b2generalised_blatz_ko_material.H

//------------------------------------------------------------------------
// b2generalised_blatz_ko_material.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 B2GENERALISED_BLATZ_KO_MATERIAL_H_
#define B2GENERALISED_BLATZ_KO_MATERIAL_H_
 
namespace b2000 {
 
// Generalised Blatz-Ko 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. (6.149).)
//
//    W = mu / 2 * f * ((I1 - 3) + 1 / b * (I3^(-b) - 1)) +
//        mu / 2 * (1 - f) * ((I2 / I3 - 3) + 1/b * (I3^b - 1))
//
// where:
// -----
// b := nu / (1 - 2 * nu), mu, nu and f the material constants and
// I1, I2, I3 the invariants of the right Cauchy-Green deformation tensor.
//
// For infinitesimal deformation, mu is the shear modulus, nu the Poisson's ratio,
// and f is related to the volume fraction of voids in the foam-rubber material.
//
// 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_generalised_blatz_ko_stress(
      const double mu, const double nu, const double f, const double green_lagrange_strain[3],
      double pk2_stress[3], double d_stress_d_strain[6], double& lambda3_old);
 
double get_2d_plane_strain_generalised_blatz_ko_stress(
      const double mu, const double nu, const double f, const double green_lagrange_strain[3],
      double pk2_stress[3], double d_stress_d_strain[6]);
 
void get_3d_generalised_blatz_ko_stress(
      const double mu, const double nu, const double f, const double green_lagrange_strain[6],
      double pk2_stress[6], double d_stress_d_strain[21]);
 
}  // namespace b2000
 
#endif /* B2GENERALISED_BLATZ_KO_MATERIAL_H_ */