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Hyperelastic.py
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244 lines (183 loc) · 8.84 KB
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# -*- coding: utf-8 -*-
"""
Created on Tue Apr 2 22:31:21 2019
@author: marechlu
"""
import numpy as np
class Hyperelastic:
def __init__(self, model, parameters, order, data_type):
self.model = model
self.order = order
self.parameters = parameters
self.param_names = []
self.data_type = data_type
if model == 'Ogden':
initialGuessMu = np.array([0.1]*self.order)
initialGuessAlpha = np.array([0.2]*self.order)
self.initialGuessParam = np.append(initialGuessMu,initialGuessAlpha)
self.nbparam = self.order*2
muVec_names = ["µ1","µ2","µ3"][0:self.order]
alphaVec_names = ["α1","α2","α3"][0:self.order]
self.param_names = np.append(muVec_names,alphaVec_names)
elif model == 'Neo Hookean':
self.initialGuessParam = np.array([0.1])
self.nbparam = 1
self.param_names = ["µ"]
elif model == 'Yeoh':
self.initialGuessParam = np.array([0.1]*self.order)
self.nbparam = self.order
self.param_names = ["C1","C2","C3"][0:self.order]
elif model == 'Mooney Rivlin':
self.initialGuessParam = np.array([0.1]*self.order)
self.nbparam = self.order
self.param_names = ["C10","C01","C20"][0:self.order]
elif model == 'Gent':
self.initialGuessParam = np.array([0.1]*2)
self.nbparam = 2
self.order=2
self.param_names = ["µ","Jm"]
elif model == 'Veronda Westmann':
self.initialGuessParam = np.array([0.1]*2)
self.nbparam = 2
self.order=2
self.param_names = ["C1","C2"]
elif model == 'Humphrey':
self.initialGuessParam = np.array([0.1]*2)
self.nbparam = 2
self.order=2
self.param_names = ["C1","C2"]
else:
print("Error")
def YeohModel(self, cVec, Strain):
"""Yeoh hyperelastic model (incompressible material under uniaxial tension)"""
if self.data_type == 'True':
lambd = np.exp(Strain)
elif self.data_type == 'Engineering':
lambd = 1 + Strain
else:
print("Data type error. Data is neither 'True' or 'Engineering'. ")
I1 = lambd**2 + 2/lambd
Stress = np.zeros((self.order,len(Strain)))
for i in range (0,self.order):
if self.data_type == 'True':
Stress[i,:] = 2*(lambd**2 - 1/lambd)*(i+1)*cVec[i]*((I1-3)**(i)) # true
elif self.data_type == 'Engineering':
Stress[i,:] = 2*(lambd - 1/(lambd**2))*(i+1)*cVec[i]*(I1-3)**(i) # eng
else:
print("Data type error. Data is neither 'True' or 'Engineering'. ")
Stress_sum = np.sum(Stress, axis=0)
return Stress_sum
def NeoHookeanModel(self, mu, Strain):
"""Neo-Hookean hyperelastic model (incompressible material under uniaxial tension)"""
if self.data_type == 'True':
lambd = np.exp(Strain) # lambd i.e lambda
Stress = 2*mu*(lambd**2 - 1/lambd)
elif self.data_type == 'Engineering':
lambd = 1 + Strain
Stress = 2*mu*(lambd - 1/(lambd**2))
else:
print("Data type error. Data is neither 'True' or 'Engineering'. ")
return Stress
def OgdenModel(self, parameters, Strain):
"""Ogden hyperelastic model (incompressible material under uniaxial tension)"""
# parameter is a 1D array : [mu0,mu1,...,mun,alpha0,alpha1,...,alphan]
muVec = parameters.reshape(2, self.order)[0]
alphaVec = parameters.reshape(2, self.order)[1]
if self.data_type == 'True':
lambd = np.exp(Strain) # lambd i.e lambda
elif self.data_type == 'Engineering':
lambd = 1 + Strain
else:
print("Data type error. Data is neither 'True' or 'Engineering'. ")
# broadcasting method to speed up computation
lambd = lambd[np.newaxis, :]
muVec = muVec[:self.order, np.newaxis]
alphaVec = alphaVec[:self.order, np.newaxis]
