared Cracking
6.1.1 Tension Cut-off
6.1.2 Tension Softening
6.1.3 Shear Retention
6.1.4 Rate-dependent Cracking
6.2 Total Strain Crack Models
6.2.1 Basic Properties
6.2.2 Tensile Behavior
6.2.3 Shear Behavior
6.2.4 Compressive Behavior
6.2.5 Lateral Influence
6.3 Crack Bandwidth
6.4 Crack Index
6.4.1 Discrete Function
6.4.2 Concrete Model Specifications for Tensile Strength
7. Viscoelasticity
7.1 Power Law
7.1.1 Ambient Influence
7.1.2 Young Hardening Concrete Models
7.2 Maxwell Chain
7.3 Kelvin Chain
7.4 Determination of Chain Parameters
7.4.1 Discrete Function
7.4.2 Concrete Creep Models
8. Creep and Shrinkage
8.1 Creep
8.2 Shrinkage
8.2.1 Discrete Function
8.2.2 Concrete Shrinkage Models
9. Special Models
9.1 Spring/Dashpot Behavior
9.1.1 Initial Strain
9.1.2 Elasticity
9.1.3 Plasticity
9.1.4 Continuous Damping
9.1.5 Base Spring Characteristics
9.2 Generalized Stress-Strain Diagrams
9.2.1 Flat Shell Elements
9.3 Interface Behavior
9.3.1 Elasticity
9.3.2 Cracking
9.3.3 Bond-slip
9.3.4 Friction
9.3.5 Combined Cracking-Shearing-Crushing
9.3.6 User-supplied
9.4 Modified Maekawa Concrete Model
9.4.1 Direct Input
9.4.2 User-supplied
9.5 Reinforcement Behavior
9.5.1 Linear Elasticity
9.5.2 Von Mises Plasticity
9.5.3 Monti-Nuti Plasticity
9.5.4 Reinforcement Specials
9.5.5 User-supplied
9.6 Soil Behavior
9.6.1 Hardin-Drnevich and Ramberg-Osgood Models
9.6.2 Initial Stress Ratio
9.6.3 Undrained Behavior
9.7 Liquefaction
9.7.1 Towhata-Iai
9.7.2 Nishi
9.7.3 Bowl
9.7.4 Added Viscosity
9.8 Wöhler Diagrams
9.9 Fluid-Structure Interaction
10. Model Code Libraries
10.1 Concrete
10.1.1 Dutch Code NEN 6720
10.1.2 European CEB-FIP Model Code 1990
10.2 Steel
10.2.1 Dutch Code NEN 6770
10.3 Reinforcement Steel
10.3.1 Dutch Code NEN 6720
11. User-supplied Models
11.1 Elasticity and Viscoelasticity
11.1.1 Young's Modulus USRYOU
11.1.2 Poisson's Ratio USRPOI
11.1.3 Hyperelasticity USRRUB
11.1.4 Concrete Creep USRCRP
11.2 Nonlinear Elasticity
11.2.1 Tangential Stiffness ELSEUS
11.2.2 Total Stress ELSGUS
11.3 Plasticity and Cracking
11.3.1 General Curve USRCRV
11.3.2 Tension Cut-off USRCRK
11.3.3 Tension Softening USRTEN
11.3.4 Shear Retention USRSHR
11.3.5 Tensile Strength USRTST
11.3.6 Mode-I Ultimate Tensile Strain USREPU
11.3.7 Mode-I Tensile Fracture Energy USRGF1
11.3.8 Shear Retention Factor USRBET
11.3.9 Compressive Strength USRCST
11.3.10 Modified Maekawa Concrete Model USRMNL
11.4 General User-supplied Material Model
11.4.1 Input Data
11.4.2 Subroutine USRMAT
11.4.3 Example
11.5 Interface USRIFC
11.6 Liquefaction
11.6.1 Input Data
11.6.2 User-defined Liquefaction USRLIQ
11.6.3 Customized Towhata-Iai TOWLIQ
11.6.4 Customized Nishi NISLIQ
11.6.5 Customized Bowl BOWLIQ

