Line data    Source code

       1              : // Copyright 2024, UChicago Argonne, LLC
       2              : // All Rights Reserved
       3              : // Software Name: NEML2 -- the New Engineering material Model Library, version 2
       4              : // By: Argonne National Laboratory
       5              : // OPEN SOURCE LICENSE (MIT)
       6              : //
       7              : // Permission is hereby granted, free of charge, to any person obtaining a copy
       8              : // of this software and associated documentation files (the "Software"), to deal
       9              : // in the Software without restriction, including without limitation the rights
      10              : // to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
      11              : // copies of the Software, and to permit persons to whom the Software is
      12              : // furnished to do so, subject to the following conditions:
      13              : //
      14              : // The above copyright notice and this permission notice shall be included in
      15              : // all copies or substantial portions of the Software.
      16              : //
      17              : // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
      18              : // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
      19              : // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
      20              : // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
      21              : // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
      22              : // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
      23              : // THE SOFTWARE.
      24              : 
      25              : #include "neml2/tensors/WR2.h"
      26              : #include "neml2/tensors/Scalar.h"
      27              : #include "neml2/tensors/Vec.h"
      28              : #include "neml2/tensors/R2.h"
      29              : #include "neml2/tensors/Rot.h"
      30              : #include "neml2/tensors/SR2.h"
      31              : #include "neml2/tensors/WSR4.h"
      32              : #include "neml2/tensors/R4.h"
      33              : 
      34              : #include "neml2/tensors/mandel_notation.h"
      35              : #include "neml2/tensors/functions/tan.h"
      36              : #include "neml2/tensors/functions/cos.h"
      37              : #include "neml2/tensors/functions/pow.h"
      38              : 
      39              : namespace neml2
      40              : {
      41           40 : WR2::WR2(const R2 & T)
      42           40 :   : WR2(full_to_skew((T - T.transpose()) / 2.0))
      43              : {
      44           40 : }
      45              : 
      46              : Scalar
      47            9 : WR2::operator()(Size i, Size j) const
      48              : {
      49            9 :   Size a = skew_reverse_index[i][j];
      50           27 :   return base_index({a}) * skew_factor[i][j];
      51            9 : }
      52              : 
      53              : Rot
      54           22 : WR2::exp() const
      55              : {
      56              :   // There are singularities at norm() = 0 and 2*pi
      57              :   // To the third order near zero this reduces to
      58              :   // *this * (1/4 + 5 * norm^4 / 96)
      59              :   // We use this formula for small rotations
      60              : 
      61              :   // The other singularity is essentially unavoidable
      62              : 
      63              :   // This is what determines which region to sit in
      64           22 :   auto norm2 = norm_sq();
      65              : 
      66              :   // So we want the result to be as accurate as machine precision
      67           22 :   auto thresh = std::pow(eps, 1.0 / 3.0);
      68              : 
      69              :   // Taylor series
      70           22 :   auto res_taylor = Rot(*this) * (0.25 + 5.0 * norm2 * norm2 / 96.0);
      71              : 
      72              :   // Actual definition
      73           22 :   auto res_actual = Rot(*this) * neml2::tan(norm2 / 2.0) / (2.0 * norm2 * neml2::cos(norm2 / 2));
      74              : 
      75           44 :   return Rot(at::where((norm2 > thresh).unsqueeze(-1), res_actual, res_taylor));
      76           22 : }
      77              : 
      78              : R2
      79            9 : WR2::dexp() const
      80              : {
      81              :   // Same singularities as WR2::exp()
      82            9 :   auto norm2 = norm_sq();
      83            9 :   auto thresh = std::pow(eps, 1.0 / 3.0);
      84              : 
      85           18 :   auto res_taylor = 5.0 * norm2 / 24.0 * Vec(*this).outer(Vec(*this)) +
      86           27 :                     (0.25 + 5.0 * norm2 * norm2 / 96.0) * R2::identity(options());
      87              : 
      88            9 :   auto f1 = neml2::tan(norm2 / 2.0) / (2.0 * norm2 * neml2::cos(norm2 / 2));
      89           18 :   auto f2 = (norm2 * neml2::pow(1.0 / neml2::cos(norm2 / 2), 3.0) +
      90           18 :              neml2::tan(norm2 / 2.0) * (norm2 * neml2::tan(norm2 / 2.0) - 2.0) *
      91           18 :                  (1.0 / neml2::cos(norm2 / 2.0))) /
      92           27 :             (2 * norm2 * norm2);
      93              : 
      94            9 :   auto res_actual = f1 * R2::identity(options()) + f2 * Vec(*this).outer(Vec(*this));
      95              : 
      96           18 :   return R2(at::where((norm2 > thresh).unsqueeze(-1).unsqueeze(-1), res_actual, res_taylor));
      97            9 : }
      98              : 
      99              : } // namespace neml2