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FEBio Studio Manual
Chapter 1 Introduction
Section 1.1 Overview of FEBioStudio
Section 1.2 About this document
Section 1.3 FEBio Basics
Section 1.4 Units in FEBio
Chapter 2 Getting Started
Section 2.1 Starting FEBio Studio
Section 2.2 Creating a New Model
Section 2.3 Opening a Model
Section 2.4 Exploring a Model
Subsection 2.4.1 Navigating the Graphics View
Subsection 2.4.2 Selecting objects
Subsection 2.4.3 Transforming an object
Section 2.5 Solving the Model
Section 2.6 Loading the Results
Chapter 3 The FEBioStudio Environment
Section 3.1 The Graphical User Interface
Subsection 3.1.1 Overview
Subsection 3.1.2 Navigating the GUI
Section 3.2 The Menu Bar
Subsection 3.2.1 The File Menu
Subsection 3.2.2 The Edit Menu
Subsection 3.2.3 The Physics Menu
Subsection 3.2.4 The FEBio Menu
Subsection 3.2.5 The Record Menu
Subsection 3.2.6 The Tools Menu
Subsection 3.2.7 The View Menu
Subsection 3.2.8 The Help Menu
Section 3.3 The Main Tool Bar
Section 3.4 The Build Tool Bar
Section 3.5 The Font Toolbar
Section 3.6 The Graphics View
Section 3.7 The Graphics Toolbar
Section 3.8 The Model Viewer
Subsection 3.8.1 The Search Panel
Subsection 3.8.2 The Model Viewer Panels
Subsection 3.8.3 Editing Selections
Section 3.9 The Build Panel
Subsection 3.9.1 The Create Panel
Subsection 3.9.2 The Edit Panel
Subsection 3.9.3 The Mesh Panel
Subsection 3.9.4 The Tools Panel
Subsubsection 3.9.4.1 Area Calculator
Subsubsection 3.9.4.2 Quadric Fit
Section 3.10 The Repository Panel
Subsection 3.10.1 Connecting to the Repository
Subsection 3.10.2 Browsing and Downloading
Subsection 3.10.3 Managinig Your Uploads
Subsection 3.10.4 The Upload Permission Request Dialog
Subsection 3.10.5 The Upload/Modify Wizard
Subsubsection 3.10.5.1 Adding or Editing Project Details
Subsubsection 3.10.5.2 The Add Publication Dialog
Subsubsection 3.10.5.3 Adding or Removing Files
Section 3.11 The Curve Editor
Section 3.12 The Mesh Inspector
Section 3.13 The Measure Tool
Section 3.14 FEBio Studio Options
Subsection 3.14.1 Background Options
Subsection 3.14.2 Camera Options
Subsection 3.14.3 Colormap Options
Subsection 3.14.4 Display Options
Subsection 3.14.5 Lighting Options
Subsection 3.14.6 Palette Options
Subsection 3.14.7 Physics Options
Subsection 3.14.8 Selection Options
Subsection 3.14.9 UI Options
Subsection 3.14.10 Units Options
Subsection 3.14.11 Model Repository Options
Chapter 4 Creating, Loading, and Saving Models
Section 4.1 Starting a new model
Section 4.2 Loading a model
Section 4.3 Saving a model
Chapter 5 Creating and Editing Geometry
Section 5.1 Creating Geometry
Section 5.2 Importing Geometry
Section 5.3 Editing Geometry
Section 5.4 Creating and Editing a Mesh
Subsection 5.4.1 Meshing Primitives
Subsection 5.4.2 Editable Surfaces
Subsection 5.4.3 Editable Meshes
Chapter 6 Materials
Section 6.1 Adding materials
Section 6.2 Setting material parameters
Section 6.3 Assigning materials
Section 6.4 Creating a Solute Table
Section 6.5 Creating a Solid-Bound Molecule Table
Section 6.6 Adding Chemical Reactions
Chapter 7 Boundary Conditions and Loads
Section 7.1 Boundary Conditions
Subsection 7.1.1 Fixed Displacement
Subsection 7.1.2 Fixed Shell Displacement
Subsection 7.1.3 Fixed Shell Rotation
Subsection 7.1.4 Zero Fluid Pressure
Subsection 7.1.5 Zero Temperature
Subsection 7.1.6 Zero Solute Concentration
Subsection 7.1.7 Prescribed Displacement
Subsection 7.1.8 Prescribed Shell Rotation
Subsection 7.1.9 Prescribed Shell Displacement
Subsection 7.1.10 Prescribed Fluid Pressure
Subsection 7.1.11 Prescribed Temperature
Subsection 7.1.12 Prescribed Solute Concentration
Section 7.2 Surface Loads
Subsection 7.2.1 Pressure
Subsection 7.2.2 Traction forces
Section 7.3 Initial Conditions
Subsection 7.3.1 Velocity
Subsection 7.3.2 Shell Velocity
Subsection 7.3.3 Temperature
Subsection 7.3.4 Concentration
Subsection 7.3.5 Initial Fluid Pressure
Section 7.4 Assigning Boundary Conditions
Chapter 8 Contact and Constraints
Section 8.1 Rigid Body Constraints
Section 8.2 Contact
Subsection 8.2.1 Rigid Interfaces
Subsection 8.2.2 Sliding Interfaces
Subsection 8.2.3 Tied Interfaces
Chapter 9 Defining Analysis Steps
Section 9.1 The Initial Step
Section 9.2 Adding an Analysis Step
Subsection 9.2.1 Analysis
Subsection 9.2.2 Time Settings
Subsection 9.2.3 Nonlinear Solver
Subsection 9.2.4 Linear Solver
Chapter 10 Running FEBio from FEBioStudio
Section 10.1 Running FEBio
Subsection 10.1.1 Advanced Settings
Section 10.2 FEBio Launch Configurations
Section 10.3 Using FEBio Plugins
