Structural Application Constitutive Laws

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(List of constitutive laws in Structural Application)
(List of constitutive laws in Structural Application)
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'''Viscofiber_Hypermatrix:''' Model for composite comprises of a Hyperelastic Matrix (neo-Hookean hyperelasticity) and Viscoelastic Fibers (Generalized Maxwell model considering 5 devices) in 2 dimensions (Membrane Element). Two classes of fibers are considered at the element level.
+
'''Viscofibers_Hypermatrix:''' Composite model comprising a Hyperelastic Matrix (neo-Hookean hyperelasticity) and Viscoelastic Fibers (Generalized Maxwell model considering 5 devices) in 2 dimensions (Membrane Element). Two classes of fibers are considered at the element level.
 
Being known as ''Viscofibers_Hypermatrix2D''. The viscoelastic parameters required are
 
Being known as ''Viscofibers_Hypermatrix2D''. The viscoelastic parameters required are
 
Fiber parameters: K1 and K2  
 
Fiber parameters: K1 and K2  

Revision as of 14:41, 7 June 2011

List of constitutive laws in Structural Application

The constitutive models and constitutive laws are mathematical formulas based on thermodynamic laws aimed at predicting the behavior or response from one or more materials. The computation internal variables and mapping of tensor spaces are typical operations performed on them.


In general, a constitutive law is defined using various parameters that define the evolution of internal variables used in the model. The most common are:

A yield function that lets us know the domain of elastic material. A constitutive model may have one or more combinations of sueprficies fluence, it depends both know the material. An example of the same mohr is Coulomb's surface, which is expressed in six functions as defined inteseccion the yield strength of material.

A function of softening or hardening . Functions that define the post-peak response of the material. They can be linear In general, a constitutive law is defined using various parameters that define the evolution of internal variables used in the model. The most common are:

The parameters to define a yield surface are: a) the yield function b) flow rate: Associate or Associate c) Status: Plane Stress, Plane Strain, Full TrID.

Shown below a Python script which creates the object yield function and softening function.

Fluency_1   = EnergyYieldFunction (myState.Plane_Stress).
Fluency_2   = VonMissesYieldFunction (myState.Plane_Stress, myPotencialPlastic.Associated).
Fluency_3   = DruckerPragerYieldFunction (myState.Plane_Stress).
fluency_4   = ModifiedMorhCoulombYieldFunction (myState.Plane_Strain, myPotencialPlastic.Not_Associated).
fluency_5   = RankineYieldFunction (myState.Plane_Strain).
print fluency_1.
# Function to use Softening.
behavior_1 = ExponentialSoftening ().
behavior_2 = LinearSoftening ().
print behavior_1


Among the most common is Hook's law or theory of elasticity, Theory of plasticity and damage models. Combinations of them can be creating, doing more complex formulation.

Isotropic: Models of elasticity in 2 dimensions (Plane Stress) and three dimensions. Being known as Isotropic2D and Isotropic3D. Only the parameters required are Young's modulus and Poisson ratio.

Simple Damage Model: Models of Damage in 2 dimensions (Plane Stress) and three dimensions. They are known as Isotropic_Damage and Isotropic_Damage_3D. The properties of the materials it need are:

  • Young Modulus,
  • Poisson Ratio,
  • Fracture Energy.
  • Fluency Criteria (The Energy Yield Function),
  • Softening Behavior (Linear or Exponential).


Simple Damage Model: Models of Damage in 2 dimensions (Plane Stress) and three dimensions. They are known as Isotropic_Damage and Isotropic_Damage_3D. The properties of the materials it need are:

  • Young Modulus,
  • Poisson Ratio,
  • Fracture Energy.
  • Fluency Criteria (The Energy Yield Function),
  • Softening Behavior (Linear or Exponential).


Plasticty: Models of plasticity in 2 dimensions (Plane Stress and Plane Strain ) and three dimensions. They are known as Plasticity_2D and Plasticity_3D. The properties of the materials it need are:

  • Young Modulus,
  • Poisson Ratio,
  • Yield Stress.
  • Plastic Modulus.
  • Fluency Criteria (The Energy Yield Function),
  • Softening Behavior (Linear or Exponential).


