Elasticipy.StressStrainTensors module

class Elasticipy.StressStrainTensors.StrainTensor(mat, force_symmetry=False)[source]

Bases: SymmetricSecondOrderTensor

Class for manipulating symmetric strain tensors or arrays of symmetric strain tensors.

Create a symmetric second-order tensor

Parameters:

mat (list or numpy.ndarray) – matrix or array to construct the symmetric tensor. It must be symmetric with respect to the two last indices (mat[…,i,j]=mat[…,j,i]), or composed of slices of upper-diagonal matrices (mat[i,j]=0 for each i>j).
force_symmetry (bool, optional) – If true, the symmetric part of the matrix will be used. It is mainly meant for debugging purpose.

Examples

We can create a symmetric tensor by privoding the full matrix, as long it is symmetric:

>>> from Elasticipy.SecondOrderTensor import SymmetricSecondOrderTensor
>>> a = SymmetricSecondOrderTensor([[11, 12, 13],[12, 22, 23],[13, 23, 33]])
>>> print(a)
Symmetric second-order tensor
[[11. 12. 13.]
 [12. 22. 23.]
 [13. 23. 33.]]

Alternatively, we can pass the upper-diagonal part only:

>>> b = SymmetricSecondOrderTensor([[11, 12, 13],[0, 22, 23],[0, 0, 33]])

and check that a==b:

>>> a==b
True

elastic_energy(stress)[source]

Compute the elastic energy.

Parameters:: stress (StressTensor) – Corresponding stress tensor
Return type:: Volumetric elastic energy

name = 'Strain tensor'[source]: Name to use when printing the tensor

principalStrains()[source]

Values of the principals strains.

If the tensor array is of shape [m,n,…], the results will be of shape [m,n,…,3].

Returns:: Principal strain values
Return type:: np.ndarray

voigt_map = [1, 1, 1, 2, 2, 2][source]: List of factors to use for building a tensor from Voigt vector(s)

volumetricStrain()[source]

Volumetric change (1st invariant of the strain tensor)

Returns:: Volumetric change
Return type:: np.array or float

class Elasticipy.StressStrainTensors.StressTensor(mat, force_symmetry=False)[source]

Bases: SymmetricSecondOrderTensor

Class for manipulating stress tensors or arrays of stress tensors.

Create a symmetric second-order tensor

Parameters:

mat (list or numpy.ndarray) – matrix or array to construct the symmetric tensor. It must be symmetric with respect to the two last indices (mat[…,i,j]=mat[…,j,i]), or composed of slices of upper-diagonal matrices (mat[i,j]=0 for each i>j).
force_symmetry (bool, optional) – If true, the symmetric part of the matrix will be used. It is mainly meant for debugging purpose.

Examples

We can create a symmetric tensor by privoding the full matrix, as long it is symmetric:

>>> from Elasticipy.SecondOrderTensor import SymmetricSecondOrderTensor
>>> a = SymmetricSecondOrderTensor([[11, 12, 13],[12, 22, 23],[13, 23, 33]])
>>> print(a)
Symmetric second-order tensor
[[11. 12. 13.]
 [12. 22. 23.]
 [13. 23. 33.]]

Alternatively, we can pass the upper-diagonal part only:

>>> b = SymmetricSecondOrderTensor([[11, 12, 13],[0, 22, 23],[0, 0, 33]])

and check that a==b:

>>> a==b
True

property J1[source]

First invariant of the deviatoric part of the stress tensor. It is always zeros, as the deviatoric part as null trace.

Returns:: zero(s)
Return type:: float or np.ndarray

property J2[source]

Second invariant of the deviatoric part of the stress tensor.

Returns:: J2 invariant
Return type:: float or np.ndarray

property J3[source]

Third invariant of the deviatoric part of the stress tensor.

Returns:: J3 invariant
Return type:: float or np.ndarray

Tresca()[source]

Tresca(-Guest) equivalent stress.

Returns:: Tresca equivalent stress
Return type:: np.ndarray or float