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# https://github.com/boschresearch/pylife
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__author__ = "Johannes Mueller"
__maintainer__ = __author__
import numpy as np
[docs]class RambergOsgood:
'''Simple implementation of the Ramberg-Osgood relation
Parameters
----------
E : float
Young's Modulus
K : float
The strength coefficient
n : float
The strain hardening coefficient
Notes
-----
The equation implemented is the one that `Wikipedia
<https://en.wikipedia.org/wiki/Ramberg%E2%80%93Osgood_relationship#Alternative_Formulations>`__
refers to as "Alternative Formulation". The parameters `n` and `k` in this
are formulation are the Hollomon parameters.
'''
def __init__(self, E, K, n):
self._E = E
self._K = K
self._n = n
[docs] def strain(self, stress):
'''Calculate the elastic plastic strain for a given stress
Parameters
----------
stress : array-like float
The stress
Returns
-------
strain : array-like float
The resulting strain
Raises
------
ValueError if stress is negative
'''
stress = np.asarray(stress)
return stress/self._E + self.plastic_strain(stress)
[docs] def plastic_strain(self, stress):
'''Calculate the plastic strain for a given stress
Parameters
----------
stress : array-like float
The stress
Returns
-------
strain : array-like float
The resulting plastic strain
Raises
------
ValueError if stress is negative
'''
self._fail_if_negative(stress)
return np.power(stress/self._K, 1./self._n)
[docs] def delta_strain(self, delta_stress):
'''Calculate the cyclic Masing strain span for a given stress span
Parameters
----------
delta_stress : array-like float
The stress span
Returns
-------
delta_strain : array-like float
The corresponding stress span
Raises
------
ValueError if delta_stress is negative
Notes
-----
A Masing like behavior is assumed for the material as described in
`Kerbgrundkonzept <https://de.wikipedia.org/wiki/Kerbgrundkonzept#Masing-Verhalten_und_Werkstoffged%C3%A4chtnis>`__.
'''
self._fail_if_negative(delta_stress)
return delta_stress/self._E + 2.*np.power(delta_stress/(2.*self._K), 1./self._n)
[docs] def lower_hysteresis(self, stress, max_stress):
'''Calculate the lower (relaxation to compression) hysteresis starting from a given maximum stress
Parameters
----------
stress : array-like float
The stress (must be below the maximum stress)
max_stress : float
The maximum stress of the hysteresis look
Returns
-------
lower_hysteresis : array-like float
The lower hysteresis branch from `max_stress` all the way to `stress`
Raises
------
ValueError if stress > max_stress
'''
stress = np.asarray(stress)
if (stress > max_stress).any():
raise ValueError("Value for 'stress' must not be higher than 'max_stress'.")
return self.strain(max_stress) - self.delta_strain(max_stress-stress)
def _fail_if_negative(self, val):
if (np.asarray(val) < 0).any():
raise ValueError("Stress value in Ramberg-Osgood equation must not be negative.")