This page describes the python modules based on the TFEL libraries.

# The tfel.math module

Three classes standing for symmetric tensors are available:

• Stensor1D: symmetric tensor in $$1D$$.
• Stensor2D: symmetric tensor in $$2D$$.
• Stensor3D: symmetric tensor in $$3D$$.

The standard mathematical operations are defined:

• addition of two symmetric tensors.
• substraction of two symmetric tensors.
• multiplication by scalar.
• in-place addition by a symmetric tensor.
• in-place substraction by a symmetric tensor.
• in-place multiplication by scalar.
• in-place division by scalar.

The following functions are available:

• sigmaeq: computes the von Mises norm of a symmetric tensor.
• tresca: computes the Tresca norm of a symmetric tensor.

Three classes standing for linear transformation of symmetric tensors to symmetric tensors:

• ST2toST1D: linear transformation of symmetric tensors to symmetric tensors in $$1D$$.
• ST2toST2D: linear transformation of symmetric tensors to symmetric tensors in $$2D$$.
• ST2toST3D: linear transformation of symmetric tensors to symmetric tensors in $$3D$$.

# The tfel.material module

The following functions are available:

• buildFromPiPlane: returns a tuple containing the three eigenvalues of the stress corresponding to the given point in the $$\pi$$-plane.
• projectOnPiPlane: projects a stress state, defined its three eigenvalues or by a symmetric tensor, on the $$\pi$$-plane.

The computeHosfordStress function, which compute the Hosford equivalent stress, is available.

The following

The following functions are available:

• makeBarlatLinearTransformation1D: builds a $$1D$$ linear transformation of the stress tensor.
• makeBarlatLinearTransformation2D: builds a $$2D$$ linear transformation of the stress tensor.
• makeBarlatLinearTransformation3D: builds a $$3D$$ linear transformation of the stress tensor.
• computeBarlatStress: computes the Barlat equivalent Barlat stress.