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Ryszard Pyrz - One of the best experts on this subject based on the ideXlab platform.
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the mori tanaka Stiffness Tensor diagonal symmetry complex fibre orientations and non dilute volume fractions
Mechanics of Materials, 2001Co-Authors: Jan Schjodtthomsen, Ryszard PyrzAbstract:Abstract This paper considers the diagonal symmetry of the Stiffness Tensors predicted using the Mori-Tanaka (MT) approach. Since the MT approach may yield asymmetric Stiffness Tensors this paper considers an alternative approach to ensure the diagonal symmetry. Furthermore, an extension of the MT approach to non-dilute volume fractions is considered. It is shown that the MT approach by Benveniste [Mech. Mater. 6 (1987) 147], may not yield diagonally symmetric Stiffness Tensors in situations when a statistical fibre orientation function is incorporated. Only when the inclusions are spherical and randomly distributed or fully aligned will the MT predicted Stiffness Tensor be diagonally symmetric. The extension to non-dilute volume fractions is seen to lie within the Hashin–Shtrikman–Walpole (HSW) bounds and comparison to other approaches and experiments found in the literature shows very good agreement.
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The Mori–Tanaka Stiffness Tensor: diagonal symmetry, complex fibre orientations and non-dilute volume fractions
Mechanics of Materials, 2001Co-Authors: Jan Schjødt-thomsen, Ryszard PyrzAbstract:Abstract This paper considers the diagonal symmetry of the Stiffness Tensors predicted using the Mori-Tanaka (MT) approach. Since the MT approach may yield asymmetric Stiffness Tensors this paper considers an alternative approach to ensure the diagonal symmetry. Furthermore, an extension of the MT approach to non-dilute volume fractions is considered. It is shown that the MT approach by Benveniste [Mech. Mater. 6 (1987) 147], may not yield diagonally symmetric Stiffness Tensors in situations when a statistical fibre orientation function is incorporated. Only when the inclusions are spherical and randomly distributed or fully aligned will the MT predicted Stiffness Tensor be diagonally symmetric. The extension to non-dilute volume fractions is seen to lie within the Hashin–Shtrikman–Walpole (HSW) bounds and comparison to other approaches and experiments found in the literature shows very good agreement.
Yves Berthaud - One of the best experts on this subject based on the ideXlab platform.
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Une nouvelle analyse des sym\'etries d'un mat\'eriau \'elastique anisotrope. Exemple d'utilisation \`a partir de mesures ultrasonores
arXiv: Classical Physics, 2010Co-Authors: Marc Louis Maurice François, Yves Berthaud, Giuseppe GeymonatAbstract:This note deals with Stiffness Tensors measured from anisotropic linear elastic materials, whose symmetry is unknown. Their possible symmetries (exact or approximative) are revealed by a pole figure. An intrinsic function allows one to obtain a Stiffness Tensor which posses the chosen symmetry, the nearest from the measured Tensor, and its associated natural symmetry basis. For each symmetry level, a distance between these Tensors is given. The measurement of the Stiffness Tensor is done with an ultrasonic direct contact method. It is applied onto a 26 faces oak specimen.
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Determination of the symmetries of an experimentally determined Stiffness Tensor; application to acoustic measurements
International Journal of Solids and Structures, 1998Co-Authors: Marc Louis Maurice François, Giuseppe Geymonat, Yves BerthaudAbstract:For most materials, the symmetry group is known a priori and deduced from the realization process. This allows many simplifications for the measurements of the Stiffness Tensor. We deal here with the case where the symmetry is a priori unknown, as for biological or geological materials, or when the process makes the material symmetry axis uncertain (some composites, monocrystals). The measurements are then more complicated and the raw Stiffness Tensor obtained does not exhibit any symmetry in the Voigt's matricial form, as it is expressed in the arbitrarily chosen specimen's base. A complete ultrasonic measurement of the Stiffness Tensor from redundant measurements is proposed. In a second time, we show how to make a plane symmetry pole figure able to give visual information about the quasi-symmetries of a raw Stiffness Tensor determined by any measurement method. Finally we introduce the concept of distance from a raw Stiffness Tensor to one of the eight symmetry classes available for a Stiffness Tensor. The method provides the nearest Tensor (to the raw Stiffness Tensor) possessing a chosen symmetry class, with its associated natural symmetry base.