Chapter 11 The Post Environment
Section 11.1 The Post Environment UI
Section 11.2 The Post Menu
Section 11.3 The Post Toolbar
Section 11.4 The Graphics View
Subsection 11.4.1 Elements of the GV
Subsection 11.4.2 Customizing the GV
Subsubsection 11.4.2.1 Selecting and moving widgets
Subsubsection 11.4.2.2 Setting the GV widget's properties
Subsubsection 11.4.2.3 Adding GV Widgets
Subsubsection 11.4.2.4 Deleting GV Widgets
Chapter 12 Saving Graphics
Section 12.1 The Capture Frame
Section 12.2 Taking a snapshot
Section 12.3 Recording an animation
Section 12.4 Camera Control
Subsection 12.4.1 Basic Camera control
Subsection 12.4.2 Element tracking
Subsection 12.4.3 Camera key-framing
Chapter 13 The Post Panel
Section 13.1 The View Tab
Section 13.2 The Material Tab
Section 13.3 The Data Tab
Subsection 13.3.1 Adding data from a text file
Subsection 13.3.2 Adding data via an equation
Subsection 13.3.3 Filtering data
Section 13.4 The State Tab
Section 13.5 The Tools Tab
Chapter 14 Post Processing
Section 14.1 Properties of the Model
Section 14.2 Displacement Map
Section 14.3 Color Map
Section 14.4 Plane Cuts
Section 14.5 Mirror Plane
Section 14.6 Vector Plot
Section 14.7 Isosurface plot
Section 14.8 Slice plot
Section 14.9 Tensor plot
Section 14.10 Streamline Plot
Section 14.11 Particle Flow Plot
Section 14.12 Additional Windows
Subsection 14.12.1 Summary Window
Subsection 14.12.2 Graph Window
Subsection 14.12.3 Graph Tools
Subsection 14.12.4 Selecting mesh items
Subsection 14.12.5 Integration Tool
Chapter 15 Visualizing 3D Image Data
Section 15.1 Loading 3D image data
Section 15.2 Visualizing 3D Image Data
Subsection 15.2.1 Image Slicer
Subsection 15.2.2 Volume Renderer
Subsection 15.2.3 Image Isosurface
Appendix A Mesh Import Formats
Section A.1 FEBio
Section A.2 NIKE3D
Section A.3 HyperMesh ASCII
Section A.4 ABAQUS
Section A.5 LSDYNA keyword
Section A.6 ANSYS
Section A.7 DXF
Section A.8 Hypersurface ASCII
Section A.9 GMsh
Section A.10 BYU format
Section A.11 VTK format
Appendix B Standard Data Fields
FEBio Theory Manual
Chapter 1 FEBio Theory Introduction
Section 1.1 Overview of FEBio (FT)
Section 1.2 About this document (FT)
Chapter 2 Continuum Mechanics
Section 2.1 Vectors and Tensors
Section 2.2 The Directional Derivative
Section 2.3 Deformation, Strain and Stress
Subsection 2.3.1 The deformation gradient tensor
Subsection 2.3.2 Strain
Subsection 2.3.3 Stress
Section 2.4 Hyperelasticity
Subsection 2.4.1 Isotropic Hyperelasticity
Subsection 2.4.2 Isotropic Elasticity in Principal Directions
Subsection 2.4.3 Nearly-Incompressible Hyperelasticity
Subsection 2.4.4 Transversely Isotropic Hyperelasticity
Section 2.5 Biphasic Material
Subsection 2.5.1 Governing Equations
Section 2.6 Biphasic-Solute Material
Subsection 2.6.1 Governing Equations
Subsection 2.6.2 Continuous Variables
Section 2.7 Triphasic and Multiphasic Materials
Subsection 2.7.1 Governing Equations
Section 2.8 Mixture of Solids
Section 2.9 Equilibrium Swelling
Subsection 2.9.1 Perfect Osmometer
Subsection 2.9.2 Cell Growth
Subsection 2.9.3 Donnan Equilibrium Swelling
Section 2.10 Chemical Reactions
Subsection 2.10.1 Solid Matrix and Solid-Bound Molecular Constituents
Subsection 2.10.2 Solutes
Subsection 2.10.3 Mixture with Negligible Solute Volume Fraction
Subsection 2.10.4 Chemical Kinetics
Section 2.11 Fluid Mechanics
Subsection 2.11.1 Mass and Momentum Balance
Subsection 2.11.2 Energy Balance
Section 2.12 Fluid-Structure Interactions
Subsection 2.12.1 FSI Governing Equations
Section 2.13 Hybrid Biphasic Material
Subsection 2.13.1 BFSI Governing Equations
Subsection 2.13.2 BFSI Continuous Variables
Chapter 3 The Nonlinear FE Method
Section 3.1 Weak formulation for Solid Materials
Subsection 3.1.1 Linearization
Subsection 3.1.2 Discretization
Section 3.2 Weak formulation for biphasic materials
Subsection 3.2.1 Linearization
Subsection 3.2.2 Discretization
Section 3.3 Weak Formulation for Biphasic-Solute Materials
Subsection 3.3.1 Linearization of Internal Virtual Work
Subsubsection 3.3.1.1 Linearization along
Subsubsection 3.3.1.2 Linearization along
Subsubsection 3.3.1.3 Linearization along
Subsection 3.3.2 Linearization of External Virtual Work
Subsection 3.3.3 Discretization
Section 3.4 Weak Formulation for Multiphasic Materials
Subsection 3.4.1 Linearization along
Subsection 3.4.2 Linearization along
Subsection 3.4.3 Linearization along
Subsection 3.4.4 Linearization of External Virtual Work
Subsection 3.4.5 Discretization
Subsection 3.4.6 Electric Potential and Partition Coefficient Derivatives
