Source code for felupe.mechanics._helpers

# -*- coding: utf-8 -*-
"""
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|   |___ |   |___ |   |    |  |_|  ||   |_| ||   |___ 
|    ___||    ___||   |___ |       ||    ___||    ___|
|   |    |   |___ |       ||       ||   |    |   |___ 
|___|    |_______||_______||_______||___|    |_______|

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 .._assembly import IntegralFormMixed
from .._field import FieldAxisymmetric
from ..constitution import AreaChange
from ..math import det


class Assemble:
    "A class with assembly methods of a SolidBody."

    def __init__(self, vector, matrix):
        self.vector = vector
        self.matrix = matrix


class Evaluate:
    "A class with evaluate methods of a SolidBody."

    def __init__(self, gradient, hessian, cauchy_stress=None, kirchhoff_stress=None):
        self.gradient = gradient
        self.hessian = hessian

        if cauchy_stress is not None:
            self.cauchy_stress = cauchy_stress
            self.kirchhoff_stress = kirchhoff_stress


class Results:
    "A class with intermediate results of a SolidBody."

    def __init__(self, stress=False, elasticity=False):

        self.force = None
        self._force = None
        self.stiffness = None
        self.kinematics = None
        self.statevars = None
        self._statevars = None

        if stress:
            self.stress = None

        if elasticity:
            self.elasticity = None

    def update_statevars(self):

        if self._statevars is not None:
            self.statevars = self._statevars


[docs]class StateNearlyIncompressible: "A State with internal fields for (nearly) incompressible solid bodies." def __init__(self, field): self.field = field self.dJdF = AreaChange().function # initial values (on mesh-points) of the displacement field self.u = field[0].values # deformation gradient self.F = field.extract() # cell-values of the internal pressure and volume-ratio fields self.p = np.zeros(field.region.mesh.ncells) self.J = np.ones(field.region.mesh.ncells)
[docs] def h(self, parallel=False): "Integrated shape-function gradient w.r.t. the deformed coordinates `x`." return IntegralFormMixed( fun=self.dJdF(self.F), v=self.field, dV=self.field.region.dV ).integrate(parallel=parallel)[0]
[docs] def v(self): "Cell volumes of the deformed configuration." dV = self.field.region.dV if isinstance(self.field[0], FieldAxisymmetric): R = self.field[0].radius dA = self.field.region.dV dV = 2 * np.pi * R * dA return (det(self.F[0]) * dV).sum(0)