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Update _models.py
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@ZAARAOUI999
ZAARAOUI999 authored Dec 19, 2023
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99 changes: 51 additions & 48 deletions hypermat/_models/_models.py
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####################### - بــسم الله الرحمــان الرحيــم - #####################

"""
HyperMAT
Created August 2023
Expand All @@ -18,11 +21,12 @@
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
"""

####################### - بــسم الله الرحمــان الرحيــم - #####################

from numpy import (ndarray as NDA, array as T, sqrt as SQRT, log as LN,
exp as EXP)
from .._ad import Variable as SN
from numpy import (sqrt as SQRT, log as LN, exp as EXP)

from .._ad._deformation import Deformation as DG


###############################################################################
##################### - HYPERELASTIC MATERIAL MODELS - ########################
###############################################################################
Expand All @@ -38,69 +42,68 @@

######################### - SERIES FUNCTION MODELS - ##########################

def mooney_rivlin(_F: SN, **_params) -> SN:
_, _J1, _J2, _J3 = _F.invariants
def mooney_rivlin(_F: DG, **_params) -> DG:
_, _J1, _J2, _ = _F.invariants
_C10, _C01 = list(_params.values())
_W = _C10 * (_J1 - 3.0) + _C01 * (_J2 - 3.0)
return _W

def neo_hooke(_F: SN, **_params) -> SN:
_, _J1, _J2, _J3 = _F.invariants
def neo_hooke(_F: DG, **_params) -> DG:
_, _J1, _J2, _ = _F.invariants
_C10 = list(_params.values())[0]
_W = _C10 * (_J1 - 3.0)
return _W

def isihara(_F: SN, **_params) -> SN:
def isihara(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_C10, _C20, _C01 = list(_params.values())
_W = _C10 * (_J1 - 3.0) + _C20 * (_J1 - 3.0)**2.0 * _C01 * (_J2 - 3.0) \

_W = _C10 * (_J1 - 3.0) + _C20 * (_J1 - 3.0)**2.0 * _C01 * (_J2 - 3.0)
return _W

def biderman(_F: SN, **_params) -> SN:
def biderman(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_C10, _C20, _C30, _C01 = list(_params.values())
_W = _C10 * (_J1 - 3.0) + _C01 * (_J2 - 3.0) + _C20 * (_J1 - 3.0)**2.0 +\
_C30 * (_J1 - 3.0)**3.0
return _W

def james_green_simpson(_F: SN, **_params) -> SN:
def james_green_simpson(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_C10, _C20, _C30, _C01, _C11 = list(_params.values())
_W = _C10 * (_J1 - 3.0) + _C01 * (_J2 - 3.0) + _C11 * (_J1 - 3.0) \
* (_J2 - 3.0) + _C20 * (_J1 - 3.0)**2.0 + _C30 * (_J1 - 3.0)**3.0
return _W

def haines_wilson(_F: SN, **_params) -> SN:
def haines_wilson(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_C10, _C20, _C30, _C01, _C02, _C11 = list(_params.values())
_W = _C10 * (_J1 - 3.0) + _C01 * (_J2 - 3.0) + _C11 * (_J1 - 3.0) \
* (_J2 - 3.0) + _C20 * (_J1 - 3.0)**2.0 + _C30 * (_J1 - 3.0)**3.0 +\
+ _C02 * (_J2 - 3.0)**2.0
return _W

def yeoh(_F: SN, **_params) -> SN:
def yeoh(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_C = list(_params.values())[:-1]
_W = 0.0
for _i, _c in enumerate(_C):
_W += _c * (_J1 - 3.0)**(_i+1)
return _W

def lion(_F: SN, **_params) -> SN:
def lion(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_C10, _C01, _C50 = list(_params.values())
_W = _C10 * (_J1 - 3.0) + _C01 * (_J2 - 3.0)**2.0 * _C50 * (_J1 - 3.0)**5.0
return _W

def haupt_sedlan(_F: SN, **_params) -> SN:
def haupt_sedlan(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_C10, _C30, _C01, _C02, _C11 = list(_params.values())
_W = _C10 * (_J1 - 3.0) + _C01 * (_J2 - 3.0) + _C11 * (_J1 - 3.0) \
* (_J2 - 3.0) + _C30 * (_J1 - 3.0)**3.0 + _C02 * (_J2 - 3.0)**2.0
return _W

def hartmann_neff(_F: SN, **_params) -> SN:
def hartmann_neff(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_alpha = list(_params.values())[0]
_Ci0 = list(_params.values())[1:-1:2]
Expand All @@ -110,26 +113,26 @@ def hartmann_neff(_F: SN, **_params) -> SN:
_W += _Ci0[_i] * (_J1 - 3.0)**(_i+1) + _C0j[_i] * (_J2**1.5 - 3.0**1.5)**(_i+1)
return _W