if self.data_type == 'True':
Stress = np.sum(2*muVec*(lambd**(alphaVec - 1) - lambd**(-((1/2)*alphaVec + 1))), axis=0)
elif self.data_type == 'Engineering':
Stress = np.sum((2*muVec*(lambd**(alphaVec - 1) - lambd**(-((1/2)*alphaVec + 1)))/lambd), axis=0)
return Stress
def MooneyRivlinModel(self, cVec, Strain):
"""Mooney Rivlin hyperelastic model (incompressible material under uniaxial tension)"""
cVec = np.append(cVec, np.zeros(3-self.order) ) #To ensure CXX is zero if unsed
C10 = cVec[0]
C01 = cVec[1]
C20 = cVec[2]
if self.data_type == 'True':
lambd = np.exp(Strain) # lambd i.e lambda
Stress = 2*(lambd**2 - 1/lambd)*(C10 + C01/lambd + 2*C20*(lambd**2 + 2/lambd -3))
elif self.data_type == 'Engineering':
lambd = 1 + Strain
Stress = (2*(lambd**2 - 1/lambd)*(C10 + C01/lambd + 2*C20*(lambd**2 + 2/lambd -3)))/lambd
else:
print("Data type error. Data is neither 'True' or 'Engineering'. ")
return Stress
def GentModel(self, parameters, Strain):
"""Gent hyperelastic model (incompressible material under uniaxial tension)"""
mu = parameters[0]
Jm = parameters[1]
if self.data_type == 'True':
lambd = np.exp(Strain) # lambd i.e lambda
elif self.data_type == 'Engineering':
lambd = 1 + Strain
else:
print("Data type error. Data is neither 'True' or 'Engineering'. ")
I1 = lambd**2 + 2/lambd
if self.data_type == 'True':
Stress = (lambd**2 - 1/lambd)*(mu*Jm / (Jm - I1 + 3))
elif self.data_type == 'Engineering':
Stress = (lambd - 1/lambd**2)*(mu*Jm / (Jm - I1 + 3))
return Stress
def VerondaWestmannModel(self, parameters, Strain):
"""Veronda-Westmann hyperelastic model (incompressible material under uniaxial tension)"""
C1=parameters[0]
C2=parameters[1]
if self.data_type == 'True':
lambd = np.exp(Strain) # lambd i.e lambda
elif self.data_type == 'Engineering':
lambd = 1 + Strain
else:
print("Data type error. Data is neither 'True' or 'Engineering'. ")
I1 = lambd**2 + 2/lambd
if self.data_type == 'True':
Stress = 2*(lambd**2 - 1/lambd) * C1*C2*(np.exp(C2*(I1-3) - 1/(2*lambd)))
elif self.data_type == 'Engineering':
Stress = (2*(lambd**2 - 1/lambd) * C1*C2*(np.exp(C2*(I1-3) - 1/(2*lambd))))/lambd
return Stress
def HumphreyModel(self, parameters, Strain):
"""Humphrey hyperelastic model (incompressible material under uniaxial tension)"""
C1=parameters[0]
C2=parameters[1]
if self.data_type == 'True':
lambd = np.exp(Strain) # lambd i.e lambda
elif self.data_type == 'Engineering':
lambd = 1 + Strain
else:
print("Data type error. Data is neither 'True' or 'Engineering'. ")
I1 = lambd**2 + 2/lambd
if self.data_type == 'True':
Stress = 2*(lambd**2 - 1/lambd) * C1*C2*(np.exp(C2*(I1-3)))
elif self.data_type == 'Engineering':
Stress = 2*(lambd - 1/lambd**2) * C1*C2*(np.exp(C2*(I1-3)))
return Stress
def ConsitutiveModel(self, parameters, Strain):
""" Constitutive Model"""
self.parameters = parameters # update parameters attribute
if self.model == 'Ogden':
Stress = self.OgdenModel(self.parameters, Strain)
elif self.model == 'Neo Hookean':
Stress = self.NeoHookeanModel(self.parameters, Strain)
elif self.model == 'Yeoh':
Stress = self.YeohModel(self.parameters, Strain)
elif self.model == 'Mooney Rivlin':
Stress = self.MooneyRivlinModel(self.parameters, Strain)
elif self.model == 'Gent':
Stress = self.GentModel(self.parameters, Strain)
elif self.model == 'Veronda Westmann':
Stress = self.VerondaWestmannModel(self.parameters, Strain)
elif self.model == 'Humphrey':
Stress = self.HumphreyModel(self.parameters, Strain)
else:
print("Error")
return Stress