Theory Guide

Contents

• Continuum Mechanics
  • General motions
    • Lagrangian and Eulerian descriptions
    • Displacement, velocity, acceleration fields
    • Material, special derivatives
    • Deformation gradient
    • Mixture theory at finite strain
  • Strain and stress
    • Strain
    • Stress
  • Balance laws
    • Elasticity
      • Lagrangian view
      • Eulerian view
    • Linear poroelasticity
    • Poroelasticity at finite strain
• Constitutive Modeling
  • Isochoric-split
  • Material Models
    • Linear elasticity
      • Incompressibility
    • Neo-Hookean
    • Neo-Hookean Isochoric-split
    • Mooney-Rivlin
    • Mooney-Rivlin Isochoric-split
    • Ogden Isochoric-split
    • Poroelasticity
      • Linear
      • Finite strain
    • Holzapfel-Gasser-Ogden (Anisotropic Neo-Hookean)
      • Fiber Distributions
      • Strain Energy Function
      • Stress Tensors
      • Linearization
      • Command-Line Interface
• Governing equations
  • Elasticity
    • Linear
    • Hyperelasticity, initial configuration
      • Newton linearization
    • Hyperelasticity, current configuration
      • Push forward, then linearize
      • Linearize in current configuration
      • Linearize, then push forward
    • Pressure boundary condition
    • Matrix-free implementation
      • Static and Quasistatic
      • Elastodynamics
  • Mixed Elasticity
    • Mixed Linear
    • Mixed Hyperelasticity, initial configuration
      • Newton linearization
    • Mixed Hyperelasticity, current configuration
    • Perturbed Lagrange-multiplier method
    • Matrix-free implementation (mixed fields)
  • Plasticity
    • General Framework
      • Free Energy Potential
      • Yield Function
      • Dissipation Potential
    • Rate-independent Isotropic von Mises Model
      • Stress Update
      • Consistent Tangent
    • Hencky hyperelasticity only
  • Rigid Contact Boundary Conditions
    • Formulation
      • Large-Deformation Frictional Contact
      • Nitsche Method
      • Weak Form
      • Newton Linearization
    • Shapes
      • Platen
  • Friction Models
    • Static Friction Models
      • Coulomb friction
      • Threlfall friction
    • Newton linearization
    • Dynamic Friction Models
  • Phase-Field Modeling of Brittle Fracture
    • Small strain
      • Damage driving force and crack irreversibility
      • Weak form
      • Newton linearization
    • AT1 and AT2 models
      • Viscous regularization
    • Hyperelasticity, initial configuration
    • Hyperelasticity, current configuration
    • Matrix-free implementation
  • Material Point Method
    • Theory
    • Initializing Material Properties
      • Conforming Mesh
      • Material Mesh
      • Voxel Data
  • Poroelasticity
    • Linear
    • Finite strain
      • Newton linearization
    • Matrix-free implementation
    • Poroelastodynamics
      • Linear
      • Finite strain