# -*- coding: utf-8 -*-
"""
This file is part of FElupe.
FElupe is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
FElupe is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FElupe. If not, see <http://www.gnu.org/licenses/>.
"""
import numpy as np
from ._models_hyperelasticity import NeoHooke
from ._models_linear_elasticity import lame_converter
[docs]class LinearElasticLargeStrain:
r"""Linear-elastic material formulation suitable for large-rotation analyses based
on the nearly-incompressible Neo-Hookean material formulation.
Arguments
---------
E : float
Young's modulus.
nu : float
Poisson ratio.
See Also
--------
NeoHooke: Nearly-incompressible isotropic hyperelastic Neo-Hooke material
formulation.
"""
def __init__(self, E=None, nu=None, parallel=False):
self.E = E
self.nu = nu
# aliases for gradient and hessian
self.energy = self.function
self.stress = self.gradient
self.elasticity = self.hessian
# initial variables for calling
# ``self.gradient(self.x)`` and ``self.hessian(self.x)``
self.x = [np.eye(3), np.zeros(0)]
mu = None
bulk = None
if self.E is not None and self.nu is not None:
gamma, mu = lame_converter(E, nu)
bulk = gamma + 2 * mu / 3
self.material = NeoHooke(mu=mu, bulk=bulk, parallel=parallel)
[docs] def function(self, x, E=None, nu=None):
"""Evaluate the strain energy (as a function of the deformation gradient).
Arguments
---------
x : list of ndarray
List with Deformation gradient ``F`` (3x3) as first item
E : float, optional
Young's modulus (default is None)
nu : float, optional
Poisson ratio (default is None)
Returns
-------
ndarray
Stress tensor (3x3)
"""
if E is None:
E = self.E
if nu is None:
nu = self.nu
gamma, mu = lame_converter(E, nu)
bulk = gamma + 2 * mu / 3
return self.material.function(x, mu=mu, bulk=bulk)
[docs] def gradient(self, x, E=None, nu=None):
"""Evaluate the stress tensor (as a function of the deformation gradient).
Arguments
---------
x : list of ndarray
List with Deformation gradient ``F`` (3x3) as first item
E : float, optional
Young's modulus (default is None)
nu : float, optional
Poisson ratio (default is None)
Returns
-------
ndarray
Stress tensor (3x3)
"""
if E is None:
E = self.E
if nu is None:
nu = self.nu
gamma, mu = lame_converter(E, nu)
bulk = gamma + 2 * mu / 3
return self.material.gradient(x, mu=mu, bulk=bulk)
[docs] def hessian(self, x, E=None, nu=None):
"""Evaluate the elasticity tensor (as a function of the deformation gradient).
Arguments
---------
x : list of ndarray
List with Deformation gradient ``F`` (3x3) as first item.
E : float, optional
Young's modulus (default is None)
nu : float, optional
Poisson ratio (default is None)
Returns
-------
ndarray
elasticity tensor (3x3x3x3)
"""
if E is None:
E = self.E
if nu is None:
nu = self.nu
gamma, mu = lame_converter(E, nu)
bulk = gamma + 2 * mu / 3
return self.material.hessian(x, mu=mu, bulk=bulk)