#! /usr/bin/env python
# The MIT License (MIT)
#
# Copyright (c) 2015, EPFL Reconfigurable Robotics Laboratory,
#                     Philip Moseley, philip.moseley@gmail.com
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.

import numpy as np


#--------------------------------------------------------------------------------
# Material model name.
#--------------------------------------------------------------------------------
def name():   return 'poly2'
def pname():  return 'Polynomial-2'
def params(): return 'C10 C01 C20 C11 C02'
def descr():  return 'Polynomial Model with order 2.'


#--------------------------------------------------------------------------------
# Function defining the uniaxial stress given strain.
#--------------------------------------------------------------------------------
def stressU(x, C10, C01, C20, C11, C02):
    L = 1.0+x
    I1 = np.power(L,2.0) + 2.0*np.power(L,-1.0)
    I2 = np.power(L,-2.0) + 2.0*L
    t1 = C10*L + C01 + 2.0*C20*L*(I1-3.0) + C11*(I1-3.0+L*(I2-3.0)) + 2.0*C02*(I2-3.0)
    return 2.0 * (1.0 - np.power(L,-3.0)) * t1


#--------------------------------------------------------------------------------
# Function defining the biaxial stress given strain.
#--------------------------------------------------------------------------------
def stressB(x, C10, C01, C20, C11, C02):
    L = 1.0+x
    I1 = 2.0*np.power(L,2.0) + np.power(L,-4.0)
    I2 = 2.0*np.power(L,-2.0) + np.power(L,4.0)
    t1 = C10 + C01*np.power(L,2.0) + 2.0*C20*(I1-3.0) + C11*(np.power(L,2)*(I1-3.0)+(I2-3.0))
    return 2.0 * (L - np.power(L,-5.0)) * t1


#--------------------------------------------------------------------------------
# Function defining the planar stress given strain.
#--------------------------------------------------------------------------------
def stressP(x, C10, C01, C20, C11, C02):
    L = 1.0+x
    I1 = np.power(L,2.0)+np.power(L,-2.0) + 1.0
    I2 = I1
    t1 = C10 + C01 + 2.0*(C20+C11+C02)*(I1-3.0)
    return 2.0 * (L - np.power(L,-3.0)) * t1


#--------------------------------------------------------------------------------
# Calculate the Ds
#--------------------------------------------------------------------------------
def compressibility(v, C10, C01, C20, C11, C02):
    u0 = 2.0*(C10+C01)
    D1 = 3.0*(1.0-2.0*v) / (u0*(1.0+v))
    return [D1,0.0]