II. Flow Analysis

12. Potential Flow
12.1 Conductivity and Capacitance
12.1.1 Constant Properties
12.1.2 Variable Properties
12.1.3 Time Dependent Diffusion Coefficient
12.2 Boundary Elements
12.2.1 Convection
12.2.2 Radiation
12.2.3 Discharge Type
12.3 Interface Elements
12.4 Cooling Pipe Elements
12.4.1 Conduction
12.4.2 Fluid Properties
12.4.3 Cooling Time
12.5 Hydration Heat
12.5.1 Heat Production
12.5.2 Conductivity and Capacitance
12.5.3 Equivalent Age
12.5.4 Arrhenius Constant
12.6 Solidification or Evaporation
12.7 Convective Field
13. Groundwater Flow
13.1 Regional Groundwater Flow
13.1.1 Aquifers
13.1.2 Resistance Layers
13.2 Detailed Groundwater Flow
13.2.1 Saturated Conductivity and Elastic Storativity
13.2.2 Relative Conductivity and Phreatic Storativity
13.2.3 Turbulence
13.2.4 Seepage Faces
13.2.5 Resistance Layers
14. Reynolds Flow - Lubrication

III. Coupled Flow-Stress Analysis

15. Soil-Pore Fluid Properties
15.1 Structural Elements
15.2 Staggered Analysis
15.3 Mixture Analysis
15.3.1 Continuum Elements
15.3.2 Interface Elements

IV. Background Theory
16. Elasticity
16.1 Orthotropic Elasticity
16.2 Nonlinear Elasticity
16.2.1 Grains Model
16.2.2 Boyce Model
16.2.3 Jardine Model
16.3 Hyperelasticity
16.3.1 Deviatoric Energy Function
16.3.2 Hydrostatic Energy Function
17. Plasticity
17.1 Isotropic Plasticity
17.1.1 Tresca
17.1.2 Von Mises
17.1.3 Mohr-Coulomb
17.1.4 Drucker-Prager
17.1.5 Rankine Principal Stress Model
17.1.6 Egg Cam-clay
17.1.7 Modified Mohr-Coulomb
17.1.8 Hoek-Brown Rock Plasticity Model
17.1.9 Fraction Model
17.1.10 Monti-Nuti Plasticity
17.2 Orthotropic Plasticity
17.2.1 Hill
17.2.2 Hoffmann
17.2.3 Rankine-Hill - Anisotropic
17.3 Viscoplasticity
17.3.1 Perzyna
17.3.2 Duvaut and Lions
17.4 Volumetric Locking
18. Cracking
18.1 Smeared Cracking
18.1.1 Tension Softening Relations
18.1.2 Shear Retention Relations
18.2 Total Strain Crack Models
18.2.1 Coaxial and Fixed Stress-Strain Concept
18.2.2 Loading and Unloading Determination
18.2.3 Stiffness Matrix
18.2.4 Lateral Expansion Effects due to Poisson's Ratio
18.2.5 Tensile Behavior
18.2.6 Shear Behavior
18.2.7 Compressive Behavior
18.2.8 Combination with Thermal or Concentration Expansion
18.2.9 Basic Material Parameters via Code Regulations
19. Viscoelasticity
19.1 Relaxation Function
19.2 Creep Function
19.2.1 Kelvin Chain Model
19.2.2 Double Power Law
19.3 Determination from Creep or Relaxation Curves
19.3.1 Curve Fit
19.3.2 From Creep to Relaxation
19.3.3 Concrete Aging
20. Time Effects on Concrete Properties using Model Codes
20.1 CEB-FIP Model Code 1990
20.1.1 Development of Strength with Time
20.1.2 Development of Modulus of Elasticity with Time
20.1.3 Creep
20.1.4 Shrinkage
20.2 ACI 209 Model Code
20.2.1 Development of Strength with Time
20.2.2 Development of Modulus of Elasticity with Time
20.2.3 Creep
20.2.4 Shrinkage
20.2.5 Correction Factors
20.3 NEN 6720 Model Code
20.3.1 Creep
20.3.2 Shrinkage
20.4 JSCE Model Code
20.4.1 Development of Strength with Time
20.4.2 Development of Modulus of Elasticity with Time
20.5 JCI Model Code
20.5.1 Development of Strength with Time
20.5.2 Development of Modulus of Elasticity with Time
21. Interface Nonlinearities
21.1 Discrete Cracking
21.1.1 Brittle Cracking
21.1.2 Linear Tension Softening
21.1.3 Nonlinear Tension Softening (Hordijk et al.)
21.1.4 Shear Retention
21.2 Crack Dilatancy
21.2.1 Rough Crack Model (Bazant & Gambarova)
21.2.2 Rough Crack Model (Gambarova & Karakoç)
21.2.3 Aggregate Interlock Relation (Walraven & Reinhardt)
21.2.4 Two-phase Model (Walraven)
21.2.5 Contact Density Model (Li et al.)
21.3 Bond-slip
21.3.1 Cubic Function (Dörr)
21.3.2 Power Law (Noakowski)
21.4 Coulomb Friction
21.5 Combined Cracking-Shearing-Crushing
21.5.1 Two-dimensional Interface Model
21.5.2 Three-dimensional Interface Behavior
22. Modified Maekawa Concrete Model
22.1 Elasto-Plastic Damage Model
22.2 Cracked Concrete Model
22.3 Crack-reclosing Option
22.4 Non-orthogonal Crack Model
22.5 Shear Transfer Models
22.5.1 Contact Density Model
22.5.2 Decay of Shear Transfer
23. Simple Soil Models
23.1 Hardin-Drnevich Model
23.2 Ramberg-Osgood Model
24. Liquefaction
24.1 Towhata-Iai Model
24.1.1 Isotropic Model
24.1.2 Deviatoric Model
24.1.3 Initial Stress State
24.2 Nishi Model
24.2.1 Elastic Component
24.2.2 Plastic Components
24.3 Bowl Model
24.3.1 Deviatoric Behavior
24.3.2 Volumetric Behavior
24.4 Added Viscosity

