Material Models

Numerous material models are available in NairnMPM. For those working with source code, you can create your own material types.

Define a Material

You create materials using a Material command block. Within that block all material properties are set using property commands. Refer to each material type to learn about its possible properties.

Linear Elastic Small Strain Materials

The materials in this section are all small-strain, linear elastic materials. They account for rotations by using a hypoelastic correction (using an approximate polar decomposition of the incremental deformation and done to second order in 2D and first order in 3D).

Name	ID	Description	Pσ	Pε	AS	3D
Isotropic	1	Linear elastic, isotropic	X	X	X	X
Transverse	2	Linear elastic, transversely isotropic with unique axis in the z direction	X	X	X	X
Orthotropic	4	Linear elastic, orthotopic material	X	X	X	X
Bistable	10	Elastic, isotropic material with two stable states having different properties	X	X	X

The table columns on the right indicate if each material can be used in plane stress (Pσ), plane strain (Pε), axisymmetric (AS), or 3D calculations.

Hyperelastic Materials

The materials in this section are designed to solve finite strain (or large deformation) problems. They are formulated using hyperelasticity methods.

Name	ID	Description	Pσ	Pε	AS	3D
Mooney	8	Elastic, isotropic and Ideal Rubber Elasticity	X	X	X	X
Neohookean	28	Elastic and isotropic material	X	X	X	X
IdealGas	22	Ideal gas as a hyperelastic material		X	X	X
TaitLiquid	27	Newtonian liquid with Tait law for pressure dependence as a hyperelastic material		X	X	X
JWLPlusPlus	22	JWL++ Detonation Material		X	X	X

The table columns on the right indicate if each material can be used in plane stress (Pσ), plane strain (Pε), axisymmetric (AS), with a 3D membrane (3M), or 3D calculations.

Elastic-Plastic Small Strain Materials

The materials in this section are all small-strain, elastic-plastic materials. They account for rotations by using a hypoelastic correction analagous to Jaumann Derivative methods. They handle plasticity by combining one of these materials with any compatible hardening law.

Name	ID	Description	Pσ	Pε	AS	3D
IsoPlasticity	9	Small-strain, isotropic, elastic-plastic material	X	X	X	X
HillPlastic	15	Anisotropic, elastic-plastic material.		X	X	X

The table columns on the right indicate if each material can be used in plane stress (Pσ), plane strain (Pε), axisymmetric (AS), or 3D calculations.

Hyperelastic-Plastic Materials

The materials in this section are formulated within the framework of hyper elasticity formulation. They can handle plasticity by combining them with any compatible hardening law.

Name	ID	Description	Pσ	Pε	AS	3D
HEIsotropic	24	Isotropic, hyperelastic-plastic material		X	X	X
HEMGEOSMaterial	25	Isotropic, hyperelastic-plastic material using a Mie-Grüneisen equation of state.		X	X	X
ClampedNeohookean	29	Isotropic, hyperelastic-plastic material with tensile and compression elongations clamped to critical values.		X	X	X

The table columns on the right indicate if each material can be used in plane stress (Pσ), plane strain (Pε), axisymmetric (AS), or 3D calculations.

Softening Materials

The materials in this section will model material softening to emulate damage and fractures.

Name	ID	Description	Pσ	Pε	AS	3D
IsoSoftening	50	Small-strain isotropic material with damage and softening	X	X	X	X
IsoPlasticSoftening	53	Small-strain isotropic material that combines plasticity with damage and softening	X	X	X	X
TransIsoSoftening	51	Small-strain transversely isotropic material with damage and softening and with unrotated axial direction in the z (or θ is axisymmetric) direction		X	X	X
OrthoSoftening	54	Small-strain orthotropic material with damage and softening		X	X	X
OrthoPlasticSoftening	56	Small-strain orthotropic material with damage, plasticity, and softening		X	X	X
IsoPhaseFieldSoftening	57	Isotropic phase field material for variational fracture mechanics	X	X	X	X
IsoDamageMechanics	58	Isotropic material that damage by isotropic or scalar damage mechanics	X	X	X	X

The table columns on the right indicate if each material can be used in plane stress (Pσ), plane strain (Pε), axisymmetric (AS), or 3D calculations. Softening materials model failure by particle undergoing decohesion. The particle remain in the simulations and will continue to open their implied cracks. Alternativelym failure particles can be removed with the DeleteDamaged Custom Task.

Viscoelastic Materials

The materials in this section are viscoelastic materials.

Name	ID	Description	Pσ	Pε	AS	3D
Viscoelastic	7	Small-strain, linear viscoelastic material with sum of relaxation times	X	X	X	X
TIViscoelastic	5	Small-strain transversely isotropic material for linear viscoelasticity with unrotated axial direction in the z (or θ is axisymmetric) direction	X	X	X	X

The table columns on the right indicate if each material can be used in plane stress (Pσ), plane strain (Pε), axisymmetric (AS), or 3D calculations.

Phase Transition Materials

The materials in this section control phase transitions between two other materials.

Name	ID	Description	Pσ	Pε	AS	3D
PhaseTransition	30	A first order phase transition between two materials		X	X	X

The table columns on the right indicate if each material can be used in plane stress (Pσ), plane strain (Pε), axisymmetric (AS), or 3D calculations.