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Determination of the symmetries of an experimentally determined Stiffness Tensor: Application to acoustic measurements
International Journal of Solids and Structures, 1998Co-Authors: Marc Louis Maurice François, Giuseppe Geymonat, Yves BerthaudAbstract:Abstract For most materials, the symmetry group is known a priori and deduced from the realization process. This allows many simplifications for the measurements of the Stiffness Tensor. We deal here with the case where the symmetry is a priori unknown, as for biological or geological materials, or when the process makes the material symmetry axis uncertain (some composites, monocrystals). The measurements are then more complicated and the raw Stiffness Tensor obtained does not exhibit any symmetry in the Voigt's matrical form, as it is expressed in the arbitrarily chosen specimen's base. A complete ultrasonic measurement of this Stiffness Tensor from redundant measurements is proposed. In a second time, we show how to make a plane symmetry pole figure able to give visual information about the quasi-symmetries of a raw Stiffness Tensor determined by any measurement method. Finally we introduce the concept of distance from a raw Stiffness Tensor to one of the eight symmetry classes available for a Stiffness Tensor. The method provides the nearest Tensor (to the raw Stiffness Tensor) possessing a chosen symmetry class, with its associated natural symmetry base.
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Une nouvelle analyse des symétries d'un matériau élastique anisotrope. Exemple d'utilisation à partir de mesures ultrasonores.
Comptes rendus de l’Académie des sciences. Série IIb Mécanique physique astronomie, 1996Co-Authors: Marc Louis Maurice François, Yves Berthaud, Giuseppe GeymonatAbstract:This note deals with Stiffness Tensors measured from anisotropic linear elastic materials, whose symmetry is unknown. Their possible symmetries (exact or approximative) are revealed by a pole figure. An intrinsic function allows one to obtain a Stiffness Tensor which posses the chosen symmetry, the nearest from the measured Tensor, and its associated natural symmetry basis. For each symmetry level, a distance between these Tensors is given. The measurement of the Stiffness Tensor is done with an ultrasonic direct contact method. It is applied onto a 26 faces oak specimen.
Marc Louis Maurice François - One of the best experts on this subject based on the ideXlab platform.
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Une nouvelle analyse des sym\'etries d'un mat\'eriau \'elastique anisotrope. Exemple d'utilisation \`a partir de mesures ultrasonores
arXiv: Classical Physics, 2010Co-Authors: Marc Louis Maurice François, Yves Berthaud, Giuseppe GeymonatAbstract:This note deals with Stiffness Tensors measured from anisotropic linear elastic materials, whose symmetry is unknown. Their possible symmetries (exact or approximative) are revealed by a pole figure. An intrinsic function allows one to obtain a Stiffness Tensor which posses the chosen symmetry, the nearest from the measured Tensor, and its associated natural symmetry basis. For each symmetry level, a distance between these Tensors is given. The measurement of the Stiffness Tensor is done with an ultrasonic direct contact method. It is applied onto a 26 faces oak specimen.
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Determination of the symmetries of an experimentally determined Stiffness Tensor; application to acoustic measurements
International Journal of Solids and Structures, 1998Co-Authors: Marc Louis Maurice François, Giuseppe Geymonat, Yves BerthaudAbstract:For most materials, the symmetry group is known a priori and deduced from the realization process. This allows many simplifications for the measurements of the Stiffness Tensor. We deal here with the case where the symmetry is a priori unknown, as for biological or geological materials, or when the process makes the material symmetry axis uncertain (some composites, monocrystals). The measurements are then more complicated and the raw Stiffness Tensor obtained does not exhibit any symmetry in the Voigt's matricial form, as it is expressed in the arbitrarily chosen specimen's base. A complete ultrasonic measurement of the Stiffness Tensor from redundant measurements is proposed. In a second time, we show how to make a plane symmetry pole figure able to give visual information about the quasi-symmetries of a raw Stiffness Tensor determined by any measurement method. Finally we introduce the concept of distance from a raw Stiffness Tensor to one of the eight symmetry classes available for a Stiffness Tensor. The method provides the nearest Tensor (to the raw Stiffness Tensor) possessing a chosen symmetry class, with its associated natural symmetry base.