Subsection 3.4.7 Chemical Reactions
Subsubsection 3.4.7.1 Virtual Work and Linearization
Subsubsection 3.4.7.2 Updating Solid-Bound Molecule Concentrations
Section 3.5 Computational Fluid Dynamics
Subsection 3.5.1 Weak Formulation
Subsection 3.5.2 Temporal Discretization and Linearization
Subsection 3.5.3 Spatial Discretization
Subsection 3.5.4 Special Boundary Conditions
Subsubsection 3.5.4.1 Backflow Stabilization
Subsubsection 3.5.4.2 Tangential Flow Stabilization
Subsubsection 3.5.4.3 Flow Resistance
Section 3.6 Weak Formulation for FSI
Subsection 3.6.1 General Formulation
Subsection 3.6.2 Time Integration
Subsection 3.6.3 Discretization
Subsection 3.6.4 Linearization of
Subsection 3.6.5 Linearization of
Subsection 3.6.6 Linearization of
Subsection 3.6.7 Linearization of
Subsection 3.6.8 Linearization of
Subsection 3.6.9 Linearization of
Subsection 3.6.10 Body force term
Subsection 3.6.11 Fluid traction acting on solid interface
Subsection 3.6.12 Special Boundary Conditions
Subsubsection 3.6.12.1 Backflow Stabilization
Subsubsection 3.6.12.2 Tangential Stabilization
Section 3.7 Weak Formulation for BFSI
Subsection 3.7.1 Virtual Work and Weak Form
Subsection 3.7.2 BFSI Linearization
Subsection 3.7.3 BFSI Spatial Discretization
Subsection 3.7.4 BFSI Traction Interface
Section 3.8 Newton-Raphson Method
Subsection 3.8.1 Full Newton Method
Subsection 3.8.2 BFGS Method
Subsection 3.8.3 Line Search Method
Section 3.9 Generalized
Method
Chapter 4 Element Library
Section 4.1 Solid Elements
Subsection 4.1.1 Hexahedral Elements
Subsection 4.1.2 Pentahedral Elements
Subsection 4.1.3 Tetrahedral Elements
Subsection 4.1.4 Quadratic Tetrahedral Elements
Section 4.2 Shell Elements
Subsection 4.2.1 Shell with mid-surface nodal displacements
Subsubsection 4.2.1.1 Elastic Shell
Subsubsection 4.2.1.2 Quadrilateral shells
Subsubsection 4.2.1.3 Triangular shells
Subsection 4.2.2 Shells with front and back face nodal displacements
Subsubsection 4.2.2.1 Elastic Shell
Subsubsection 4.2.2.2 External work of surface forces
Subsubsection 4.2.2.3 Shell on top of solid element
Subsubsection 4.2.2.4 Shell sandwiched between solid elements
Subsubsection 4.2.2.5 Rigid-Shell Interface
Chapter 5 Constitutive Models
Section 5.1 Linear Elasticity
Section 5.2 Compressible Materials
Subsection 5.2.1 Isotropic Elasticity
Subsection 5.2.2 Orthotropic Elasticity
Subsection 5.2.3 Neo-Hookean Hyperelasticity
Subsection 5.2.4 Natural Neo-Hookean
Subsection 5.2.5 Ogden Unconstrained
Subsection 5.2.6 Holmes-Mow
Subsection 5.2.7 Conewise Linear Elasticity
Subsection 5.2.8 Donnan Equilibrium Swelling
Subsection 5.2.9 Perfect Osmometer Equilibrium Osmotic Pressure
Subsection 5.2.10 Large Poisson's Ratio Ligament
Subsection 5.2.11 Porous Neo-Hookean Material
Subsection 5.2.12 Cell Growth
Section 5.3 Nearly-Incompressible Materials
Subsection 5.3.1 Mooney-Rivlin Hyperelasticity
Subsection 5.3.2 Ogden Hyperelastic
Subsection 5.3.3 Veronda-Westmann Hyperelasticity
Subsection 5.3.4 Arruda-Boyce Hyperelasticity
Subsection 5.3.5 Transversely Isotropic Hyperelastic
Subsection 5.3.6 Ellipsoidal Fiber Distribution
Subsection 5.3.7 Fiber with Exponential Power law
Subsection 5.3.8 Fung Orthotropic
Subsection 5.3.9 Tension-Compression Nonlinear Orthotropic
Section 5.4 Viscoelasticity
Section 5.5 Reactive Viscoelasticity
Section 5.6 Reactive Damage Mechanics
Subsection 5.6.1 Bond-Breaking Reaction
Subsection 5.6.2 Free Energy Density and Stress
Subsection 5.6.3 Damage Criterion
Subsection 5.6.4 Reaction Kinetics and Thermodynamics
Subsection 5.6.5 Constitutive Models
Subsubsection 5.6.5.1 Strain Energy Density
Subsubsection 5.6.5.2 Simo Damage Criterion
Subsubsection 5.6.5.3 Specific Strain Energy
Subsubsection 5.6.5.4 Von Mises Stress
Subsubsection 5.6.5.5 Maximum Normal Stress
Subsubsection 5.6.5.6 Maximum Shear Stress
Subsubsection 5.6.5.7 Maximum Normal Lagrange Strain
Subsubsection 5.6.5.8 Octahedral Lagrange Strain
Section 5.7 Hydraulic Permeability
Subsection 5.7.1 Constant Isotropic Permeability
Subsection 5.7.2 Exponential Isotropic Permeability
Subsection 5.7.3 Holmes-Mow
Subsection 5.7.4 Referentially Isotropic Permeability
Subsection 5.7.5 Referentially Orthotropic Permeability
Subsection 5.7.6 Referentially Transversely Isotropic Permeability
Section 5.8 Solute Diffusivity
Subsection 5.8.1 Constant Isotropic Diffusivity
Subsection 5.8.2 Constant Orthotropic Diffusivity
Subsection 5.8.3 Referentially Isotropic Diffusivity
Subsection 5.8.4 Referentially Orthotropic Diffusivity
