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materials.py
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materials.py
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# -*- coding: utf-8 -*-
"""
Created on Fri Sep 3 09:56:48 2010
@author: dave
"""
import numpy as np
import scipy
import scipy.linalg
# numpy print options:
np.set_printoptions(precision=10, suppress=True)
precision = np.float64
def num(number):
"""
Force the globally defined precision to a given number
A string is a valid input, but it seems to have the same results as just
entering a number.
"""
if precision.__name__ == 'float128':
number = np.float128(number)
elif precision.__name__ == 'float64':
number = np.float64(number)
elif precision.__name__ == 'float32':
number = np.float32(number)
return number
class Materials:
"""Material properties
"""
def __init__(self):
"""Material properties
Class which creates variables with material properties
The material array has the following lay-out
0. thickness
1. E_1
2. E_2
3. G_12
4. nu_12
5. sig_hat_1t
6. sig_hat_1c
7. sig_hat_2t
8. sig_hat_2c
9. tau_hat_12
10. eps_hat_1t
11. eps_hat_1c
12. eps_hat_2t
13. eps_hat_2c
14. gam_hat_12
15. density
16. nu_21
"""
# number of material properties
self.nr_prop = 17
self.fibres()
self.cores()
# data structure, same as table 4.2:
self.struct = ['thickness','E_1','E_2','G_12','nu_12','sig_hat_1t',\
'sig_hat_1c','sig_hat_2t','sig_hat_2c','tau_hat_12','eps_hat_1t',\
'eps_hat_1c','eps_hat_2t','eps_hat_2c','gam_hat_12','rho', 'nu_21']
def cores(self):
"""Materials suited for sandwich cores
"""
self.cores = dict()
name = 'PVC_H45'
self.cores[name] = scipy.zeros((self.nr_prop),dtype=precision)
self.cores[name][15] = num(48) # density
self.cores[name][6] = num(-0.55e6) # compressive strength **
self.cores[name][1] = num(40e6) # compressive modules, E1
self.cores[name][2] = num(40e6) # compressive modules, E2
self.cores[name][5] = num(1.2e6) # tensile strength **
self.cores[name][7] = num(1.1e6) # tensile strength ***
self.cores[name][9] = num(0.5e6) # shear strength ***
self.cores[name][3] = num(18e6) # shear modules, G12
self.cores[name][14] = num(0.1) # shear strain ***
self.cores[name][0] = num(1) # standard thickness, set to 1
self.cores[name][4] = num(0) # poisson ratio
self.cores[name][8] = -self.cores[name][7]
self.cores[name][10] = self.cores[name][5] / self.cores[name][1]
self.cores[name][11] = self.cores[name][6] / self.cores[name][1]
self.cores[name][12] = self.cores[name][7] / self.cores[name][2]
self.cores[name][13] = self.cores[name][8] / self.cores[name][2]
# see page 8.16 of An introduction to Sandwich Structures
# nu_21 = nu_12 * E_2 / E_1
self.cores[name][16] = self.cores[name][4] * self.cores[name][2] / \
self.cores[name][1]
name = 'PVC_H60'
self.cores[name] = scipy.zeros((self.nr_prop),dtype=precision)
self.cores[name][15] = num(60) # density
self.cores[name][6] = num(-0.8e6) # compressive strength **
self.cores[name][1] = num(60e6) # compressive modules, E1
self.cores[name][2] = num(60e6) # compressive modules, E2
self.cores[name][5] = num(1.6e6) # tensile strength **
self.cores[name][7] = num(1.4e6) # tensile strength ***
self.cores[name][9] = num(0.7e6) # shear strength ***
self.cores[name][3] = num(22e6) # shear modules ***, G12
self.cores[name][14] = num(0.13) # shear strain ***
self.cores[name][0] = num(1) # standard thickness, set to 1
self.cores[name][4] = num(0) # poisson ratio
self.cores[name][8] = -self.cores[name][7]
# eps_hat = sig_hat / E
self.cores[name][10] = self.cores[name][5] / self.cores[name][1]
self.cores[name][11] = self.cores[name][6] / self.cores[name][1]
self.cores[name][12] = self.cores[name][7] / self.cores[name][2]
