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In this section we discuss the constitutive laws that are implemented in the MPMApplication and for each of them we list the variables that must be defined in the ParticleMaterials.json file.

Linear Elasticity

The linear elastic constitutive law is identified by the following labels:

  • LinearElasticIsotropicPlaneStrain2DLaw: two-dimensional problem, plane strain formulation;
  • LinearElasticIsotropicPlaneStress2DLaw: two-dimensional problem, plane stress formulation;
  • LinearElasticIsotropic3DLaw: three-dimensional problem.

These are the admissible (string) values that can be assigned to the field "name" of the "constitutive_law" section in the file ParticleMaterials.json. More details about the input file ParticleMaterials.json can be found here.

The variables that must be included in the "Variables" section of the input file ParticleMaterials.json are:

  • DENSITY
  • YOUNG_MODULUS
  • POISSON_RATIO

Hyperelastic NeoHookean

The hyperelastic NeoHookean constitutive law is identified by the following labels:

  • HyperElasticNeoHookeanPlaneStrain2DLaw: two-dimensional problem, plane strain and irreducible formulation;
  • HyperElasticNeoHookeanPlaneStrainUP2DLaw: two-dimensional problem, plane strain and mixed formulation;
  • HyperElasticNeoHookean3DLaw: three-dimensional problem, irreducible formulation;
  • HyperElasticNeoHookeanUP3DLaw: three-dimensional problem, mixed formulation.

These are the admissible (string) values that can be assigned to the field "name" of the "constitutive_law" section in the file ParticleMaterials.json. More details about the input file ParticleMaterials.json can be found here.

The variables that must be included in the "Variables" section of the input file ParticleMaterials.json are:

  • DENSITY
  • YOUNG_MODULUS
  • POISSON_RATIO

Mohr Coulomb

The plastic Mohr Coulomb constitutive law is identified by the following labels:

  • HenckyMCPlasticPlaneStrain2DLaw: two-dimensional problem, plane-strain formulation;
  • HenckyMCPlastic3DLaw: three-dimensional problem.

These are the admissible (string) values that can be assigned to the field "name" of the "constitutive_law" section in the file ParticleMaterials.json. More details about the input file ParticleMaterials.json can be found here.

The variables that must be included in the "Variables" section of the input file ParticleMaterials.json are:

  • DENSITY
  • YOUNG_MODULUS
  • POISSON_RATIO
  • COHESION
  • INTERNAL_FRICTION_ANGLE
  • INTERNAL_DILATANCY_ANGLE

Mohr Coulomb Strain Softening

The Mohr Coulomb with Strain Softening constitutive law is identified by the following labels:

  • HenckyMCStrainSofteningPlasticPlaneStrain2DLaw: two-dimensional problem, plane-strain formulation;
  • HenckyMCStrainSofteningPlastic3DLaw: three-dimensional problem.

These are the admissible (string) values that can be assigned to the field "name" of the "constitutive_law" section in the file ParticleMaterials.json. More details about the input file ParticleMaterials.json can be found here.

The variables that must be included in the "Variables" section of the input file ParticleMaterials.json are:

  • DENSITY
  • YOUNG_MODULUS
  • POISSON_RATIO
  • COHESION: cohesion (peak)
  • COHESION_RESIDUAL: cohesion (residual)
  • INTERNAL_FRICTION_ANGLE: internal friction angle (peak)
  • INTERNAL_FRICTION_ANGLE_RESIDUAL: internal friction angle (residual)
  • INTERNAL_DILATANCY_ANGLE: internal dilatancy angle (peak)
  • INTERNAL_DILATANCY_ANGLE_RESIDUAL: internal dilatancy angle (residual)
  • SHAPE_FUNCTION_BETA: exponential softening beta coefficient

Modified Cam Clay

The modified cam clay constitutive law is identified by the following labels:

  • HenckyBorjaCamClayPlasticPlaneStrain2DLaw: two-dimensional problem, plane-strain formulation;
  • HenckyBorjaCamClayPlastic3DLaw: three-dimensional problem.

These are the admissible (string) values that can be assigned to the field "name" of the "constitutive_law" section in the file ParticleMaterials.json. More details about the input file ParticleMaterials.json can be found here.

The variables that must be included in the "Variables" section of the input file ParticleMaterials.json are:

  • DENSITY
  • PRE_CONSOLIDATION_STRESS: preconsolidation pressure
  • OVER_CONSOLIDATION_RATIO: over Consolidation Ratio (OCR)
  • SWELLING_SLOPE: slope of swelling line
  • NORMAL_COMPRESSION_SLOPE: slope of Normal Consolidation Line (NCL)
  • CRITICAL_STATE_LINE: slope of Critical State Line (CSL)
  • INITIAL_SHEAR_MODULUS: initial Shear Modulus
  • ALPHA_SHEAR: volumetric-deviatoric coupling constant

Newtonian Fluid

The displacement-based Newtonian fluid constitutive law is identified by the following labels:

  • DispNewtonianFluidPlaneStrain2DLaw: two-dimensional problem, plane-strain formulation;
  • DispNewtonianFluid3DLaw: three-dimensional problem.

These are the admissible (string) values that can be assigned to the field "name" of the "constitutive_law" section in the file ParticleMaterials.json. More details about the input file ParticleMaterials.json can be found here.

The variables that must be included in the "Variables" section of the input file ParticleMaterials.json are:

  • DENSITY
  • BULK_MODULUS
  • DYNAMIC_VISCOSITY