Section 5.9 Solute Solubility
Subsection 5.9.1 Constant Solubility
Section 5.10 Osmotic Coefficient
Subsection 5.10.1 Constant Osmotic Coefficient
Section 5.11 Active Contraction Model
Section 5.12 Prescribed Active Contraction
Subsection 5.12.1 Uniaxial Active Contraction
Subsection 5.12.2 Transversely Isotropic Active Contraction
Subsection 5.12.3 Isotropic Active Contraction
Section 5.13 Chemical Reaction Production Rate
Subsection 5.13.1 Mass Action Forward
Subsection 5.13.2 Mass Action Reversible
Subsection 5.13.3 Michaelis-Menten
Section 5.14 Specific Reaction Rate
Subsection 5.14.1 Constant Specific Reaction Rate
Subsection 5.14.2 Huiskes Remodeling
Section 5.15 Viscous Fluids
Chapter 6 Dynamics
Section 6.1 Newmark Integration
Section 6.2 Elastodynamics
Subsection 6.2.1 Governing Equations
Subsection 6.2.2 Virtual Work
Subsection 6.2.3 Generalized
Subsection 6.2.4 Linearization
Subsubsection 6.2.4.1 Internal Work
Subsubsection 6.2.4.2 External Work
Subsection 6.2.5 Discretization
Subsection 6.2.6 Energy-Momentum Conservation Scheme
Subsubsection 6.2.6.1 Energy Balance
Section 6.3 Rigid Body Dynamics
Subsection 6.3.1 Rigid Body Rotation
Subsubsection 6.3.1.1 Exponential Map
Subsubsection 6.3.1.2 Cayley Transform
Subsubsection 6.3.1.3 Linearization Along Rotational Increment
Subsection 6.3.2 General Rigid Body Motion
Subsection 6.3.3 Rigid Body Momentum Balance
Subsection 6.3.4 Time Discretization
Subsubsection 6.3.4.1 Newmark Integration for Rigid Body Dynamics
Subsection 6.3.5 Generalized-
Method for Rigid Body Dynamics
Chapter 7 Contact and Coupling
Section 7.1 Sliding Interfaces
Subsection 7.1.1 Contact Kinematics
Subsection 7.1.2 Weak Form of Two Body Contact
Subsection 7.1.3 Linearization of the Contact Integral
Subsection 7.1.4 Discretization of the Contact Integral
Subsection 7.1.5 Discretization of the Contact Stiffness
Subsection 7.1.6 Augmented Lagrangian Method
Subsection 7.1.7 Automatic Penalty Calculation
Subsection 7.1.8 Alternative Formulations
Subsubsection 7.1.8.1 Facet-To-Facet Sliding
Subsubsection 7.1.8.2 Sliding-Tension-Compression
Section 7.2 Biphasic Contact
Subsection 7.2.1 Contact Integral
Subsection 7.2.2 Gap Function
Subsection 7.2.3 Penalty Method
Subsection 7.2.4 Discretization
Section 7.3 Biphasic-Solute Contact
Subsection 7.3.1 Contact Integral
Subsection 7.3.2 Gap Function
Subsection 7.3.3 Penalty Method
Subsection 7.3.4 Discretization
Section 7.4 Multiphasic Contact
Subsection 7.4.1 Contact Integral
Subsection 7.4.2 Gap Function
Subsection 7.4.3 Penalty Method
Subsection 7.4.4 Discretization
Section 7.5 Tied Contact
Subsection 7.5.1 Gap Function
Subsection 7.5.2 Tied Contact Integral
Subsection 7.5.3 Linearization of the Contact Integral
Subsection 7.5.4 Discretization
Section 7.6 Tied Biphasic Contact
Subsection 7.6.1 Contact Integral
Subsection 7.6.2 Gap Function
Subsection 7.6.3 Penalty Method
Subsection 7.6.4 Discretization
Section 7.7 Tied Multiphasic Contact
Subsection 7.7.1 Gap Function
Subsection 7.7.2 Penalty Method
Subsection 7.7.3 Discretization
Section 7.8 Tied Fluid Interface
Subsection 7.8.1 Contact Integral
Subsection 7.8.2 Gap Functions
Subsection 7.8.3 Penalty Method
Subsection 7.8.4 Discretization
Section 7.9 Rigid Connectors
Subsection 7.9.1 Virtual Work
Subsection 7.9.2 Joint Axes
Subsection 7.9.3 Relative Joint Motion
Subsection 7.9.4 Joint Reaction Forces and Moments
Subsubsection 7.9.4.1 Reaction Forces from Springs
Subsubsection 7.9.4.2 Reaction Moments from Torsional Springs
Subsubsection 7.9.4.3 Reaction Forces from Dampers
Subsubsection 7.9.4.4 Reaction Moments from Torsional Dampers
Subsubsection 7.9.4.5 Summary of Reaction Forces and Moment in Joints
Subsection 7.9.5 Prescribed Joint Forces and Moments
Subsubsection 7.9.5.1 Prescribed Force at Joint
Subsubsection 7.9.5.2 Prescribed Moment at Joint
Subsection 7.9.6 Prescribed Joint Motion
Subsubsection 7.9.6.1 Prescribed Displacement at Joint
Subsubsection 7.9.6.2 Prescribed Rotation at Joint
Subsection 7.9.7 Other Rigid Connectors
Subsubsection 7.9.7.1 Spring Between Rigid Bodies
Subsubsection 7.9.7.2 Damper Between Rigid Bodies
Subsubsection 7.9.7.3 Contractile Force Between Rigid Bodies
Section 7.10 Rigid-Deformable Coupling
Chapter 8 Optimization
Section 8.1 The Objective Function
Section 8.2 The Levenberg-Marquardt Method
Bibliography
FEBio User Manual
Chapter 1 Introduction (User Manual)
Section 1.1 Overview of FEBio (UM)
Section 1.2 About this document (UM)
Chapter 2 Running FEBio
Section 2.1 Running FEBio on Windows
Subsection 2.1.1 Windows XP
