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| /*! | ||
| * \file include/TFEL/Material/Eshelby.hxx | ||
| * \author Antoine Martin | ||
| * \date 15 October 2024 | ||
| * \brief This file declares the Eshelby tensor for an ellipsoidal inclusion embedded in an isotropic matrix. | ||
| * \copyright Copyright (C) 2006-2018 CEA/DEN, EDF R&D. All rights | ||
| * reserved. | ||
| * This project is publicly released under either the GNU GPL Licence | ||
| * or the CECILL-A licence. A copy of thoses licences are delivered | ||
| * with the sources of TFEL. CEA or EDF may also distribute this | ||
| * project under specific licensing conditions. | ||
| */ | ||
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| #ifndef LIB_TFEL_MATERIAL_ESHELBY_HXX | ||
| #define LIB_TFEL_MATERIAL_ESHELBY_HXX | ||
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| #include "TFEL/Math/st2tost2.hxx" | ||
| #include "TFEL/Material/StiffnessTensor.hxx" | ||
| #include <stdexcept> | ||
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| namespace tfel::material | ||
| { | ||
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| namespace homogenization{ | ||
| namespace elasticity{ | ||
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| /*! | ||
| * This function builds the Eshelby tensor of a circular cylinder embedded in an isotropic matrix, considering a PLANE STRAIN modelling hypothesis | ||
| * \return an object of type st2tost2<2u,real> | ||
| * \tparam real: underlying type | ||
| * \param[in] nu: Poisson's ratio of the matrix | ||
| */ | ||
| template <typename real> | ||
| TFEL_HOST_DEVICE tfel::math::st2tost2<2u,real> computeCircularCylinderEshelbyTensor(const real&); | ||
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| /*! | ||
| * This function builds the Eshelby tensor of an elliptic cylinder embedded in an isotropic matrix, considering a PLANE STRAIN modelling hypothesis | ||
| * The function returns the Eshelby tensor in the basis (e1,e2) where e1 corresponds to the biggest axis | ||
| * \return an object of type st2tost2<2u,real> | ||
| * \tparam real: underlying type | ||
| * \param[in] nu: Poisson's ratio of the matrix | ||
| * \param[in] e: aspect ratio of the elliptic basis | ||
| */ | ||
| template <typename real> | ||
| TFEL_HOST_DEVICE tfel::math::st2tost2<2u,real> computeEllipticCylinderEshelbyTensor(const real&, const real&); | ||
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| /*! | ||
| * This function builds the Eshelby tensor of a sphere embedded in an isotropic matrix. | ||
| * \return an object of type st2tost2<3u,real> | ||
| * \tparam real: underlying type | ||
| * \param[in] nu: Poisson's ratio of the matrix | ||
| */ | ||
| template <typename real> | ||
| TFEL_HOST_DEVICE tfel::math::st2tost2<3u,real> computeSphereEshelbyTensor(const real&); | ||
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| /*! | ||
| * This function builds the Eshelby tensor of an axisymmetrical ellipsoid embedded in an isotropic matrix. | ||
| * The function returns the Eshelby tensor in the basis (e1,e2,e3) where e1 corresponds to (one of) the biggest ax(es) | ||
| * \return an object of type st2tost2<3u,real> | ||
| * \tparam real: underlying type | ||
| * \param[in] nu: Poisson's ratio of the matrix | ||
| * \param[in] e: aspect ratio of the ellipsoid (e>1 : prolate, e<1 : oblate) | ||
| * \param[in] precf, precd, precld: default arguments which aim at preventing the numerical instability of the formula when the ellipsoid is almost a sphere. When the absolute value of (e-1) is below precf (resp. precd, precld) for real=float (resp. real= double, long double), the returned tensor is computeSphereEshelbyTensor(nu). | ||
| * | ||
| * The expressions can be found in Torquato, Random Heterogeneous Materials (2002). | ||
| */ | ||
| template <typename real> | ||
| TFEL_HOST_DEVICE tfel::math::st2tost2<3u,real> computeAxisymmetricalEshelbyTensor( | ||
| const real&, | ||
| const real&, | ||
| const real = real{8e-3}, | ||
| const real = real{1.5e-4}, | ||
| const real = real{1e-5}); | ||
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| /*! | ||
| * This function builds the Eshelby tensor of a general ellipsoid embedded in an isotropic matrix. | ||
| * The function returns the Eshelby tensor in the basis (e1,e2,e3) where e1 (resp. e2, e3) is aligned with the axis with the first (resp. the second and third) biggest length | ||
| * \return an object of type st2tost2<3u,real> | ||
| * \tparam real: underlying type | ||
| * \tparam LengthType: type of the dimensions of the ellipsoid | ||
| * \param[in] nu: Poisson's ratio of the matrix | ||
| * \param[in] a: length of the first semi-axis | ||
| * \param[in] b: length of the second semi-axis | ||
| * \param[in] c: length of the third semi-axis | ||
