pymatgen.analysis.elasticity.strain module

This module provides classes and methods used to describe deformations and strains, including applying those deformations to structure objects and generating deformed structure sets for further calculations.

class Deformation(deformation_gradient)

Bases: SquareTensor

Subclass of SquareTensor that describes the deformation gradient tensor

Create a Deformation object. Note that the constructor uses __new__ rather than __init__ according to the standard method of subclassing numpy ndarrays.

Parameters:

deformation_gradient (3x3 array-like) – the 3x3 array-like representing the deformation gradient

apply_to_structure(structure)

Apply the deformation gradient to a structure.

Parameters:

structure (Structure object) – the structure object to be modified by the deformation

classmethod from_index_amount(matrixpos, amt)

Factory method for constructing a Deformation object from a matrix position and amount

Parameters:

• matrixpos (tuple) – tuple corresponding the matrix position to have a perturbation added

• amt (float) – amount to add to the identity matrix at position matrixpos

get_perturbed_indices(tol: float = 1e-08)

Gets indices of perturbed elements of the deformation gradient, i. e. those that differ from the identity

property green_lagrange_strain

Calculates the Euler-Lagrange strain from the deformation gradient

is_independent(tol: float = 1e-08)

Checks to determine whether the deformation is independent

symbol = 'd'

class DeformedStructureSet(structure: Structure, norm_strains=None, shear_strains=None, symmetry=False)

Bases: Sequence

class that generates a set of independently deformed structures that can be used to calculate linear stress-strain response

Construct the deformed geometries of a structure. Generates m + n deformed structures according to the supplied parameters.

Parameters:

• structure (Structure) – structure to undergo deformation

• norm_strains (list of floats) – strain values to apply to each normal mode.

• shear_strains (list of floats) – strain values to apply to each shear mode.

• symmetry (bool) – whether or not to use symmetry reduction.

class Strain(strain_matrix)

Bases: SquareTensor

Subclass of SquareTensor that describes the Green-Lagrange strain tensor.

Create a Strain object. Note that the constructor uses __new__ rather than __init__ according to the standard method of subclassing numpy ndarrays. Note also that the default constructor does not include the deformation gradient

Parameters:

strain_matrix (3x3 array-like) – the 3x3 array-like representing the Green-Lagrange strain

classmethod from_deformation(deformation: ArrayLike) → Strain

Factory method that returns a Strain object from a deformation gradient

Parameters:

deformation (ArrayLike) – 3x3 array defining the deformation

classmethod from_index_amount(idx, amount)

Like Deformation.from_index_amount, except generates a strain from the zero 3x3 tensor or voigt vector with the amount specified in the index location. Ensures symmetric strain.

Parameters:

• idx (tuple or integer) – index to be perturbed, can be Voigt or full-tensor notation

• amount (float) – amount to perturb selected index

get_deformation_matrix(shape: Literal['upper', 'lower', 'symmetric'] = 'upper')

Returns the deformation matrix.

Parameters:

shape ('upper' | 'lower' | 'symmetric') – method for determining deformation ‘upper’ produces an upper triangular defo ‘lower’ produces a lower triangular defo ‘symmetric’ produces a symmetric defo

symbol = 'e'

property von_mises_strain

Equivalent strain to Von Mises Stress

convert_strain_to_deformation(strain, shape: Literal['upper', 'lower', 'symmetric'])

This function converts a strain to a deformation gradient that will produce that strain. Supports three methods:

Parameters:

• strain (3x3 array-like) – strain matrix

• shape – (‘upper’ | ‘lower’ | ‘symmetric’): method for determining deformation ‘upper’ produces an upper triangular defo ‘lower’ produces a lower triangular defo ‘symmetric’ produces a symmetric defo