Subsection 2.1.2 Windows 7
Subsection 2.1.3 Running FEBio from Explorer
Section 2.2 Running FEBio on Linux or MAC
Section 2.3 The Command Line
Section 2.4 The FEBio Prompt
Section 2.5 The Configuration File
Section 2.6 Using Multiple Processors
Section 2.7 FEBio Output
Subsection 2.7.1 Screen output
Subsection 2.7.2 Output files
Section 2.8 Advanced Options
Subsection 2.8.1 Interrupting a Run
Subsection 2.8.2 Debugging a Run
Subsection 2.8.3 Setting break points
Subsection 2.8.4 Restarting a Run
Chapter 3 Free Format Input
Section 3.1 Free Format Overview
Subsection 3.1.1 Format Specification Versions
Subsection 3.1.2
Notes on backward compatibility
Subsection 3.1.3 Multiple Input Files
Subsubsection 3.1.3.1 Include Keyword
Subsubsection 3.1.3.2 The `from' Attribute
Section 3.2 Module Section
Section 3.3 Control Section
Subsection 3.3.1 Control Parameters
Subsection 3.3.2 Time Stepper parameters
Subsection 3.3.3 Common Solver Parameters
Subsection 3.3.4 Solver Parameters for a Structural Mechanics Analysis
Subsection 3.3.5 Solver Parameters for Biphasic Analysis
Subsection 3.3.6 Solver Parameters for Solute and Multiphasic Analyses
Subsection 3.3.7 Solver Parameters for Heat Analysis
Subsection 3.3.8 Solver Parameters for Fluid and Fluid-FSI Analyses
Section 3.4 Globals Section
Subsection 3.4.1 Constants
Subsection 3.4.2 Solutes
Subsection 3.4.3 Solid-Bound Molecules
Section 3.5 Material Section
Section 3.6 Mesh Section
Subsection 3.6.1 Nodes Section
Subsection 3.6.2 Elements Section
Subsubsection 3.6.2.1 Solid Elements
Subsubsection 3.6.2.2 Shell Elements
Subsection 3.6.3 NodeSet Section
Subsection 3.6.4 Edge Section
Subsection 3.6.5 Surface Section
Subsection 3.6.6 ElementSet Section
Subsection 3.6.7 DiscreteSet Section
Subsection 3.6.8 SurfacePair Section
Section 3.7 MeshDomains Section
Subsection 3.7.1 SolidDomain Section
Subsection 3.7.2 ShellDomain Section
Section 3.8 MeshData Section
Subsection 3.8.1 Data Generators
Subsection 3.8.2 ElementData
Subsection 3.8.3 SurfaceData
Subsection 3.8.4 EdgeData
Subsection 3.8.5 NodeData
Section 3.9 Initial Section
Subsection 3.9.1 The Prestrain Initial Condition
Section 3.10 Boundary Section
Subsection 3.10.1 Prescribed Nodal Degrees of Freedom
Subsection 3.10.2 Fixed Nodal Degrees of Freedom
Subsection 3.10.3 Rigid Nodes
Subsection 3.10.4 Linear Constraints
Section 3.11 Rigid Section
Subsection 3.11.1 Rigid Constraints
Subsubsection 3.11.1.1 Fix Rigid Constraint
Subsubsection 3.11.1.2 Prescribe Rigid Constraint
Subsubsection 3.11.1.3 Force Rigid Constraint
Subsubsection 3.11.1.4 Initial Rigid Velocity
Subsubsection 3.11.1.5 Initial Rigid Angular Velocity
Subsection 3.11.2 Rigid Connectors
Subsubsection 3.11.2.1 Rigid Spherical Joint
Subsubsection 3.11.2.2 Rigid Revolute Joint
Subsubsection 3.11.2.3 Rigid Prismatic Joint
Subsubsection 3.11.2.4 Rigid Cylindrical Joint
Subsubsection 3.11.2.5 Rigid Planar Joint
Subsubsection 3.11.2.6 Rigid Lock Joint
Subsubsection 3.11.2.7 Rigid Spring
Subsubsection 3.11.2.8 Rigid Damper
Subsubsection 3.11.2.9 Rigid Angular Damper
Subsubsection 3.11.2.10 Rigid Contractile Force
Section 3.12 Loads Section
Subsection 3.12.1 Nodal Loads
Subsubsection 3.12.1.1 nodal_load
Subsubsection 3.12.1.2 nodal_force
Subsection 3.12.2 Surface Loads
Subsubsection 3.12.2.1 Pressure Load
Subsubsection 3.12.2.2 Traction Load
Subsubsection 3.12.2.3 Mixture Normal Traction
Subsubsection 3.12.2.4 Fluid Flux
Subsubsection 3.12.2.5 Solute Flux
Subsubsection 3.12.2.6 Heat Flux
Subsubsection 3.12.2.7 Convective Heat Flux
Subsubsection 3.12.2.8 Fluid Traction
Subsubsection 3.12.2.9 Fluid Pressure
Subsubsection 3.12.2.10 Fluid Normal Traction
Subsubsection 3.12.2.11 Fluid Backflow Stabilization
Subsubsection 3.12.2.12 Fluid Tangential Stabilization
Subsubsection 3.12.2.13 Fluid Normal Velocity
Subsubsection 3.12.2.14 Fluid Velocity
Subsubsection 3.12.2.15 Fluid Rotational Velocity
Subsubsection 3.12.2.16 Fluid Resistance
Subsubsection 3.12.2.17 Fluid-FSI Traction
Subsubsection 3.12.2.18 Biphasic-FSI Traction
Subsection 3.12.3 Body Loads
Subsubsection 3.12.3.1 Constant Body Force
Subsubsection 3.12.3.2 Non-Constant Body Force
Subsubsection 3.12.3.3 Centrifugal Body Force
Subsubsection 3.12.3.4 Heat Source
Subsubsection 3.12.3.5 Surface Attraction
Section 3.13 Contact Section
Subsection 3.13.1 Sliding Interfaces
Subsection 3.13.2 Biphasic Contact
Subsection 3.13.3 Biphasic-Solute and Multiphasic Contact
Subsection 3.13.4 Rigid Wall Interfaces
Subsection 3.13.5 Tied Interfaces
Subsection 3.13.6 Tied Elastic Interfaces