Hyperelastic: Models of Hyperelasticity (Neo-Hookean quasi-incompressible) in 2 dimensions (Membrane Element) and three dimensions. Being known as Hyperelastic2D and Hyperelastic3D. The parameters required are Shear modulus and Bulk modulus for the 3D case and additional 2 parameters for 2D to consider or not retraction: Retraction Time and Alpha. The properties of the materials it need are:

  • Shear modulus,
  • Bulk modulus,
  • Retraction Time (only for 2D case),
  • Alpha (only for 2D case).


Viscoelastic: Model of Viscoelasticity (Generalized Maxwell model considering 5 devices) in 2 dimensions (Membrane Element). Vicoelasticity combined with neo-Hookean Hyperelasticity. Being known as Viscoelastic2D. The viscoelastic parameters required are Relaxation Time and Beta for each Maxwell device for the 2D case, and additional 4 parameters for the Hyperelastic part: Shear modulus, Bulk modulus, Retraction Time and Alpha (see above: Hyperelastic). Important: the Maxwell parameters are declared in the python script used to run the problem. In short, the list of parameters needed:

  • Relaxation Time (for each Maxwell device),
  • Beta (for each Maxwell device),
  • Shear modulus,
  • Bulk modulus,
  • Retraction Time,
  • Alpha.


Viscofibers: Model of Viscoelasticity (Generalized Maxwell model considering 5 devices) in 2 dimensions (Membrane Element). Vicoelasticity combined with neo-Hookean Hyperelasticity. Being known as Viscoelastic2D. The viscoelastic parameters required are Fiber parameters: K1 and K2 Direction of the fibers at the element level: 6 components (x, y and z directions for each fiber). Relaxation Time and Beta for each Maxwell device for the 2D case, and additional 4 parameters for the Hyperelastic part: Shear modulus, Bulk modulus, Retraction Time and Alpha (see above: Hyperelastic). Important: the Maxwell parameters are declared in the python script used to run the problem. In short, the list of parameters needed:

  • Fiber parameters,
  • Direction of the fibers,
  • Relaxation Time (for each Maxwell device),
  • Beta (for each Maxwell device),
  • Shear modulus,
  • Bulk modulus,
  • Retraction Time,
  • Alpha.


Viscofibers_Hypermatrix: Composite model comprising a Hyperelastic Matrix (neo-Hookean hyperelasticity) and Viscoelastic Fibers (Generalized Maxwell model considering 5 devices) in 2 dimensions (Membrane Element). Two classes of fibers are considered at the element level. Being known as Viscofibers_Hypermatrix2D. The viscoelastic parameters required are Fiber parameters: K1 and K2 Direction of the fibers at the element level: 6 components (x, y and z directions for each fiber). Relaxation Time and Beta for each Maxwell device for the 2D case, and additional 4 parameters for the Hyperelastic part: Shear modulus, Bulk modulus, Retraction Time and Alpha (see above: Hyperelastic). Important: the Maxwell parameters are declared in the python script used to run the problem. In short, the list of parameters needed:

  • Fiber parameters,
  • Direction of the fibers,
  • Relaxation Time (for each Maxwell device),
  • Beta (for each Maxwell device),
  • Shear modulus,
  • Bulk modulus,
  • Retraction Time,
  • Alpha.


Summary

  • Isotropic2D()
  • Isotropic3D()
  • Isotropic_Damage()
  • Isotropic_Damage3D()
  • Plasticity_2D()
  • Plasticity_3D()
  • Hyperelastic2D()
  • Hyperelastic3D()
  • Viscoelastic2D()

