Abaqus Theory Guide
Introduction and Basic Equations
Components of a vector or a matrix in a coordinate system
Director and rotation field updates
Variations of the rotation field
Coupling of rotations: constant velocity joint
Deformation, strain, and strain rates
Strain in general three-dimensional motions
Rate of deformation and strain increment
The additive strain rate decomposition
Equilibrium, stress, and state storage
About procedures and basic equations
Basic finite element equations
Nonlinear solution methods in Abaqus/Standard
Quasi-Newton solution technique
Eigenvalue buckling prediction
Equivalent rigid body dynamic motion
Rotational bulk viscosity for shell elements
Eigenvalue extraction for symmetric systems
Variables associated with the natural modes of a model
Linear dynamic analysis using modal superposition
Damping options for modal dynamics
Solution to the uncoupled system
Solution to the coupled system
Structural damping in modal dynamic analysis
Response of nodal and element variables
Complete Quadratic Combination Method
Steady-state linear dynamic analysis
The frequency response function
Base motions in modal-based procedures
Direct steady-state dynamic analysis
Subspace-based steady-state dynamic analysis
Steady-state transport analysis and mass diffusion
Steady-state transport analysis
Kinematics of steady-state rolling
Performing a harmonic analysis about a nonlinear base state
Discretization and time integration
Effective stress principle for porous media
Discretized equilibrium statement for a porous medium
Constitutive behavior in a porous medium
Continuity statement for the wetting liquid phase in a porous medium
Volumetric strain in the liquid and grains
Solution strategy for coupled diffusion/deformation
Poroelastic acoustic medium in frequency domain
Inertial and damping dynamic properties and equilibrium equations
Coupled fluid structure, piezoelectric, and coupled thermal-electrical analysis
Coupled acoustic-structural medium analysis
Physical boundary conditions in acoustic analysis
Formulation for direct integration transient dynamics
Formulation for steady-state response using nodal degrees of freedom
Formulation for eigenvalue extraction and mode-based procedures
Volumetric drag and fluid viscosity
Impedance and admittance at fluid boundaries
An improvement on radiation boundary conditions for plane waves
Equilibrium and flux conservation
Constitutive behavior: material coupling
Coupled thermal-electrical analysis
Thermal energy due to electrical current
Uncoupled heat transfer analysis
Cavity radiation flux and Jacobian contributions
View factor between elementary areas
Substructuring and submodeling
Substructuring and substructure analysis
Fixed direction gravity loading
J-integral in three dimensions
Stress intensity factor extraction
Prediction of the direction of crack propagation
Maximum tangential stress criterion
Maximum energy release rate criterion
About design sensitivity analysis
Design sensitivity analysis for static stress analysis
Total displacement DSA formulation for nonlinear equilibrium problems
Incremental displacement DSA formulation for history-dependent equilibrium problems
Design sensitivity analysis for frequency analysis
Choosing the finite difference interval
About the Abaqus element library
About the Abaqus solid element library
Hybrid incompressible solid element formulation
Solid isoparametric quadrilaterals and hexahedra
Integration of homogeneous solids
Fully integrated first-order isoparametric elements
Integration of composite solids
Continuum elements with incompatible modes
Geometrically linear formulation
Geometrically nonlinear formulation
Triangular, tetrahedral, and wedge elements
Generalized plane strain elements
Parametric interpolation and integration
Stiffness in the current state
Axisymmetric elements allowing nonlinear bending
Strain and rotation increments
Stiffness in the current state
Pressure loads and load stiffness
Hybrid and pore pressure elements
Lateral face terms due to impedance conditions
Coupling between acoustic and solid infinite elements
Parametric interpolation and integration
Stiffness in the current state
About the Abaqus beam element library
Beam element in undeformed configuration
Change of position, warping, and normal direction
Solution with Newton's algorithm
The rate of change of virtual work
Beams with unconstrained warping
Beams with elastic torsion and constrained warping
Closed, thin walled cross-sections
Internal virtual work rate Jacobian
Mass and inertia for Timoshenko beams
About meshed beam cross-sections
Defining the shear center and warping function for 1-DOF warping elements
Defining the shear center and warping function for 3-DOF warping elements
About the Abaqus shell element library
Shear flexible small-strain shell elements
Triangular facet shell elements
Finite-strain shell element formulation
Membrane deformation and curvature
Second variation of the membrane strain
Second variation of the curvature
In-plane displacement hourglass control
Rotary inertia scaling for explicit dynamics
Rotational bulk viscosity for explicit dynamics
Fully integrated finite-membrane-strain shell formulation
Small-strain shell elements in Abaqus/Explicit
Corotational coordinate system
Axisymmetric shell element allowing asymmetric loading
Orthonormal surface coordinate system and coordinate transformation
Corotational coordinate system
Incremental degrees of freedom: interpolations and configuration updates
Strain increment and stress resultant update
Pressure loads and load stiffness
Penalty constraints: transverse shear and drill rotation
Transverse shear stiffness in composite shells and offsets from the midsurface
Offset: reference surface versus midsurface
Rotary inertia for five degree of freedom shell elements
Rebar modeling in two dimensions