Subsection 3.13.7 Tied Biphasic Interfaces
Subsection 3.13.8 Tied Multiphasic Interfaces
Subsection 3.13.9 Sticky Interfaces
Section 3.14 Constraints Section
Subsection 3.14.1 Symmetry Plane
Subsection 3.14.2 Normal Fluid Velocity Constraint
Subsection 3.14.3 The Prestrain Update Rules
Subsubsection 3.14.3.1 Using Update rules
Subsubsection 3.14.3.2 prestrain update rule
Subsubsection 3.14.3.3 The in-situ stretch update rule
Section 3.15 Discrete Section
Subsection 3.15.1 Discrete Materials
Subsubsection 3.15.1.1 Linear Spring
Subsubsection 3.15.1.2 Nonlinear spring
Subsubsection 3.15.1.3 Hill
Subsection 3.15.2 Discrete Section
Subsection 3.15.3 Rigid Cable
Section 3.16 Step Section
Section 3.17 LoadData Section
Subsection 3.17.1 The loadcurve controller
Subsection 3.17.2 The math controller
Subsection 3.17.3 The PID controller
Section 3.18 Output Section
Subsection 3.18.1 Logfile
Subsubsection 3.18.1.1 Node_Data Class
Subsubsection 3.18.1.2 Face_Data Class
Subsubsection 3.18.1.3 Element_Data Class
Subsubsection 3.18.1.4 Rigid_Body_Data Class
Subsubsection 3.18.1.5 Rigid_Connector_Data Class
Subsection 3.18.2 Plotfile
Subsubsection 3.18.2.1 Plotfile Variables
Chapter 4 Materials
Section 4.1 Elastic Solids
Subsection 4.1.1 Specifying Fiber Orientation or Material Axes
Subsubsection 4.1.1.1 Transversely Isotropic Materials
Subsubsection 4.1.1.2 Orthotropic Materials
Subsection 4.1.2 Uncoupled Materials
Subsubsection 4.1.2.1 Arruda-Boyce
Subsubsection 4.1.2.2 Ellipsoidal Fiber Distribution Uncoupled
Subsubsection 4.1.2.3 Ellipsoidal Fiber Distribution Mooney-Rivlin
Subsubsection 4.1.2.4 Ellipsoidal Fiber Distribution Veronda-Westmann
Subsubsection 4.1.2.5 Fung Orthotropic
Subsubsection 4.1.2.6 Holzapfel-Gasser-Ogden
Subsubsection 4.1.2.7 Mooney-Rivlin
Subsubsection 4.1.2.8 Muscle Material
Subsubsection 4.1.2.9 Ogden
Subsubsection 4.1.2.10 Tendon Material
Subsubsection 4.1.2.11 Tension-Compression Nonlinear Orthotropic
Subsubsection 4.1.2.12 Transversely Isotropic Mooney-Rivlin
Subsubsection 4.1.2.13 Transversely Isotropic Veronda-Westmann
Subsubsection 4.1.2.14 Uncoupled Solid Mixture
Subsubsection 4.1.2.15 Veronda-Westmann
Subsubsection 4.1.2.16 Mooney-Rivlin Von Mises Distributed Fibers
Subsection 4.1.3 Unconstrained Materials
Subsubsection 4.1.3.1 Carter-Hayes
Subsubsection 4.1.3.2 Cell Growth
Subsubsection 4.1.3.3 Cubic CLE
Subsubsection 4.1.3.4 Donnan Equilibrium Swelling
Subsubsection 4.1.3.5 Ellipsoidal Fiber Distribution
Subsubsection 4.1.3.6 Ellipsoidal Fiber Distribution Neo-Hookean
Subsubsection 4.1.3.7 Ellipsoidal Fiber Distribution with Donnan Equilibrium Swelling
Subsubsection 4.1.3.8 Fung Orthotropic Compressible
Subsubsection 4.1.3.9 Holmes-Mow
Subsubsection 4.1.3.10 Holzapfel-Gasser-Ogden Unconstrained
Subsubsection 4.1.3.11 Isotropic Elastic
Subsubsection 4.1.3.12 Orthotropic Elastic
Subsubsection 4.1.3.13 Orthotropic CLE
Subsubsection 4.1.3.14 Osmotic Pressure from Virial Expansion
Subsubsection 4.1.3.15 Natural Neo-Hookean
Subsubsection 4.1.3.16 Neo-Hookean
Subsubsection 4.1.3.17 Coupled Mooney-Rivlin
Subsubsection 4.1.3.18 Coupled Veronda-Westmann
Subsubsection 4.1.3.19 Ogden Unconstrained
Subsubsection 4.1.3.20 Perfect Osmometer Equilibrium Osmotic Pressure
Subsubsection 4.1.3.21 Porous Neo-Hookean
Subsubsection 4.1.3.22 Solid Mixture
Subsubsection 4.1.3.23 Spherical Fiber Distribution
Subsubsection 4.1.3.24 Spherical Fiber Distribution from Solid-Bound Molecule
Subsubsection 4.1.3.25 Coupled Transversely Isotropic Mooney-Rivlin
Subsubsection 4.1.3.26 Coupled Transversely Isotropic Veronda-Westmann
Subsubsection 4.1.3.27 Large Poisson's Ratio Ligament
Section 4.2 Fibers
Subsection 4.2.1 Unconstrained Fiber Models
Subsubsection 4.2.1.1 Fiber with Exponential-Power Law
Subsubsection 4.2.1.2 Fiber with Neo-Hookean Law
Subsubsection 4.2.1.3 Fiber with Toe-Linear Response
Subsection 4.2.2 Uncoupled Fiber Models
Subsubsection 4.2.2.1 Fiber with Exponential-Power Law, Uncoupled Formulation
Subsubsection 4.2.2.2 Fiber with Neo-Hookean Law Uncoupled
Subsubsection 4.2.2.3 Fiber with Toe-Linear Response, Uncoupled Formulation
Section 4.3 Continuous Fiber Distribution
Subsection 4.3.1 Unconstrained Continuous Fiber Distribution
Subsection 4.3.2 Uncoupled Continuous Fiber Distribution
Subsection 4.3.3 Distribution
Subsubsection 4.3.3.1 Spherical
Subsubsection 4.3.3.2 Ellipsoidal
Subsubsection 4.3.3.3
Subsubsection 4.3.3.4 Circular
Subsubsection 4.3.3.5 Elliptical
Subsubsection 4.3.3.6 von Mises Distribution
Subsection 4.3.4 Scheme