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Determination of the symmetries of an experimentally determined Stiffness Tensor: Application to acoustic measurements
International Journal of Solids and Structures, 1998Co-Authors: Marc Louis Maurice François, Giuseppe Geymonat, Yves BerthaudAbstract:Abstract For most materials, the symmetry group is known a priori and deduced from the realization process. This allows many simplifications for the measurements of the Stiffness Tensor. We deal here with the case where the symmetry is a priori unknown, as for biological or geological materials, or when the process makes the material symmetry axis uncertain (some composites, monocrystals). The measurements are then more complicated and the raw Stiffness Tensor obtained does not exhibit any symmetry in the Voigt's matrical form, as it is expressed in the arbitrarily chosen specimen's base. A complete ultrasonic measurement of this Stiffness Tensor from redundant measurements is proposed. In a second time, we show how to make a plane symmetry pole figure able to give visual information about the quasi-symmetries of a raw Stiffness Tensor determined by any measurement method. Finally we introduce the concept of distance from a raw Stiffness Tensor to one of the eight symmetry classes available for a Stiffness Tensor. The method provides the nearest Tensor (to the raw Stiffness Tensor) possessing a chosen symmetry class, with its associated natural symmetry base.
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Une nouvelle analyse des symétries d'un matériau élastique anisotrope. Exemple d'utilisation à partir de mesures ultrasonores.
Comptes rendus de l’Académie des sciences. Série IIb Mécanique physique astronomie, 1996Co-Authors: Marc Louis Maurice François, Yves Berthaud, Giuseppe GeymonatAbstract:This note deals with Stiffness Tensors measured from anisotropic linear elastic materials, whose symmetry is unknown. Their possible symmetries (exact or approximative) are revealed by a pole figure. An intrinsic function allows one to obtain a Stiffness Tensor which posses the chosen symmetry, the nearest from the measured Tensor, and its associated natural symmetry basis. For each symmetry level, a distance between these Tensors is given. The measurement of the Stiffness Tensor is done with an ultrasonic direct contact method. It is applied onto a 26 faces oak specimen.
Giuseppe Geymonat - One of the best experts on this subject based on the ideXlab platform.
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Une nouvelle analyse des sym\'etries d'un mat\'eriau \'elastique anisotrope. Exemple d'utilisation \`a partir de mesures ultrasonores
arXiv: Classical Physics, 2010Co-Authors: Marc Louis Maurice François, Yves Berthaud, Giuseppe GeymonatAbstract:This note deals with Stiffness Tensors measured from anisotropic linear elastic materials, whose symmetry is unknown. Their possible symmetries (exact or approximative) are revealed by a pole figure. An intrinsic function allows one to obtain a Stiffness Tensor which posses the chosen symmetry, the nearest from the measured Tensor, and its associated natural symmetry basis. For each symmetry level, a distance between these Tensors is given. The measurement of the Stiffness Tensor is done with an ultrasonic direct contact method. It is applied onto a 26 faces oak specimen.
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Determination of the symmetries of an experimentally determined Stiffness Tensor; application to acoustic measurements
International Journal of Solids and Structures, 1998Co-Authors: Marc Louis Maurice François, Giuseppe Geymonat, Yves BerthaudAbstract:For most materials, the symmetry group is known a priori and deduced from the realization process. This allows many simplifications for the measurements of the Stiffness Tensor. We deal here with the case where the symmetry is a priori unknown, as for biological or geological materials, or when the process makes the material symmetry axis uncertain (some composites, monocrystals). The measurements are then more complicated and the raw Stiffness Tensor obtained does not exhibit any symmetry in the Voigt's matricial form, as it is expressed in the arbitrarily chosen specimen's base. A complete ultrasonic measurement of the Stiffness Tensor from redundant measurements is proposed. In a second time, we show how to make a plane symmetry pole figure able to give visual information about the quasi-symmetries of a raw Stiffness Tensor determined by any measurement method. Finally we introduce the concept of distance from a raw Stiffness Tensor to one of the eight symmetry classes available for a Stiffness Tensor. The method provides the nearest Tensor (to the raw Stiffness Tensor) possessing a chosen symmetry class, with its associated natural symmetry base.
