Overview
Materials define the physical properties of structural elements. milcapy uses elastic material models characterized by modulus of elasticity, Poisson’s ratio, and specific weight.
add_material()
Adds a material to the structural model.
model.add_material(
name="concrete",
modulus_elasticity=2.1e6,
poisson_ratio=0.2,
specific_weight=2400
)
Parameters
Unique identifier for the material. This name is used when defining sections.
Modulus of elasticity (E) in force per area units (e.g., kN/m², MPa, psi).Must be greater than 0.
Poisson’s ratio (ν) - dimensionless material property.Must be in the range (-1, 0.5). Common values:
- Concrete: 0.15 - 0.20
- Steel: 0.27 - 0.30
- Aluminum: 0.33
Specific weight or mass density.Units depend on your force system:
- Force-based: N/m³, kN/m³, lb/ft³
- Mass-based: kg/m³, slug/ft³
Set to 0 to ignore self-weight. Returns
Returns the created Material object with the following properties:
name: Material nameE: Modulus of elasticityv: Poisson’s ratiog: Specific weightG: Shear modulus (computed as E / (2(1 + ν)))alpha: Coefficient of thermal expansion (default: 1e-6)
Material Properties
Once created, materials have the following computed properties:
Shear Modulus (G)
The shear modulus is automatically calculated from the elastic modulus and Poisson’s ratio:
material = model.add_material("steel", 2.0e5, 0.3)
print(f"Shear modulus: {material.G}") # 76923.08
Examples
Common Structural Materials
from milcapy import SystemModel
model = SystemModel()
# Concrete (SI units: MPa, kg/m³)
model.add_material(
name="C25_concrete",
modulus_elasticity=25000, # MPa
poisson_ratio=0.2,
specific_weight=2400 # kg/m³
)
# Structural Steel (SI units)
model.add_material(
name="A36_steel",
modulus_elasticity=200000, # MPa
poisson_ratio=0.3,
specific_weight=7850 # kg/m³
)
# Aluminum
model.add_material(
name="aluminum_6061",
modulus_elasticity=69000, # MPa
poisson_ratio=0.33,
specific_weight=2700 # kg/m³
)
# Wood
model.add_material(
name="douglas_fir",
modulus_elasticity=13000, # MPa
poisson_ratio=0.35,
specific_weight=500 # kg/m³
)
Material Without Self-Weight
# For analysis where self-weight is negligible or handled separately
model.add_material(
name="idealized_steel",
modulus_elasticity=2.0e5,
poisson_ratio=0.3,
specific_weight=0 # No self-weight
)
US Customary Units
# Steel in ksi and lb/ft³
model.add_material(
name="steel_us",
modulus_elasticity=29000, # ksi
poisson_ratio=0.3,
specific_weight=490 # lb/ft³
)
# Concrete in ksi and lb/ft³
model.add_material(
name="concrete_us",
modulus_elasticity=3600, # ksi
poisson_ratio=0.2,
specific_weight=150 # lb/ft³
)
Unit Consistency
Ensure all units are consistent throughout your model. milcapy does not perform unit conversions.
SI Units Example
# All units in N, m, Pa
model.add_material(
name="concrete",
modulus_elasticity=25e9, # Pa (25 GPa)
poisson_ratio=0.2,
specific_weight=24000 # N/m³
)
Common Unit Systems
| System | Force | Length | Pressure | Density |
|---|
| SI | N | m | Pa (N/m²) | kg/m³ |
| SI (kN) | kN | m | kPa (kN/m²) | kg/m³ |
| SI (MPa) | N | mm | MPa (N/mm²) | kg/mm³ |
| US Customary | lb | ft | psf (lb/ft²) | lb/ft³ |
| US (kip) | kip | in | ksi (kip/in²) | kip/in³ |
Validation
The add_material() function performs the following validations:
Modulus of Elasticity: Must be greater than 0
Poisson’s Ratio: Must be in range (-1, 0.5)
Specific Weight: Must be non-negative (≥ 0)
Unique Name: Material name must not already exist in the model
Error Examples
# These will raise ValueError
# Invalid elastic modulus
model.add_material("bad_mat", -1000, 0.2) # E must be > 0
# Invalid Poisson's ratio
model.add_material("bad_mat", 25000, 0.6) # ν must be < 0.5
# Negative specific weight
model.add_material("bad_mat", 25000, 0.2, -100) # g must be ≥ 0
# Duplicate name
model.add_material("concrete", 25000, 0.2)
model.add_material("concrete", 30000, 0.2) # Name already exists
Material Types
milcapy uses generic elastic materials. The material behavior is linear elastic with the following constitutive relationship:
3D Stress-Strain Relationship
For isotropic materials:
σ = E * ε (uniaxial)
τ = G * γ (shear)
- σ = normal stress
- ε = normal strain
- τ = shear stress
- γ = shear strain
- E = modulus of elasticity
- G = shear modulus = E / (2(1 + ν))
Self-Weight Application
When specific_weight is specified, self-weight can be activated through load patterns:
model.add_material(
name="concrete",
modulus_elasticity=25000,
poisson_ratio=0.2,
specific_weight=2400
)
model.add_rectangular_section("beam", "concrete", 0.3, 0.5)
# Enable self-weight in a load pattern
model.add_load_pattern(
name="Dead Load",
self_weight_multiplier=1.0 # Full self-weight
)
# Or apply partial self-weight
model.add_load_pattern(
name="Construction Load",
self_weight_multiplier=0.5 # 50% of self-weight
)
W = specific_weight × section_area × member_length × self_weight_multiplier
Advanced: Thermal Properties
Material objects include thermal expansion coefficients (currently for future use):
material = model.add_material("steel", 2.0e5, 0.3)
# These are set to default values (1e-6)
print(material.alpha) # Linear thermal expansion coefficient
print(material.beta) # Surface thermal expansion coefficient
print(material.gamma) # Volumetric thermal expansion coefficient
See Also