Subsubsection 4.3.4.1 Gauss-Kronrod Trapezoidal Rule
Subsubsection 4.3.4.2 Finite Element Integration Rule
Subsubsection 4.3.4.3 Trapezoidal Rule
Section 4.4 Viscoelastic Solids
Subsection 4.4.1 Uncoupled Viscoelastic Materials
Subsection 4.4.2 Unconstrained Viscoelastic Materials
Section 4.5 Reactive Viscoelastic Solid
Subsection 4.5.1 Relaxation Functions
Subsubsection 4.5.1.1 Exponential
Subsubsection 4.5.1.2 Exponential Distortional
Subsubsection 4.5.1.3 Fung
Subsubsection 4.5.1.4 Park
Subsubsection 4.5.1.5 Park Distortional
Subsubsection 4.5.1.6 Power
Subsubsection 4.5.1.7 Power Distortional
Section 4.6 Reactive Damage Mechanics
Subsection 4.6.1 General Specification of Damage Materials
Subsection 4.6.2 Cumulative Distribution Functions
Subsubsection 4.6.2.1 Simo
Subsubsection 4.6.2.2 Log-Normal
Subsubsection 4.6.2.3 Weibull
Subsubsection 4.6.2.4 Quintic Polynomial
Subsubsection 4.6.2.5 Step
Subsection 4.6.3 Damage Criterion
Subsubsection 4.6.3.1 Simo
Subsubsection 4.6.3.2 Strain Energy Density
Subsubsection 4.6.3.3 Specific Strain Energy
Subsubsection 4.6.3.4 Von Mises Stress
Subsubsection 4.6.3.5 Maximum Shear Stress
Subsubsection 4.6.3.6 Maximum Normal Stress
Subsubsection 4.6.3.7 Maximum Normal Lagrange Strain
Section 4.7 Multigeneration Solids
Subsection 4.7.1 General Specification of Multigeneration Solids
Section 4.8 Biphasic Materials
Subsection 4.8.1 General Specification of Biphasic Materials
Subsection 4.8.2 Permeability Materials
Subsubsection 4.8.2.1 Constant Isotropic Permeability
Subsubsection 4.8.2.2 Exponential Isotropic Permeability
Subsubsection 4.8.2.3 Holmes-Mow
Subsubsection 4.8.2.4 Referentially Isotropic Permeability
Subsubsection 4.8.2.5 Referentially Orthotropic Permeability
Subsubsection 4.8.2.6 Referentially Transversely Isotropic Permeability
Subsection 4.8.3 Fluid Supply Materials
Subsubsection 4.8.3.1 Starling Equation
Section 4.9 Biphasic-Solute Materials
Subsection 4.9.1 Guidelines for Biphasic-Solute Analyses
Subsubsection 4.9.1.1 Prescribed Boundary Conditions
Subsubsection 4.9.1.2 Prescribed Initial Conditions
Subsection 4.9.2 General Specification of Biphasic-Solute Materials
Subsection 4.9.3 Diffusivity Materials
Subsubsection 4.9.3.1 Constant Isotropic Diffusivity
Subsubsection 4.9.3.2 Constant Orthotropic Diffusivity
Subsubsection 4.9.3.3 Referentially Isotropic Diffusivity
Subsubsection 4.9.3.4 Referentially Orthotropic Diffusivity
Subsubsection 4.9.3.5 Albro Isotropic Diffusivity
Subsection 4.9.4 Solubility Materials
Subsubsection 4.9.4.1 Constant Solubility
Subsection 4.9.5 Osmotic Coefficient Materials
Subsubsection 4.9.5.1 Constant Osmotic Coefficient
Section 4.10 Triphasic and Multiphasic Materials
Subsection 4.10.1 Guidelines for Multiphasic Analyses
Subsubsection 4.10.1.1 Initial State of Swelling
Subsubsection 4.10.1.2 Prescribed Boundary Conditions
Subsubsection 4.10.1.3 Prescribed Initial Conditions
Subsubsection 4.10.1.4 Prescribed Effective Solute Flux
Subsubsection 4.10.1.5 Prescribed Electric Current Density
Subsubsection 4.10.1.6 Electrical Grounding
Subsection 4.10.2 General Specification of Multiphasic Materials
Subsection 4.10.3 Solvent Supply Materials
Subsubsection 4.10.3.1 Starling Equation
Section 4.11 Chemical Reactions
Subsection 4.11.1 Guidelines for Chemical Reaction Analyses
Subsection 4.11.2 General Specification for Chemical Reactions
Subsection 4.11.3 Chemical Reaction Materials
Subsubsection 4.11.3.1 Law of Mass Action for Forward Reactions
Subsubsection 4.11.3.2 Law of Mass Action for Reversible Reactions
Subsubsection 4.11.3.3 Michaelis-Menten Reaction
Subsection 4.11.4 Specific Reaction Rate Materials
Subsubsection 4.11.4.1 Constant Reaction Rate
Subsubsection 4.11.4.2 Huiskes Reaction Rate
Section 4.12 Rigid Body
Section 4.13 Active Contraction
Subsection 4.13.1 Contraction in Mixtures of Uncoupled Materials
Subsubsection 4.13.1.1 Uncoupled Prescribed Uniaxial Active Contraction
Subsubsection 4.13.1.2 Uncoupled Prescribed Transversely Isotropic Active Contraction
Subsubsection 4.13.1.3 Uncoupled Prescribed Isotropic Active Contraction
Subsubsection 4.13.1.4 Prescribed Fiber Stress
Subsection 4.13.2 Contraction in Mixtures of Unconstrained Materials
Subsubsection 4.13.2.1 Prescribed Uniaxial Active Contraction
Subsubsection 4.13.2.2 Prescribed Transversely Isotropic Active Contraction
Subsubsection 4.13.2.3 Prescribed Isotropic Active Contraction
Subsubsection 4.13.2.4 Prescribed Fiber Stress
Section 4.14 Viscous Fluids
Subsection 4.14.1 General Specification of Fluid Materials