V. Appendix
A. Available Element Types
B. Material Properties Forms
B.1 Model Code Libraries
B.1.1 Concrete
B.1.2 Steel
B.1.3 Reinforcement Steel
B.2 Linear Elasticity
B.2.1 Isotropic
B.2.2 Orthotropic
B.2.3 Reinforcement
B.2.4 Interfaces
B.2.5 Spring
B.3 Mass
B.3.1 Mass Density
B.3.2 Point Mass
B.4 Damping
B.4.1 Viscous
B.4.2 Structural
B.4.3 Isotropic
B.4.4 Orthotropic
B.4.5 Strain Energy Based
B.5 Static Nonlinearity
B.5.1 Concrete and Brittle Materials
B.5.2 Soil and Rock
B.5.3 Masonry
B.5.4 Composites
B.5.5 Interfaces
B.5.6 Metals
B.5.7 Rubbers
B.5.8 Contact
B.5.9 Reinforcement
B.5.10 Springs
B.6 Transient Nonlinearity
B.6.1 Power Law Viscoelasticity
B.6.2 ACI 209 Model Code Creep
B.6.3 Transient Creep
B.6.4 Spring/Dashpot
B.7 Expansion
B.8 Woehler
B.9 Flow
B.9.1 Isotropic
B.9.2 Orthotropic
B.9.3 Anisotropic
B.9.4 Boundary
B.9.5 Interface
B.9.6 Cooling Pipe
B.9.7 Convective Field
B.10 Detailed Groundwater Flow
B.10.1 Isotropic
B.10.2 Orthotropic
B.10.3 Anisotropic
B.10.4 Boundary
B.10.5 Interface
B.10.6 Convective Field
B.11 Aquifers
B.11.1 Isotropic
B.11.2 Orthotropic
B.11.3 Anisotropic
B.11.4 Interface
B.12 Lubrication
B.13 Cross-section
B.14 Pore Fluid
B.15 External

Bibliography
Index
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DIANA-9.3 User's Manual - Material Library
First ed.

Copyright (c) 2008 by TNO DIANA BV.