def carroll(_F: SN, **_params) -> SN:
def carroll(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_A, _B, _C = list(_params.values())
_W = _A * _J1 + _B * _J1**4.0 + _C * _J2**0.5
return _W

def nunes(_F: SN, **_params) -> SN:
def nunes(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_C1, _C2 = list(_params.values())
_W = _C1 * (_J1 - 3.0) + (4.0 / 3.0) * _C2 * (_J2 - 3.0)**(3.0 / 4.0)
return _W

def bahreman_darijani(_F: SN, **_params) -> SN:
def bahreman_darijani(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_A2, _B2, _A4, _A6 = list(_params.values())
_W = _A2 * (_J1 - 3.0) + _B2 * (_J2 - 3.0) + _A4 * (_J1**2.0 - 2.0 * _J2 - 3.0) +\
_A6 * (_J1**3.0 - 3.0 * _J1 * _J2)
return _W

def zhao(_F: SN, **_params) -> SN:
def zhao(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_C1, _C2, _C3, _C4 = list(_params.values())
_W = _C1 * (_J1 - 3.0) + _C2 * (_J2 - 3.0) + _C3 * (_J1**2.0 - 2.0 * _J2 - 3.0) +\
Expand All @@ -138,95 +141,95 @@ def zhao(_F: SN, **_params) -> SN:

################## - LIMITING CHAIN EXTENSIBILITY MODELS - ####################

def warner(_F: SN, **_params) -> SN:
def warner(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu, _Im = list(_params.values())
_A = LN(1.0 - (_J1 - 3.0) / (_Im - 3.0))
_W = - 0.5 * _mu * _Im * _A
return _W

def kilian(_F: SN, **_params) -> SN:
def kilian(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu, _JL = list(_params.values())
_A = SQRT((_J1 - 3.0) / _JL)
_W = - _mu * _JL * (LN(1.0 - _A) + _A)
return _W

def van_der_waals(_F: SN, **_params) -> SN:
def van_der_waals(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu, _lambda_m, _beta, _a, _K = list(_params.values())
_A = -(_lambda_m**2.0 - 3.0) * (LN(1.0 - _beta) + _beta) - (2.0 / 3.0) * _a *\
(0.5 * (_J1 - 3.0))**1.5
_W = _mu * _A
return _W

def gent(_F: SN, **_params) -> SN:
def gent(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_E, _Im = list(_params.values())
_A = LN(1.0 - (_J1 - 3.0) / (_Im - 3.0))
_W = - (_E / 6.0) * (_Im - 3.0) * _A
return _W

def takamizawa_hayashi(_F: SN, **_params) -> SN:
def takamizawa_hayashi(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_c, _Jm = list(_params.values())
_A = LN(1.0 - ((_J1 - 2.0) / _Jm)**2.0)
_W = _c * _A
return _W

def yeoh_fleming(_F: SN, **_params) -> SN:
def yeoh_fleming(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_A, _B, _Im, _C10 = list(_params.values())
_C = (_Im - 3.0) * (1.0 - EXP(-_B * (_J1 - 3.0) / (_Im - 3.0)))
_D = (_Im - 3.0) * LN(1.0 - (_J1 - 3.0) / (_Im - 3.0))
_W = (_A / _B) * _C - _C10 * _D
return _W

def gent_3ps(_F: SN, **_params) -> SN:
def gent_3ps(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu, _alpha, _Im, _K = list(_params.values())
_A = - _alpha * (_Im - 3.0) * LN(1.0 - (_J1 - 3.0) / (_Im - 3.0))
_B = (1.0 - _alpha) * (_J2 - 3.0)
_W = 0.5 * _mu * (_A + _B)
return _W

def pucci_saccomandi(_F: SN, **_params) -> SN:
def pucci_saccomandi(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu, _k, _Jm = list(_params.values())
_A = LN(1.0 - (_J1 - 2.0) / _Jm)
_W = _k * LN(_J2 / 3.0) - 0.5 * _mu * _Jm * _A
return _W

def horgan_saccomandi(_F: SN, **_params) -> SN:
def horgan_saccomandi(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu, _J = list(_params.values())
_A = LN((_J**2.0 * (1.0 - _J1) + _J * _J2 - 1.0) / (_J - 1.0)**3.0)
_W = - 0.5 * _mu * _J * _A
return _W

def beatty(_F: SN, **_params) -> SN:
def beatty(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_c, _Im = list(_params.values())
_A = - _c * _Im * (_Im - 3.0) / (2.0 * _Im - 3.0)
_B = LN((1.0 - (_J1 - 3.0) / (_Im - 3.0)) / (1.0 + (_J1 - 3.0) / _Im))
_W = _A * _B
return _W