self.cores[name][13] = self.cores[name][8] / self.cores[name][2]
self.cores[name][16] = self.cores[name][4] * self.cores[name][2] / \
self.cores[name][1]
name = 'PVC_H80'
self.cores[name] = scipy.zeros((self.nr_prop),dtype=precision)
self.cores[name][15] = num(80) # density
self.cores[name][6] = num(-1.2e6) # compressive strength **
self.cores[name][1] = num(85e6) # compressive modules, E1
self.cores[name][2] = num(85e6) # compressive modules, E2
self.cores[name][5] = num(2.2e6) # tensile strength **
self.cores[name][7] = num(2.0e6) # tensile strength ***
self.cores[name][9] = num(1.0e6) # shear strength ***
self.cores[name][3] = num(31e6) # shear modules ***, G12
self.cores[name][14] = num(0.20) # shear strain ***
self.cores[name][0] = num(1) # standard thickness, set to 1
self.cores[name][4] = num(0) # poisson ratio
self.cores[name][8] = -self.cores[name][7]
# eps_hat = sig_hat / E
self.cores[name][10] = self.cores[name][5] / self.cores[name][1]
self.cores[name][11] = self.cores[name][6] / self.cores[name][1]
self.cores[name][12] = self.cores[name][7] / self.cores[name][2]
self.cores[name][13] = self.cores[name][8] / self.cores[name][2]
self.cores[name][16] = self.cores[name][4] * self.cores[name][2] / \
self.cores[name][1]
name = 'PVC_H100'
self.cores[name] = scipy.zeros((self.nr_prop),dtype=precision)
self.cores[name][15] = num(100) # density
self.cores[name][6] = num(-1.7e6) # compressive strength **
self.cores[name][1] = num(125e6) # compressive modules, E1
self.cores[name][2] = num(125e6) # compressive modules, E2
self.cores[name][5] = num(3.1e6) # tensile strength **
self.cores[name][7] = num(2.4e6) # tensile strength ***
self.cores[name][9] = num(1.4e6) # shear strength ***
self.cores[name][3] = num(40e6) # shear modules ***, G12
self.cores[name][14] = num(0.24) # shear strain ***
self.cores[name][0] = num(1) # standard thickness, set to 1
self.cores[name][4] = num(0) # poisson ratio
self.cores[name][8] = -self.cores[name][7]
# eps_hat = sig_hat / E
self.cores[name][10] = self.cores[name][5] / self.cores[name][1]
self.cores[name][11] = self.cores[name][6] / self.cores[name][1]
self.cores[name][12] = self.cores[name][7] / self.cores[name][2]
self.cores[name][13] = self.cores[name][8] / self.cores[name][2]
self.cores[name][16] = self.cores[name][4] * self.cores[name][2] / \
self.cores[name][1]
name = 'PVC_H130'
self.cores[name] = scipy.zeros((self.nr_prop),dtype=precision)
self.cores[name][15] = num(130) # density
self.cores[name][6] = num(-2.6e6) # compressive strength **
self.cores[name][1] = num(175e6) # compressive modules, E1
self.cores[name][2] = num(175e6) # compressive modules, E2
self.cores[name][5] = num(4.2e6) # tensile strength **
self.cores[name][7] = num(3.0e6) # tensile strength ***
self.cores[name][9] = num(2.0e6) # shear strength ***
self.cores[name][3] = num(55e6) # shear modules ***, G12
self.cores[name][14] = num(0.29) # shear strain ***
self.cores[name][0] = num(1) # standard thickness, set to 1
self.cores[name][4] = num(0) # poisson ratio
self.cores[name][8] = -self.cores[name][7]
# eps_hat = sig_hat / E
self.cores[name][10] = self.cores[name][5] / self.cores[name][1]
self.cores[name][11] = self.cores[name][6] / self.cores[name][1]
self.cores[name][12] = self.cores[name][7] / self.cores[name][2]
self.cores[name][13] = self.cores[name][8] / self.cores[name][2]
self.cores[name][16] = self.cores[name][4] * self.cores[name][2] / \
self.cores[name][1]
name = 'PVC_H160'
self.cores[name] = scipy.zeros((self.nr_prop),dtype=precision)
self.cores[name][15] = num(160) # density
self.cores[name][6] = num(-3.4e6) # compressive strength **
self.cores[name][1] = num(230e6) # compressive modules, E1