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Determination of the symmetries of an experimentally determined Stiffness Tensor: Application to acoustic measurements
International Journal of Solids and Structures, 1998Co-Authors: Marc Louis Maurice François, Giuseppe Geymonat, Yves BerthaudAbstract:Abstract For most materials, the symmetry group is known a priori and deduced from the realization process. This allows many simplifications for the measurements of the Stiffness Tensor. We deal here with the case where the symmetry is a priori unknown, as for biological or geological materials, or when the process makes the material symmetry axis uncertain (some composites, monocrystals). The measurements are then more complicated and the raw Stiffness Tensor obtained does not exhibit any symmetry in the Voigt's matrical form, as it is expressed in the arbitrarily chosen specimen's base. A complete ultrasonic measurement of this Stiffness Tensor from redundant measurements is proposed. In a second time, we show how to make a plane symmetry pole figure able to give visual information about the quasi-symmetries of a raw Stiffness Tensor determined by any measurement method. Finally we introduce the concept of distance from a raw Stiffness Tensor to one of the eight symmetry classes available for a Stiffness Tensor. The method provides the nearest Tensor (to the raw Stiffness Tensor) possessing a chosen symmetry class, with its associated natural symmetry base.
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Une nouvelle analyse des symétries d'un matériau élastique anisotrope. Exemple d'utilisation à partir de mesures ultrasonores.
Comptes rendus de l’Académie des sciences. Série IIb Mécanique physique astronomie, 1996Co-Authors: Marc Louis Maurice François, Yves Berthaud, Giuseppe GeymonatAbstract:This note deals with Stiffness Tensors measured from anisotropic linear elastic materials, whose symmetry is unknown. Their possible symmetries (exact or approximative) are revealed by a pole figure. An intrinsic function allows one to obtain a Stiffness Tensor which posses the chosen symmetry, the nearest from the measured Tensor, and its associated natural symmetry basis. For each symmetry level, a distance between these Tensors is given. The measurement of the Stiffness Tensor is done with an ultrasonic direct contact method. It is applied onto a 26 faces oak specimen.
Dieter H. Pahr - One of the best experts on this subject based on the ideXlab platform.
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predicting the trabecular bone Stiffness Tensor with spherical convolutional neural networks
25th Congress of the European Society of Biomechanics Vienna; 2019-07-07 - 2019-07-10, 2019Co-Authors: Fabian Sinzinger, Dieter H. Pahr, Rodrigo MorenoAbstract:Predicting The Trabecular Bone Stiffness Tensor with Spherical Convolutional Neural Networks
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Prediction of apparent trabecular bone Stiffness through fourth-order fabric Tensors
Biomechanics and Modeling in Mechanobiology, 2016Co-Authors: Rodrigo Moreno, Örjan Smedby, Dieter H. PahrAbstract:The apparent Stiffness Tensor is an important mechanical parameter for characterizing trabecular bone. Previous studies have modeled this parameter as a function of mechanical properties of the tissue, bone density, and a second-order fabric Tensor, which encodes both anisotropy and orientation of trabecular bone. Although these models yield strong correlations between observed and predicted Stiffness Tensors, there is still space for reducing accuracy errors. In this paper, we propose a model that uses fourth-order instead of second-order fabric Tensors. First, the totally symmetric part of the Stiffness Tensor is assumed proportional to the fourth-order fabric Tensor in the logarithmic scale. Second, the asymmetric part of the Stiffness Tensor is derived from relationships among components of the harmonic Tensor decomposition of the Stiffness Tensor. The mean intercept length (MIL), generalized MIL (GMIL), and fourth-order global structure Tensor were computed from images acquired through microcomputed tomography of 264 specimens of the femur. The predicted Tensors were compared to the Stiffness Tensors computed by using the micro-finite element method ( $$\upmu $$ μ FE), which was considered as the gold standard, yielding strong correlations ( $$R^2$$ R 2 above 0.962). The GMIL Tensor yielded the best results among the tested fabric Tensors. The Frobenius error, geodesic error, and the error of the norm were reduced by applying the proposed model by 3.75, 0.07, and 3.16 %, respectively, compared to the model by Zysset and Curnier (Mech Mater 21(4):243–250, 1995 ) with the second-order MIL Tensor. From the results, fourth-order fabric Tensors are a good alternative to the more expensive $$\upmu $$ μ FE Stiffness predictions.