| * \param[in] precf, precd, precld: default arguments which aim at preventing the numerical instability of the formula when the ellipsoid is almost axisymmetrical. When the absolute value of (a-b)/c (or (a-c)/b or (b-c)/a) is below precf (resp. precd, precld) for real=float (resp. real= double, long double), the returned tensor is computeAxisymmetricalEshelbyTensor. | ||
| * | ||
| * The expressions for the case of three distinct semi-axes can be found in Eshelby (1957). | ||
| */ | ||
| template <typename real, typename LengthType> | ||
| TFEL_HOST_DEVICE tfel::math::st2tost2<3u,real> computeEshelbyTensor( | ||
| const real&, | ||
| const LengthType&, | ||
| const LengthType&, | ||
| const LengthType&, | ||
| const real = real{8e-3}, | ||
| const real = real{1.5e-4}, | ||
| const real = real{1e-5}); | ||
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| /*! | ||
| * This function builds the strain localisation tensor of a general ellipsoid | ||
| * with a general elasticity, embedded in an isotropic matrix. | ||
| * The localisation tensor \f$A\f$ is defined as follows : \f[\epsilon = A:E_0\f] where \f$E_0\f$ is the uniform strain tensor imposed at infinity, | ||
| * and \f$\epsilon\f$ is the strain tensor solution of Eshelby problem for the ellipsoid. | ||
| * The ellipsoid also has a specific orientation given by the vectors \f$n_a\f$, \f$n_b\f$. | ||
| * \return an object of type st2tost2, which is the fourth-order localisation tensor \f$A\f$ | ||
| * \tparam real: underlying type | ||
| * \tparam StressType: type of the elastic constants related to the matrix and the ellipsoid | ||
| * \tparam LengthType: type of the dimensions of the ellipsoid | ||
| * \param [in] young,nu: Young modulus and Poisson's ratio of the matrix | ||
| * \param [in] young_i,nu_i: Young modulus and Poisson's ratio of the inclusions | ||
| * \param [in] n_a: direction of the principal axis whose length is \f$a\f$ | ||
| * \param [in] a: length of semi-axis relative to the direction \f$n_a\f$ | ||
| * \param [in] n_b: direction of the principal axis whose length is \f$b\f$ | ||
| * \param [in] b: length of semi-axis relative to the direction \f$n_b\f$ | ||
| * \param [in] c: length of the remaining semi-axis | ||
| */ | ||
| template <typename real, typename StressType, typename LengthType> | ||
| TFEL_HOST_DEVICE tfel::math::st2tost2<3u,real> computeEllipsoidLocalisationTensor( | ||
| const StressType&, | ||
| const real&, | ||
| const StressType&, | ||
| const real&, | ||
| const tfel::math::tvector<3u,real>&, | ||
| const LengthType&, | ||
| const tfel::math::tvector<3u,real>&, | ||
| const LengthType&, | ||
| const LengthType&); | ||
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| /*! | ||
| * This function builds the strain localisation tensor of an axisymmetrical ellipsoid | ||
| * with a general elasticity, embedded in an isotropic matrix. | ||
| * The ellipsoid also has a specific orientation given by the vector \f$n_a\f$, axis of the ellipsoid, whose semi-length is \f$a\f$. | ||
| * \return an object of type st2tost2 | ||
| * \tparam real: underlying type | ||
| * \tparam StressType: type of the elastic constants related to the matrix and the ellipsoid | ||
| * \param [in] young,nu: Young modulus and Poisson's ratio of the matrix | ||
| * \param [in] young_i,nu_i: Young modulus and Poisson's ratio of the inclusions | ||
| * \param [in] n_a: direction of the axis of the ellipsoid (whose semi-length is \f$a\f$) | ||
| * \param [in] a: length of semi-axis relative to the direction \f$n_a\f$ | ||
| */ | ||
| template <typename real, typename StressType> | ||
| TFEL_HOST_DEVICE tfel::math::st2tost2<3u,real> computeAxisymmetricalEllipsoidLocalisationTensor( | ||
| const StressType&, | ||
| const real&, | ||
| const StressType&, | ||
| const real&, | ||
| const tfel::math::tvector<3u,real>&, | ||
| const real&); | ||
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| /*! | ||
| * This function builds the strain localisation tensor of a sphere | ||
| * with a general elasticity, embedded in an isotropic matrix. | ||
| * \return an object of type st2tost2 | ||
| * \tparam real: underlying type | ||
| * \tparam StressType: type of the elastic constants related to the matrix and the ellipsoid | ||
| * \param [in] young,nu: Young modulus and Poisson's ratio of the matrix | ||
| * \param [in] young_i,nu_i: Young modulus and Poisson's ratio of the inclusions | ||
| */ | ||
| template <typename real, typename StressType> | ||
| TFEL_HOST_DEVICE tfel::math::st2tost2<3u,real> computeSphereLocalisationTensor( | ||
| const StressType&, | ||
| const real&, | ||
| const StressType&, | ||
| const real&); | ||
|
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| }//end of namespace elasticity | ||
| }//end of namespace homogenization | ||
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| } // end of namespace tfel::material | ||
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| #include "TFEL/Material/Eshelby.ixx" | ||
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| #endif /* LIB_TFEL_MATERIAL_ESHELBY_HXX */ |
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