How To: Units, Geometry, & Materials

Units

The default Unit System is MKS or MeterKilogramSecond. We allow the following customizations:

• Specify custom unit for geometry through the Scenario unit (default MKS)

• Specify custom unit for loads (default MKS)

• Specify custom unit for materials (default MKS)

Unit System Keywords	Mass	Force	Stress	Length	Temperature	Energy
MeterKilogramSecond	kg	N	Pa	m	K	J
CentimeterGramSecond	g	dyne	dyne/cm²	cm	K	dyne·cm
MillimeterMegagramSecond	Mg	N	MPa	mm	K	mJ
FootPoundSecond	slug	lbf	lbf/ft²	ft	Ra	lbf·ft
InchPoundSecond	lbf s²/in (slinch)	lbf	psi	in	Ra	lbf·in

Geometry

Geometry is specified through a Model object

• MeshModel from surface mesh can be defined in two ways.

  • filename to define mesh from a file (STL, PLY)

    • instance_id a unique name

    mesh_geometry = MeshModel(filename="beam.stl")
    mesh_geometry.instance_id = "beam"
    

  • Constructing mesh face-by-face

    # define an empty mesh
    mesh_geometry = MeshModel()
    mesh_geometry.instance_id = "fixed_boundary"
    
    # add vertices to the mesh and get the vertex id as output
    v0 = mesh_geometry.addVertex([0.0, 0.0, 0.0])
    v1 = mesh_geometry.addVertex([1.0, 0.0, 0.0])
    v2 = mesh_geometry.addVertex([0.0, 1.0, 0.0])
    
    # add faces defined by the vertex id
    mesh_geometry.addFacet(v0, v1, v2)
    

  • Mesh refinement (usually used for finer interpolation of results during visualization). Uses MeshModel.refine with refinement_level as an input which is the largest allowed triangle edge as a ratio of the bounding box diagonal.

    # mesh geometry created above is further refined
    mesh_geometry.refine(refinement_level=0.02)
    

• VDB Model

  • Using a .vdb file

    vdb_geometry= VDBModel("box.vdb")
    

  • In memory using a VDB object

    import pyopenvdb as vdb
    
    # create a vdb double grid object
    cube = vdb.DoubleGrid()
    cube.fill(min=(100, 100, 100), max=(199, 199, 199), value=1.0)
    
    # create an Intact Model from VDB object
    vdb_geometry = pyintact.VDBModel(cube)
    
    # create a tesselation of the vdb to get a MeshModel and its list of vertices for sampling
    mesh = vdb_geometry.tesselate() # mesh is a MeshModel()
    num_vertices = mesh.vertexCount()
    print(num_vertices)
    

Materials

Structural

• IsotropicMaterialDescriptor to create an Isotropic material. (Unit is MeterKilogramSecond)

  • density is the material density

  • youngs_modulus is the elastic modulus

  • poisson_ratio is the Poisson ratio

  steel_structural = IsotropicMaterialDescriptor()
  
  # Set the density to 7845 kg/m^3, modulus to 200 GPa and poison ratio to 0.29
  steel_structural.density = 7845
  steel_structural.youngs_modulus = 200e9
  steel_structural.poisson_ratio = 0.29
  

• OrthotropicMaterialDescriptor to create an Orthotropic material. Orthotropic materials are often used to represent composites and wood, where the material properties along one axis are significantly different from the properties along the other axes. (Unit is MeterKilogramSecond)

  • density is the material density

  • Ex is the elastic modulus in the material’s x-direction

  • Ey is the elastic modulus in the material’s y-direction

  • Ez is the elastic modulus in the material’s z-direction

  • Gxy is the shear modulus in the xy plane

  • Gxz is the shear modulus in the xz plane

  • Gyz is the shear modulus in the yz plane

  • vxy is the poisson ratio in the xy plane

  • vxz is the poisson ratio in the xx plane

  • vyz is the poisson ratio in the yz plane

  • transform is the optional material transform to arbitrarily rotate the axes along which the material properties are defined. Specified as a list of 9 floating point numbers corresponding to a 3x3 matrix. Note the first 3 floating point numbers corresponds to the first row.

  # Create an orthotropic material (Red Pine)
  material = OrthotropicMaterialDescriptor()
  material.density = 460.0             # kg/m³
  material.Ex = 11.2e9                 # Pa
  material.Ey = 492.8e6                # Pa
  material.Ez = 985.6e6                # Pa
  material.Gxy = 907.2e6               # Pa
  material.Gxz = 1.08e9                # Pa
  material.Gyz = 123.2e6               # Pa
  material.vxy = 0.315
  material.vxz = 0.347
  material.vyz = 0.308
  material.transform = [1.0, 0.0, 0.0,
                      0.0, 1.0, 0.0,
                      0.0, 0.0, 1.0] # optional in this case
  

Thermal

• ThermalMaterialDescriptor to create a thermal material. (Default unit is MeterKilogramSecond)

  • density is the material density

  • conductivity is the conductivity of the material

  • specific_heat is the specific heat of the material

  thermal_material = ThermalMaterialDescriptor()
  
  # Set the density, conductivity, and specific heat of the material
  thermal_material.density = 2700.0 # kg/m^3
  thermal_material.conductivity = 170  # W/(m·K)
  thermal_material.specific_heat = 500  # J/(kg·K)
  
  # Optionally set the coefficient of thermal expansion when using
  # the thermal material in a thermo linear elasticity scenario.
  thermal_material.expansion_coefficient = 23.0e-6
  

Component and Assembly

• A Component is created as a MaterialDomain and takes three inputs

  • A Model object (MeshModel or VDBModel specifically)

  • A material name

  • A ScenarioDescriptor object (see Simulation Setup)

  bar1_structural = MaterialDomain(mesh_geometry, "Steel", structural_scenario)
  bar2_structural = MaterialDomain(vdb_geometry, "Steel", structural_scenario)
  

• Assembly is a list of components that are bonded together

  structural_assembly = [bar1_structural, bar2_structural]