self.cores[name][2] = num(230e6) # compressive modules, E2
self.cores[name][5] = num(5.4e6) # tensile strength **
self.cores[name][7] = num(3.9e6) # tensile strength ***
self.cores[name][9] = num(2.6e6) # shear strength ***
self.cores[name][3] = num(73e6) # shear modules ***, G12
self.cores[name][14] = num(0.30) # shear strain ***
self.cores[name][0] = num(1) # standard thickness, set to 1
self.cores[name][4] = num(0) # poisson ratio
self.cores[name][8] = -self.cores[name][7]
# eps_hat = sig_hat / E
self.cores[name][10] = self.cores[name][5] / self.cores[name][1]
self.cores[name][11] = self.cores[name][6] / self.cores[name][1]
self.cores[name][12] = self.cores[name][7] / self.cores[name][2]
self.cores[name][13] = self.cores[name][8] / self.cores[name][2]
self.cores[name][16] = self.cores[name][4] * self.cores[name][2] / \
self.cores[name][1]
name = 'PVC_H200'
self.cores[name] = scipy.zeros((self.nr_prop),dtype=precision)
self.cores[name][15] = num(200) # density
self.cores[name][6] = num(-4.5e6) # compressive strength **
self.cores[name][1] = num(310e6) # compressive modules, E1
self.cores[name][2] = num(310e6) # compressive modules, E2
self.cores[name][5] = num(7.0e6) # tensile strength **
self.cores[name][7] = num(4.8e6) # tensile strength ***
self.cores[name][9] = num(3.3e6) # shear strength ***
self.cores[name][3] = num(90e6) # shear modules ***, G12
self.cores[name][14] = num(0.30) # shear strain ***
self.cores[name][0] = num(1) # standard thickness, set to 1
self.cores[name][4] = num(0) # poisson ratio
self.cores[name][8] = -self.cores[name][7]
# eps_hat = sig_hat / E
self.cores[name][10] = self.cores[name][5] / self.cores[name][1]
self.cores[name][11] = self.cores[name][6] / self.cores[name][1]
self.cores[name][12] = self.cores[name][7] / self.cores[name][2]
self.cores[name][13] = self.cores[name][8] / self.cores[name][2]
self.cores[name][16] = self.cores[name][4] * self.cores[name][2] / \
self.cores[name][1]
name = 'PVC_H250'
self.cores[name] = scipy.zeros((self.nr_prop),dtype=precision)
self.cores[name][15] = num(250) # density
self.cores[name][6] = num(-5.8e6) # compressive strength **
self.cores[name][1] = num(400e6) # compressive modules, E1
self.cores[name][2] = num(400e6) # compressive modules, E2
self.cores[name][5] = num(8.8e6) # tensile strength **
self.cores[name][7] = num(6.4e6) # tensile strength ***
self.cores[name][9] = num(4.5e6) # shear strength ***
self.cores[name][3] = num(108e6) # shear modules ***, G12
self.cores[name][14] = num(0.30) # shear strain ***
self.cores[name][0] = num(1) # standard thickness, set to 1
self.cores[name][4] = num(0) # poisson ratio
self.cores[name][8] = -self.cores[name][7]
# eps_hat = sig_hat / E
self.cores[name][10] = self.cores[name][5] / self.cores[name][1]
self.cores[name][11] = self.cores[name][6] / self.cores[name][1]
self.cores[name][12] = self.cores[name][7] / self.cores[name][2]
self.cores[name][13] = self.cores[name][8] / self.cores[name][2]
self.cores[name][16] = self.cores[name][4] * self.cores[name][2] / \
self.cores[name][1]
name = 'ZEROS'
self.cores[name] = scipy.ones((self.nr_prop),dtype=precision)
self.cores[name] = self.cores[name]*num(1e-20)
# and set high failure criteria for sigma, tau hats
self.cores[name][5:10] = num(1e10)
# and set high failure criteria for epsilon, gamma hats
self.cores[name][10:15] = num(1)
def fibres(self):
"""based on:
Laminate and Sanwich Structures, Foundations of Fibre composites
table 4.2, page 4.5
"""
self.fibres = dict()
name = 'carbon'
self.fibres[name] = scipy.zeros((self.nr_prop),dtype=precision)
# self.carbon['thickness']
self.fibres[name][0] = num(0.000127)
# self.carbon['E_1']
self.fibres[name][1] = num(147e9)