List of Constitutive Law

Constitutive Law Properties Properties Variables Element Type
Isotropic2d() Young Modulus YOUNG_MODULUS Total_Lagrangian and Linear Element
Poisson Ratio POISSON_RATIO Total_Lagrangian and Linear Element
Isotropic3d() Young Modulus YOUNG_MODULUS Total_Lagrangian and Linear Element
Poisson Ratio POISSON_RATIO Total_Lagrangian and Linear Element
Isotropic_Damage() Young Modulus YOUNG_MODULUS Total_Lagrangian
Poisson Ratio POISSON_RATIO Total_Lagrangian
Fracture Energy FRACTURE_ENERGY Total_Lagrangian
Traction_Strength FT Total_Lagrangian
Compresion_Strength FC Total_Lagrangian
Fluency Criteria (Only Yield Energy Criterium) N/A Total_Lagrangian
Softening Behavior (Only Exponencial Softening) N/A Total_Lagrangian
Isotropic_Damage3D() Young Modulus YOUNG_MODULUS Total_Lagrangian
Poisson Ratio POISSON_RATIO Total_Lagrangian
Fracture Energy FRACTURE_ENERGY Total_Lagrangian
Traction_Strength FT Total_Lagrangian
Compresion_Strength FC Total_Lagrangian
Fluency Criteria (Only Yield Energy Criterium) N/A Total_Lagrangian
Softening Behavior (Only Exponencial Softening) N/A Total_Lagrangian
Platicity_2d() (Von Misses and Tresca) Young Modulus YOUNG_MODULUS Total_Lagrangian
Poisson Ratio POISSON_RATIO Total_Lagrangian
Yield Stress YIELD_STRESS Total_Lagrangian
Isotropic Hardening Modulus ISOTROPIC_HARDENING_MODULUS Total_Lagrangian
Kinematic Hardening Modulus KINEMATIC_HARDENING_MODULUS Total_Lagrangian
Fluency Criteria (Only Yield Energy Criterium) N/A Total_Lagrangian
Softening Behavior (Only Exponencial Softening) N/A Total_Lagrangian
Platicity_2d() (Morh Coulomb Model) Young Modulus YOUNG_MODULUS Total_Lagrangian
Poisson Ratio POISSON_RATIO Total_Lagrangian
Fracture Energy FRACTURE_ENERGY Total_Lagrangian
Crushing Energy CRUSHING_ENERGY Total_Lagrangian
Friction Internal Angle MAX_FRICTION_INTERNAL_ANGLE Total_Lagrangian
Friction Internal Angle MAX_DILATANCY_ANGLE Total_Lagrangian
Traction_Strength FT Total_Lagrangian
Compresion_Strength FC Total_Lagrangian
Fluency Criteria (Only Yield Energy Criterium) N/A Total_Lagrangian
Softening Behavior (Only Exponencial Softening) N/A Total_Lagrangian
Hyperelastic2d() Shear Modulus MU Membrane Element
Bulk Modulus BULK_MODULUS Membrane Element
Retraction Time RETRACTION_TIME Membrane Element
Alpha ALPHA Membrane Element
Hyperelastic3d() Shear Modulus MU Total_Lagrangian
Bulk Modulus BULK_MODULUS Total_Lagrangian
Viscoelastic2d() Relaxation Time (5 parameters) N/A Membrane Element
Beta (5 parameters) N/A Membrane Element
Shear Modulus MU Membrane Element
Bulk Modulus BULK_MODULUS Membrane Element
Retraction Time RETRACTION_TIME Membrane Element
Alpha ALPHA Membrane Element
Viscofibers2d() Fiber parameters K1 and K2 (2 parameters) N/A Membrane Element
Fiber direction (6 components) N/A Membrane Element
Relaxation Time (5 parameters) N/A Membrane Element
Beta (5 parameters) N/A Membrane Element
Shear Modulus MU Membrane Element
Bulk Modulus BULK_MODULUS Membrane Element
Retraction Time RETRACTION_TIME Membrane Element
Alpha ALPHA Membrane Element
Viscofibers_Hypermatrix2d() Fiber parameters K1 and K2 (2 parameters) N/A Membrane Element
Fiber direction (6 components) N/A Membrane Element
Relaxation Time (5 parameters) N/A Membrane Element
Beta (5 parameters) N/A Membrane Element
Shear Modulus MU Membrane Element
Bulk Modulus BULK_MODULUS Membrane Element
Retraction Time RETRACTION_TIME Membrane Element
Alpha ALPHA Membrane Element

List of flux

Fluency Flux State
Von Misses Asociated Plane Stress, Plane Strain , TriD
Energy Asociated Plane Stress, Plane Strain , TriD
Tresca Asociated Plane Stress, Plane Strain , TriD
Morh-Coulomb Asociated and NonAsociated Plane Stress, Plane Strain , TriD
Rankine Asociated Plane Stress, Plane Strain , TriD
Drucker Prager Asociated Plane Stress, Plane Strain , TriD
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