materials

gripyth.materials

Material properties and constitutive relations.

This library is agnostic of units. Inputs must be given in units that are consistent with each other. For example: E in N/mm², ν without unit, Gc in N/mm, ell in mm.

CLASS	DESCRIPTION
DissipationFunction	Available dissipation functions.
Material	Physical properties of a material.
PlaneStrain	Strain type.
PlaneStress	Stress type.
StressState	Types of a material stress or strain.

DissipationFunction

Bases: Enum

Available dissipation functions.

Material dataclass

Physical properties of a material.

METHOD	DESCRIPTION
__init__	Returns properties for an isotropic material.

ATTRIBUTE	DESCRIPTION
E	Young's modulus TYPE: float
G	shear modulus TYPE: float
Gc	fracture energy TYPE: float
K	bulk modulus TYPE: float
ell	regularization length TYPE: float
p	exponential power in expression for fatigue degradation TYPE: float
res_stiff	residual stiffness TYPE: float
α_T	fatigue history variable threshold TYPE: float
λ	first Lamé parameter TYPE: float
ν	Poisson's ratio TYPE: float

E instance-attribute

E: float = E

Young's modulus

G instance-attribute

G: float = E / 2 * 1 + ν

shear modulus

Gc instance-attribute

Gc: float = Gc

fracture energy

K instance-attribute

K: float = E / 3 * 1 - 2 * ν

bulk modulus

ell instance-attribute

ell: float = ell

regularization length

p instance-attribute

p: float = p

exponential power in expression for fatigue degradation

res_stiff instance-attribute

res_stiff: float = res_stiff

residual stiffness

α_T instance-attribute

α_T: float = α_T

fatigue history variable threshold

λ instance-attribute

λ: float = E * ν / 1 + ν * 1 - 2 * ν

first Lamé parameter

ν instance-attribute

ν: float = ν

Poisson's ratio

__init__

__init__(
    E: float = 210,
    ν: float = 0.3,
    Gc: float = 0.0027,
    ell: float = 0.1,
    res_stiff: float = 0,
    α_T: float = 10000000000.0,
    p: float = 2.0,
    dissipation: DissipationFunction = DissipationFunction.AT2,
    L_max: float = 1.0,
    tol_AT1_recovery: float = 0.001,
    tol_irrev: float = 0.001,
)

Returns properties for an isotropic material.

For isotropic materials, the moduli are interdependent:

$$\begin{array}{rl}G& =\frac{E}{2(1+\nu )}\\ K& =\frac{E}{3(1-2\nu )}\\ \lambda & =\frac{E\nu }{(1+\nu )(1-2\nu )}\end{array}$$

Conversely, the following relationships also hold:

$$\begin{array}{rl}E& =\frac{G(3\lambda +2G)}{\lambda +G}\\ \nu & =\frac{\lambda }{2(\lambda +G)}\end{array}$$

PlaneStrain

Bases: StressState

Strain type.

METHOD	DESCRIPTION
elasticity_tensor	Constructs the elastic stiffness matrix of a material.

elasticity_tensor staticmethod

elasticity_tensor(E: float, ν: float) -> NDArray[float64]

Constructs the elastic stiffness matrix of a material.

Returns the elastic stiffness 3×3 matrix C based on Young's modulus E and Poisson's ratio ν. ```

PlaneStress

Bases: StressState

Stress type.

METHOD	DESCRIPTION
elasticity_tensor	Constructs the elastic stiffness matrix of a material.

elasticity_tensor staticmethod

elasticity_tensor(E: float, ν: float) -> NDArray[float64]

Constructs the elastic stiffness matrix of a material.

Returns the elastic stiffness 3×3 matrix C based on Young's modulus E and Poisson's ratio ν. ```

StressState

Types of a material stress or strain.

METHOD	DESCRIPTION
elasticity_tensor	Constructs the elastic stiffness matrix of a material.

elasticity_tensor staticmethod

elasticity_tensor(E: float, ν: float) -> NDArray[float64]

Constructs the elastic stiffness matrix of a material.

Returns the elastic stiffness 3×3 matrix C based on Young's modulus E and Poisson's ratio ν. ```