Membrane Materials

The materials in this section will model membranes using lines of particles in 2D or planes of particles in 3D. Membranes are in development and only available in OSParticulas. They have been useful in some simulations. They are based in deformation within the membrane and likely do not model bending stiffness well. Further development is needed.

Name	ID	Description	2M	3M
MooneyMembrane	40	Membrane material based on a Mooney-Rivlin material	X	X
HEAnisotropic	21	Anisotropic, hyperelastic material	X	X

The table columns on the right indicate if each material can be used for a membrane in 2D calculations (2M) or in 3D calculations (3M).

Rigid Materials

Rigid materials can be used either to apply moving velocity, temperature, or concentration boundary conditions or to interact with non-rigid material by contact mechanics.

Name	ID	Description	Pσ	Pε	AS	3D
RigidBC	11	A rigid material that sets moving boundary conditions on the grid	X	X	X	X
RigidContact	35	A rigid material that that interacts with other materials by contact	X	X	X	X
RigidBlock	36	A rigid material that that interacts with other materials by contact and whose motion is driven by contact forces	X	X	X	X

The table columns on the right indicate if each material can be used in plane stress (Pσ), plane strain (Pε), axisymmetric (AS), or 3D calculations.

Material Class Hierarchy

Materials are C++ classes. The following class hierarchy shows the orginzation of those C++ classes in the NairnMPM source code. A material in green is an abstract class that is never assigned to particles. All others are material classes (by their name or their ID in parentheses). For those creating their own materials, they must be inserted in this hierarchy using a unique name and ID:

• MaterialBase
  • Elastic
    • Isotropic (1)
      • IsoPlasticity (9)
      • Bistable (10)
      • IsoSoftening (50)
        • IsoPlasticSoftening (53)
        • IsoDamageMechanics (58)
      • IsoPhaseFieldSoftening (57)
    • Transverse (2)
      • Orthotropic (4)
        • AnisoPlasticity
          • HillPlastic (15)
      • TransIsoSoftening (51)
        • OrthoSoftening (54)
          • OrthoPlasticSoftening (56)
      • TIViscoelastic (5)
  • HyperElastic
    • Mooney (8)
      • MooneyMembrane (40)
    • HEIsotropic (24)
      • HEMGEOSMaterial (25)
      • IsoED (70)
    • HEAnisotropic (21)
    • IdealGas (22)
    • TaitLiquid (27)
    • Neohookean (28)
      • ClampedNeohookean (29)
      • ReactionPhase (31)
    • JWLPlusPlus (32)
  • Viscoelastic (7)
    • (See TIViscoelastic (5) above)
  • PhaseTransition (30)
  • Rigid (11)
    • RigidContact (35)
    • RigidBlock (36)
  • TractionLaw
    • TriangularTraction (12)
      • ExponentialTraction (34)
        • TrilinearTraction (20)
          • MixedModeTraction (33)
      • CoupledTraction (23)
      • LinearTraction (14)
    • CubicTraction (14)
    • PressureTraction (26)
    • CohesiveMembrane (41)
  • ContactLaw
    • IgnoreContact (60)
      • CoulombFriction (61)
        • AdhesiveFriction (63)
        • LiquidContact (64)
      • LinearInterface (62)
        • NonlinearInterface (65)
          • DebondingInterface (66)

Material Class Ordered List

Here are the above material in numeric order by material ID:

• 1: Isotropic
• 2: Transverse
• 3: (reserved for deprecated transversely isotropic material)
• 4: Orthotropic
• 5: TIViscoelastic
• 6: (reserved for deprecated transversely isotropic viscoelastic material)
• 7: Viscoelastic
• 8: Mooney
• 9: IsoPlasticity
• 10: Bistable
• 11: Rigid
• 12: TriangularTraction (a traction law material)
• 13: LinearTraction (a traction law material)
• 14: CubicTraction (a traction law material)
• 15: HillPlastic
• 20: TrilinearTraction (a traction law material)
• 21: HEAnisotropic
• 22: IdealGas
• 23: CoupledTraction (a traction law material)
• 24: HEIsotropic
• 25: HEMGEOSMaterial
• 26: PressureTraction (a traction law material)
• 27: TaitLiquid
• 28: Neohookean
• 29: ClampedNeohookean
• 30: PhaseTransition
• 31: ReactionPhase
• 32: JWLPlusPlus
• 33: MixedModeTraction
• 34: ExponentialTraction
• 35: RigidContact
• 36: RigidBlock
• 40: MooneyMembrane
• 41: CohesiveMembrane
• 50: IsoSoftening
• 51: TransIsoSoftening
• 52: (reserved for deprecated transversely isotropic softening material)
• 53: IsoPlasticSoftening
• 54: OrthoSoftening
• 55: IsoPlasticInterface
• 56: OrthoPlasticSoftening
• 57: IsoPhaseFieldSoftening
• 58: IsoDamageMechanics
• 60: IgnoreContact (a contact law material)
• 61: CoulombFriction (a contact law material)
• 63: AdhesiveFriction (a contact law material)
• 64: LiquidContact (a contact law material)
• 62: LinearInterface (a contact law material)
• 65: NonlinearInterface (a contact law material)
• 66: DebondingInterface (a contact law material)
• 70: IsoED