# self.carbon['E_2']
self.fibres[name][2] = num(9e9)
# self.carbon['G_12']
self.fibres[name][3] = num(3.3e9)
# self.carbon['nu_12']
self.fibres[name][4] = num(0.31)
# self.carbon['sig_hat_1t']
self.fibres[name][5] = num(2260e6)
# self.carbon['sig_hat_1c']
self.fibres[name][6] = num(-1200e6)
# self.carbon['sig_hat_2t']
self.fibres[name][7] = num(50e6)
# self.carbon['sig_hat_2c']
self.fibres[name][8] = num(-190e6)
# self.carbon['tau_hat_12']
self.fibres[name][9] = num(100e6)
# self.carbon['eps_hat_1t']
self.fibres[name][10] = num(0.015)
# self.carbon['eps_hat_1c']
self.fibres[name][11] = num(-0.008)
# self.carbon['eps_hat_2t']
self.fibres[name][12] = num(0.005)
# self.carbon['eps_hat_2c']
self.fibres[name][13] = num(-0.021)
# self.carbon['gam_hat_12']
self.fibres[name][14] = num(0.03)
self.fibres[name][15] = num(1600)
self.fibres[name][16] = self.fibres[name][4] * \
self.fibres[name][2] / self.fibres[name][1]
name = 'carbon_hm'
self.fibres[name] = scipy.zeros((self.nr_prop),dtype=precision)
self.fibres[name][0] = num(0.000127)
self.fibres[name][1] = num(181e9)
self.fibres[name][2] = num(10.3e9)
self.fibres[name][3] = num(7.17e9)
self.fibres[name][4] = num(0.28)
self.fibres[name][5] = num(1500e6)
self.fibres[name][6] = num(-1500e6)
self.fibres[name][7] = num(40e6)
self.fibres[name][8] = num(-246e6)
self.fibres[name][9] = num(68e6)
self.fibres[name][10] = num(0.0083)
self.fibres[name][11] = num(-0.0083)
self.fibres[name][12] = num(0.0039)
self.fibres[name][13] = num(-0.0239)
self.fibres[name][14] = num(0.0095)
self.fibres[name][15] = num(1600)
self.fibres[name][16] = self.fibres[name][4] * \
self.fibres[name][2] / self.fibres[name][1]
name = 'e_glass'
self.fibres[name] = scipy.zeros((self.nr_prop),dtype=precision)
self.fibres[name][0] = num(0.000127)
self.fibres[name][1] = num(40e9)
self.fibres[name][2] = num(9.8e9)
self.fibres[name][3] = num(2.8e9)
self.fibres[name][4] = num(0.3)
self.fibres[name][5] = num(1100e6)
self.fibres[name][6] = num(-600e6)
self.fibres[name][7] = num(20e6)
self.fibres[name][8] = num(-140e6)
self.fibres[name][9] = num(70e6)
self.fibres[name][10] = num(0.028)
self.fibres[name][11] = num(-0.015)
self.fibres[name][12] = num(0.002)
self.fibres[name][13] = num(-0.014)
self.fibres[name][14] = num(0.025)
self.fibres[name][15] = num(1700)
self.fibres[name][16] = self.fibres[name][4] * \
self.fibres[name][2] / self.fibres[name][1]
def display(self, material, prec_format1=' 1.06f', prec_format2=' 1.02e'):
"""Print in human readable format the material properties
INPUT: material, the material array
"""
print ' 0. thickness :', format(float(material[0]), prec_format1)
print ' 1. E_1 :', format(float(material[1]), prec_format2)
print ' 2. E_2 :', format(float(material[2]), prec_format2)
print ' 3. G_12 :', format(float(material[3]), prec_format2)
print ' 4. nu_12 :', format(float(material[4]), prec_format1)
# stressess
print ' 5. sig_hat_1t :', format(float(material[5]), prec_format2)
print ' 6. sig_hat_1c :', format(float(material[6]), prec_format2)
print ' 7. sig_hat_2t :', format(float(material[7]), prec_format2)
print ' 8. sig_hat_2c :', format(float(material[8]), prec_format2)
print ' 9. tau_hat_12 :', format(float(material[9]), prec_format2)
# strains
print '10. eps_hat_1t :', format(float(material[10]), prec_format1)
print '11. eps_hat_1c :', format(float(material[11]), prec_format1)
print '12. eps_hat_2t :', format(float(material[12]), prec_format1)
print '13. eps_hat_2c :', format(float(material[13]), prec_format1)
print '14. gam_hat_12 :', format(float(material[14]), prec_format1)
print '15. rho :', format(float(material[15]), prec_format2)
print '16. nu_21 :', format(float(material[16]), prec_format2)
print ''