#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# ---------------------------------------------------------------------
#
# _____ _ _ _ _____ _____
# | ____|__| | ___| |_ _____(_)___ ___| ___| ____|
# | _| / _` |/ _ \ \ \ /\ / / _ \ / __/ __| |_ | _|
# | |__| (_| | __/ |\ V V / __/ \__ \__ \ _| | |___
# |_____\__,_|\___|_| \_/\_/ \___|_|___/___/_| |_____|
#
#
# Unit of Strength of Materials and Structural Analysis
# University of Innsbruck,
# 2017 - today
#
# Daniel Reitmair daniel.reitmair@uibk.ac.at
#
# This file is part of EdelweissFE.
#
# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License as published by the Free Software Foundation; either
# version 2.1 of the License, or (at your option) any later version.
#
# The full text of the license can be found in the file LICENSE.md at
# the top level directory of EdelweissFE.
# ---------------------------------------------------------------------
import numpy as np
from edelweissfe.materials.base.basehypoelasticmaterial import BaseHypoElasticMaterial
[docs]
class LinearElasticMaterial(BaseHypoElasticMaterial):
"""Linear elastic material for 2D and 3D cases.
Parameters
----------
materialProperties
The numpy array containing the material properties.
Notes
----
**Material Properties**
- E: Elasticity module (Young's modulus).
- v: Poisson's ratio."""
[docs]
def getNumberOfRequiredStateVars(self) -> int:
"""Returns number of needed material state Variables per integration point in the material.
Returns
-------
int
Number of needed material state Vars."""
return 0
def __init__(self, materialProperties: np.ndarray):
self._materialProperties = materialProperties
self._E = materialProperties[0] # set E
self._v = materialProperties[1] # set v
if len(materialProperties) > 2:
self._density = materialProperties[2]
# E and v never change for this instance (ChangeMaterialProperty creates a new one), so the
# elasticity matrices are assembled once.
self._EiPlaneStress = (
self._E / (1 - self._v**2) * np.array([[1, self._v, 0], [self._v, 1, 0], [0, 0, (1 - self._v) / 2]])
)
self._Ei = (
self._E
/ ((1 + self._v) * (1 - 2 * self._v))
* np.array(
[
[(1 - self._v), self._v, self._v, 0, 0, 0],
[self._v, (1 - self._v), self._v, 0, 0, 0],
[self._v, self._v, (1 - self._v), 0, 0, 0],
[0, 0, 0, (1 - 2 * self._v) / 2, 0, 0],
[0, 0, 0, 0, (1 - 2 * self._v) / 2, 0],
[0, 0, 0, 0, 0, (1 - 2 * self._v) / 2],
]
)
)
[docs]
def elasticityMatrixPlaneStress(self) -> np.ndarray:
"""The 2D plane stress material elasticity matrix.
Returns
-------
np.ndarray
The elasticity matrix."""
return self._EiPlaneStress
[docs]
def elasticityMatrix(self) -> np.ndarray:
"""The 3D material elasticity matrix.
Returns
-------
np.ndarray
The elasticity matrix."""
return self._Ei
[docs]
def assignCurrentStateVars(self, currentStateVars: np.ndarray):
"""Assign new current state vars.
Parameters
----------
currentStateVars
Array containing the material state vars."""
[docs]
def computePlaneStress(
self,
stress: np.ndarray,
dStress_dStrain: np.ndarray,
dStrain: np.ndarray,
time: float,
dTime: float,
):
"""Computes the stresses for a 2D material with plane stress.
Parameters
----------
stress
Vector containing the stresses.
dStress_dStrain
Matrix containing dStress/dStrain.
dStrain
Strain vector increment at time step t to t+dTime.
time
Array of step time and total time.
dTime
Current time step size."""
Ei = self._EiPlaneStress
index = [0, 1, 3]
dStress_dStrain[:] = Ei
stress[index] += Ei @ dStrain[index]
dStrain[2] = -self._v / (1 - self._v) * (dStrain[0] + dStrain[1]) # dStrain33 for plane stress
[docs]
def computeStress(
self,
stress: np.ndarray,
dStress_dStrain: np.ndarray,
dStrain: np.ndarray,
time: float,
dTime: float,
):
"""Computes the stresses for a 3D material.
Parameters
----------
stress
Vector containing the stresses.
dStress_dStrain
Matrix containing dStress/dStrain.
dStrain
Strain vector increment at time step t to t+dTime.
time
Array of step time and total time.
dTime
Current time step size."""
Ei = self._Ei
dStress_dStrain[:] = Ei
stress += Ei @ dStrain
[docs]
def getResult(self, result: str) -> float:
"""Get the result, as a persistent view which is continiously
updated by the material.
Parameters
----------
result
The name of the result.
Returns
-------
float
The result.
"""
raise Exception("This result doesn't exist for the current material.")