Subsection 4.14.2 Viscous Fluid Materials
Subsubsection 4.14.2.1 Newtonian Fluid
Subsubsection 4.14.2.2 Carreau Model
Subsubsection 4.14.2.3 Carreau-Yasuda Model
Subsubsection 4.14.2.4 Powell-Eyring Model
Subsubsection 4.14.2.5 Cross Model
Subsection 4.14.3 General Specification of Fluid-FSI Materials
Subsection 4.14.4 General Specification of Biphasic-FSI Materials
Section 4.15 Prestrain material
Subsection 4.15.1 Introduction
Subsection 4.15.2 The Prestrain Material
Subsubsection 4.15.2.1 prestrain gradient
Subsubsection 4.15.2.2 in-situ stretch
Section 4.16 Continuous Damage
Subsection 4.16.1 Damage Fiber Power
Subsection 4.16.2 Damage Fiber Exponential
Chapter 5 Restart Input file
Section 5.1 Introduction
Section 5.2 The Archive Section
Section 5.3 The Control Section
Section 5.4 The LoadData Section
Section 5.5 The Step Section
Section 5.6 Example
Subsection 5.6.1 Example 1
Subsection 5.6.2 Example 2
Chapter 6 Multi-Step Analysis
Section 6.1 The Step Section
Subsection 6.1.1 Boundary Conditions
Subsection 6.1.2 Relative Boundary Conditions
Section 6.2 An Example
Chapter 7 Parameter Optimization
Section 7.1 Optimization Input File
Subsection 7.1.1 Task Section
Subsection 7.1.2 Options Section
Subsection 7.1.3 Parameters Section
Subsection 7.1.4 Objective Section
Subsubsection 7.1.4.1 The data-fit model
Subsubsection 7.1.4.2 The target model
Subsubsection 7.1.4.3 The element-data model
Subsubsection 7.1.4.4 The node-data model
Subsection 7.1.5 Constraints Section
Section 7.2 Running a Parameter Optimization
Section 7.3 An Example Input File
Chapter 8 Troubleshooting
Section 8.1 Before You Run Your Model
Subsection 8.1.1 The Finite Element Mesh
Subsection 8.1.2 Materials
Subsection 8.1.3 Boundary Conditions
Section 8.2 Debugging a Model
Section 8.3 Common Issues
Subsection 8.3.1 Inverted elements
Subsubsection 8.3.1.1 Material instability
Subsubsection 8.3.1.2 Time step too large
Subsubsection 8.3.1.3 Elements too distorted
Subsubsection 8.3.1.4 Shells are too thick
Subsubsection 8.3.1.5 Rigid body modes
Subsection 8.3.2 Failure to converge
Subsubsection 8.3.2.1 No loads applied
Subsubsection 8.3.2.2 Convergence Tolerance Too Tight
Subsubsection 8.3.2.3 Forcing convergence
Subsubsection 8.3.2.4 Problems due to Contact
Section 8.4 Guidelines for Contact Problems
Subsection 8.4.1 The penalty method
Subsection 8.4.2 Augmented Lagrangian Method
Subsection 8.4.3 Initial Separation
Section 8.5 Cautionary Note for Steady-State Biphasic and Multiphasic Analyses
Section 8.6 Guidelines for Multiphasic Analyses
Subsection 8.6.1 Initial State of Swelling
Subsection 8.6.2 Prescribed Boundary Conditions
Subsection 8.6.3 Prescribed Initial Conditions
Subsection 8.6.4 Prescribed Effective Solute Flux
Subsection 8.6.5 Prescribed Electric Current Density
Subsection 8.6.6 Electrical Grounding
Section 8.7 Guidelines for Fluid Analyses
Subsection 8.7.1 Degrees of Freedom and Boundary Conditions
Subsection 8.7.2 Biased Meshes for Boundary Layers
Subsection 8.7.3 Computational Efficiency Broyden's Method
Subsection 8.7.4 Dynamic versus Steady-State Analyses
Subsection 8.7.5 Isothermal Compressible Flow versus Acoustics
Subsection 8.7.6 Fluid-Structure Interactions
Section 8.8 Understanding the Solution
Subsection 8.8.1 Mesh convergence
Subsection 8.8.2 Constraint enforcement
Section 8.9 Guidelines for Using Prestrain
Section 8.10 Limitations of FEBio
Subsection 8.10.1 Geometrical instabilities
Subsection 8.10.2 Material instabilities
Subsection 8.10.3 Remeshing
Subsection 8.10.4 Force-driven Problems
Subsection 8.10.5 Solutions obtained on Multi-processor Machines
Section 8.11 Where to Get More Help
Chapter 9 Configuration File
Section 9.1 Overview
Section 9.2 Configuring Linear Solvers
Subsection 9.2.1 Pardiso
Subsection 9.2.2 Skyline
Subsection 9.2.3 FGMRES
Subsection 9.2.4 CG
Subsection 9.2.5 BoomerAMG
Subsection 9.2.6 Schur
Subsection 9.2.7 Examples
Chapter 10 FEBio Plugins
Section 10.1
Using Plugins
Section 10.2 Error Messages
Appendix A Heterogeneous model parameters
Section A.1 Math parameters
Section A.2 Mapped parameters
Appendix B Referencing Parameters
Appendix C Math Expression
Section C.1 Functions
Section C.2 Constants
Bibliography
FEBio Website
FEBio Theory Manual
Chapter 3 The Nonlinear FE Method
Section 3.6 Weak Formulation for FSI
Subsection 3.6.4 Linearization of
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3.6.4
Linearization of
where
Similarly,
and
The discretized version produces
where
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