# def horgan_murphy(_F: SN, **_params) -> SN: #TODO
# def horgan_murphy(_F: DG, **_params) -> DG: #TODO
# _C, _J1, _J2, _J3 = _F.invariants
# return

########## - POWER LAW, EXPONENTIAL OR LOGARITHMIC FUNCTION MODELS - ##########

def knowles(_F: SN, **_params) -> SN:
def knowles(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu, _b, _n = list(_params.values())
_a1 = _mu / (2.0 * _b)
_a2 = (1.0 + ((_b / _n) * (_J1 - 3.0)))**_n
_W = _a1 * (_a2 - 1.0)
return _W

def swanson(_F: SN, **_params) -> SN:
def swanson(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_AB = list(_params.values())[:-1]
_n = len(_AB)//2
Expand All @@ -238,28 +241,28 @@ def swanson(_F: SN, **_params) -> SN:
_W = 1.5 * _A + 1.5 * _B
return _W

def yamashita_kawabata(_F: SN, **_params) -> SN:
def yamashita_kawabata(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_C1, _C2, _C3, _N = list(_params.values())
_W = _C1 * (_J1 - 3.0) + _C2 * (_J2 - 3.0) + _C3 / (_N + 1.0) *\
(_J1 - 3.0)**(_N + 1.0)
return _W

def davis_de_thomas(_F: SN, **_params) -> SN:
def davis_de_thomas(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_A, _n, _C, _k = list(_params.values())
_W = 0.5 * _A / (1.0 - 0.5 * _n) * (_J1 - 3.0 + _C**2.0)**(1.0 - 0.5 * _n) +\
+ _k * (_J1 - 3.0)**2.0
return _W

def gregory(_F: SN, **_params) -> SN:
def gregory(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_A, _B, _C, _m, _n = list(_params.values())
_W = 0.5 * _A / (1.0 - 0.5 * _n) * (_J1 - 3.0 + _C**2.0)**(1.0 - 0.5 * _n) +\
0.5 * _B / (1.0 + 0.5 * _m) * (_J1 - 3.0 + _C**2.0)**(1.0 + 0.5 * _m)
return _W

def modified_gregory(_F: SN, **_params) -> SN:
def modified_gregory(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_A, _alpha, _M, _B, _beta, _N = list(_params.values())
_alpha1 = 1.0 + _alpha
Expand All @@ -268,55 +271,55 @@ def modified_gregory(_F: SN, **_params) -> SN:
_B / _beta1 * (_J1 - 3.0 + _N**2.0)**_beta1
return _W

def aimn(_F: SN, **_params) -> SN:
def aimn(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu = list(_params.values())
_W = 0.5 * _mu * (_J1/_J2 + 2.0 * _J3**0.5)
return _W

def beda(_F: SN, **_params) -> SN:
def beda(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu = list(_params.values())
_W = 0.5 * _mu * (_J1/_J2 + 2.0 * _J3**0.5)
return _W

def lopez_pamies(_F: SN, **_params) -> SN:
def lopez_pamies(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu = list(_params.values())
_W = 0.5 * _mu * (_J1/_J2 + 2.0 * _J3**0.5)
return _W

def gen_yeoh(_F: SN, **_params) -> SN:
def gen_yeoh(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu = list(_params.values())
_W = 0.5 * _mu * (_J1/_J2 + 2.0 * _J3**0.5)
return _W

def hart_smith(_F: SN, **_params) -> SN:
def hart_smith(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu = list(_params.values())
_W = 0.5 * _mu * (_J1/_J2 + 2.0 * _J3**0.5)
return _W

def veronda_westmann(_F: SN, **_params) -> SN:
def veronda_westmann(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu = list(_params.values())
_W = 0.5 * _mu * (_J1/_J2 + 2.0 * _J3**0.5)
return _W

def fung_demiray(_F: SN, **_params) -> SN:
def fung_demiray(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu = list(_params.values())
_W = 0.5 * _mu * (_J1/_J2 + 2.0 * _J3**0.5)
return _W

def blatz_ko(_F: SN, **_params) -> SN:
def blatz_ko(_F: DG, **_params) -> DG:
_, _J1, _J2, _J3 = _F.invariants
_mu = list(_params.values())
_W = 0.5 * _mu * (_J1/_J2 + 2.0 * _J3**0.5)
return _W

def ogden(_F: SN, **_params) -> SN:
def ogden(_F: DG, **_params) -> DG:
_λ1, _λ2, _λ3 = _F.stretches
_params = list(_params.values())
_mu = _params[0::2]
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