Rebar modeling in three dimensions
Rebar modeling in shell, membrane, and surface elements
Cross-sectional deformation quantities
Some simplifying approximations
Frame elements with lumped plasticity
Degrees of freedom on the element
Large-displacement and large-rotation formulation
Buckling strut response for frame elements
Buckling prediction and the ISO equation
Distributing coupling constraints
Initial stress stiffness terms
Hydrostatic fluid calculations
Hydraulic fluid with thermal expansion
Mechanical Constitutive Theories
About mechanical constitutive models
Integration of plasticity models
Stress potentials for anisotropic metal plasticity
Rate-dependent metal plasticity (creep)
Models for metals subjected to cyclic loading
Linear kinematic hardening model
Nonlinear isotropic/kinematic hardening model
Multilinear kinematic hardening model
Evolution of the plastic strains and f
Integration of the elastoplastic equations
Computing the linearization moduli
ORNL plasticity theory of stainless steel
ORNL creep theory for stainless steel
Heat generation caused by plastic straining
Logarithmic porous elasticity model
Power law–based porous elasticity model
Models for granular or polymer behavior
Hardening, rate dependence, and creep
Hyperbolic and general exponent models
Drucker-Prager/Cap model for geological materials
Crushable foam model with volumetric hardening
Crushable foam model with isotropic hardening
An inelastic constitutive model for concrete
Elastic-plastic model for concrete
Crack detection and damaged elasticity
Damaged plasticity model for concrete and other quasi-brittle materials
About the inviscid concrete damaged plasticity model
Damage and stiffness degradation
A cracking model for concrete and other brittle materials
Elastic-cracking model for concrete
Crack direction transformations
Constitutive model for jointed materials
Elasticity and joint opening/closing
Plastic behavior of joint systems
Plastic behavior of bulk material
Large-strain elasticity and hysteresis
Hyperelastic material behavior
Definitions and basic kinematic results
Rate of change of the internal virtual work
Particular forms of the strain energy potential
Fitting of hyperelastic and hyperfoam constants
Stress-strain relations for the polynomial strain energy potential
Stress-strain relations for the reduced polynomial strain energy potential
Stress-strain relations for the hyperelastic Ogden strain energy potential
Stress-strain relations for the hyperelastic Arruda-Boyce strain energy potential
Stress-strain relations for the hyperelastic Van der Waals energy potential
Stress-strain relations for the hyperfoam strain energy potential
Linear least squares fit for the polynomial model
Linear least squares fit for the reduced polynomial model
Nonlinear least squares fit for the Ogden model
Nonlinear least squares fit for the Arruda-Boyce model
Nonlinear least squares fit for the Van der Waals model
Anisotropic hyperelastic material behavior
Particular forms of the strain energy potential
Mullins effect and permanent set
Automatic time stepping procedure
Integration of the hydrostatic stress
Integration of the deviatoric stress
Cauchy versus Kirchhoff stress
Frequency domain viscoelasticity
Small-sliding interaction between bodies
Identification of tangent plane based on nearest neighbor interaction
Contact formulation as a constrained variational principle
Formulation for two-dimensional small-sliding deformable contact
Formulation for three-dimensional small-sliding deformable contact
Formulation for two-dimensional small-sliding rigid contact
Formulation for three-dimensional small-sliding rigid contact
Finite-sliding interaction between deformable bodies
Two-dimensional and axisymmetric slide line elements
Finite-sliding interaction between a deformable and a rigid body
Softened contact defined with an exponential pressure-overclosure relationship
Softened contact defined with a tabular pressure-overclosure relationship
Softened contact defined with a linear pressure-overclosure relationship
Softened contact implementation
Pressure and fluid flow in pore pressure contact
The pore fluid constraints on the contact interface for infinite interface permeability
The pore fluid constraints on the contact interface for finite interface permeability
Frictional stress due to forced sliding in static analysis
Friction contributions for complex eigenvalue extraction analysis
Viscous stick formulation for steady-state transport
Heat generation caused by frictional sliding
Heat generation caused by electrical current
Surface-based acoustic-structural medium interaction
The equations on the contact interface between the structure and the acoustic medium
Solid/structural main, fluid secondary
Fluid main, solid/structural secondary
Centrifugal, Coriolis, and rotary acceleration forces
Baseline correction of accelerograms
Drag, inertia, and buoyancy loading
Continuously distributed drag and inertia loading
Point drag and inertia loading
Fluid particle velocities and accelerations for Stokes 5th order wave
Incident wave loading and pressure penetration loading
Loading due to an incident dilatational wave field
Underwater explosion—bubble load amplitude
Reflections outside the computational domain
Pressure penetration loading with surface-based contact
Pressure load stiffness on a surface in three-dimensional space
Pressure load stiffness on a surface in two-dimensional space
Load stiffness for beam elements
Pressure loadings on elbow elements
Deformation, strain, and strain rates
Equilibrium, stress, and state storage
Steady-state transport analysis
Coupled thermal-electrical analysis
Hydrostatic fluid calculations
Mullins effect and permanent set
Deformation, strain, and strain rates
Equilibrium, stress, and state storage
Hydrostatic fluid calculations