b2compressible_mooney_rivlin.H

//------------------------------------------------------------------------
// b2compressible_mooney_rivlin.H --
//
//
// written by Mathias Doreille
//            Thomas Blome <thomas.blome@dlr.de>
//
// Copyright (c) 2009 SMR Engineering & Development SA
//               2502 Bienne, Switzerland
//
// Copyright (c) 2023 Deutsches Zentrum für Luft- und Raumfahrt (DLR) e.V.
//                    Linder Höhe, 51147 Köln
//
// All Rights Reserved.  Proprietary source code.  The contents of
// this file may not be disclosed to third parties, copied or
// duplicated in any form, in whole or in part, without the prior
// written permission of SMR.
//------------------------------------------------------------------------
 
#ifndef B2COMPRESSIBLE_MOONEY_RIVLIN_H_
#define B2COMPRESSIBLE_MOONEY_RIVLIN_H_
 
namespace b2000 {
 
// Compressible Mooney Rivlin material for 2D and 3D.
//
// The strain energy density (in its coupled form) is:
// (See e.g. "Nonlinear Solid Mechanics", by G.A. Holzapfel, 2nd ed., p. 247, eq. (6.147).)
//
//    W = C1 * (I1 - 3) + C2 * (I2 - 3) + k / 2 * (I3^(1/2) - 1)^2 - (C1 + 2 * C2) * ln(I3)
//
// where:
// -----
// C1, C2 (nu == 2*(C1+C2) == shear modulus) and k (bulk modulus) the material constants,
// and I1, I2, I3 the invariants of the right Cauchy-Green deformation tensor.
//
// The functions return the 2nd Piola-Kirchhoff stress tensor and its
// derivative as a function of the Green-Lagrangian strain tensor. The
// tensors are stored using the notation [11, 22, 33, 12, 23, 13]. The
// derivatives are stored as a lower packed triangular matrix.
 
double get_2d_plane_stress_compressible_mooney_rivlin_stress(
      const double C1, const double C2, const double k, const double green_lagrange_strain[3],
      double pk2_stress[3], double d_stress_d_strain[6]);
 
double get_2d_plane_strain_compressible_mooney_rivlin_stress(
      const double C1, const double C2, const double k, const double green_lagrange_strain[3],
      double pk2_stress[3], double d_stress_d_strain[6]);
 
void get_3d_compressible_mooney_rivlin_stress(
      const double C1, const double C2, const double k, const double green_lagrange_strain[6],
      double pk2_stress[6], double d_stress_d_strain[21]);
 
}  // namespace b2000
 
#endif /* B2COMPRESSIBLE_MOONEY_RIVLIN_H_ */