pymatgen.analysis.elasticity.stress — pymatgen 2020.7.3 documentation

# Source code for pymatgen.analysis.elasticity.stress

    # coding: utf-8
    # Copyright (c) Pymatgen Development Team.
    # Distributed under the terms of the MIT License.

    """
    This module provides the Stress class used to create, manipulate, and
    calculate relevant properties of the stress tensor.
    """

    from pymatgen.core.tensors import SquareTensor
    import math
    import numpy as np
    import warnings

    __author__ = "Joseph Montoya"
    __copyright__ = "Copyright 2012, The Materials Project"
    __credits__ = "Maarten de Jong, Mark Asta, Anubhav Jain"
    __version__ = "1.0"
    __maintainer__ = "Joseph Montoya"
    __email__ = "montoyjh@lbl.gov"
    __status__ = "Production"
    __date__ = "July 24, 2018"

    class Stress(SquareTensor):
        """
        This class extends SquareTensor as a representation of the
        stress
        """
        symbol = "s"

        def __new__(cls, stress_matrix):
            """
            Create a Stress object.  Note that the constructor uses __new__
            rather than __init__ according to the standard method of
            subclassing numpy ndarrays.

            Args:
                stress_matrix (3x3 array-like): the 3x3 array-like
                    representing the stress
            """
            obj = super().__new__(cls, stress_matrix)
            return obj.view(cls)

        @property
        def dev_principal_invariants(self):
            """
            returns the principal invariants of the deviatoric stress tensor,
            which is calculated by finding the coefficients of the characteristic
            polynomial of the stress tensor minus the identity times the mean
            stress
            """
            return self.deviator_stress.principal_invariants*np.array([1, -1, 1])

        @property
        def von_mises(self):
            """
            returns the von mises stress
            """
            if not self.is_symmetric():
                raise ValueError("The stress tensor is not symmetric, Von Mises "
                                 "stress is based on a symmetric stress tensor.")
            return math.sqrt(3*self.dev_principal_invariants[1])

        @property
        def mean_stress(self):
            """
            returns the mean stress
            """
            return 1./3.*self.trace()

        @property
        def deviator_stress(self):
            """
            returns the deviatoric component of the stress
            """
            if not self.is_symmetric:
                raise warnings.warn("The stress tensor is not symmetric, "
                                    "so deviator stress will not be either")
            return self - self.mean_stress*np.eye(3)

        def piola_kirchoff_1(self, def_grad):
            """
            calculates the first Piola-Kirchoff stress

            Args:
                def_grad (3x3 array-like): deformation gradient tensor
            """
            if not self.is_symmetric:
                raise ValueError("The stress tensor is not symmetric, \
                                 PK stress is based on a symmetric stress tensor.")
            def_grad = SquareTensor(def_grad)
            return def_grad.det*np.dot(self, def_grad.inv.trans)

        def piola_kirchoff_2(self, def_grad):
            """
            calculates the second Piola-Kirchoff stress

            Args:
                def_grad (3x3 array-like): rate of deformation tensor
            """

            def_grad = SquareTensor(def_grad)
            if not self.is_symmetric:
                raise ValueError("The stress tensor is not symmetric, \
                                 PK stress is based on a symmetric stress tensor.")
            return def_grad.det*np.dot(np.dot(def_grad.inv, self),
                                       def_grad.inv.trans)