4.1.1.9.1.6. pyfem.util.kinematics module

class Kinematics(nDim: int, nStr: int)

Bases: object

Container for kinematic state variables at a material point.

This class stores the kinematic state of a material point in a finite element analysis, including the deformation gradient tensor and various strain measures. The class is typically used within constitutive models to track the deformation and strain history of material points during nonlinear finite element analysis.

F

Deformation gradient tensor of shape (nDim, nDim). Maps reference coordinates to spatial coordinates.

Type:

np.ndarray

E

Green-Lagrange strain tensor of shape (nDim, nDim). Symmetric strain measure based on deformation gradient.

Type:

np.ndarray

strain

Strain vector of shape (nStr,). Contains strain components in voigt notation (2, 3, or 6 components).

Type:

np.ndarray

dgdstrain

Derivative of some scalar with respect to strain, shape (nStr,). Used in constitutive and material models.

Type:

np.ndarray

g

A scalar variable (e.g., equivalent strain, damage parameter).

Type:

float

Parameters:

• nDim (int) – Number of spatial dimensions of the problem. Must be 2 or 3.

• nStr (int) – Number of strain components. Typically 2 (2D), 3 (axisymmetric), or 6 (3D full tensor in Voigt notation).

Examples

Create a 3D kinematics object: >>> kin = Kinematics(nDim=3, nStr=6) >>> kin.F.shape (3, 3) >>> kin.strain.shape (6,)

Create a 2D plane strain kinematics object: >>> kin = Kinematics(nDim=2, nStr=3) >>> kin.F.shape (2, 2)

F: ndarray

Deformation gradient tensor.

E: ndarray

Green-Lagrange strain tensor.

strain: ndarray

Strain vector in Voigt notation.

dgdstrain: ndarray

Derivative of scalar quantity with respect to strain.

g: float

Scalar quantity (e.g., equivalent strain or damage parameter).