메뉴 건너뛰기




Volumn 82, Issue 3, 2006, Pages 273-296

On the averaging of symmetric positive-definite tensors

Author keywords

Averaging; Elasticity tensor; Geometric mean; Kullback Leibler mean; Symmetric positive definite tensors

Indexed keywords

COMPUTATIONAL GEOMETRY; ELASTICITY; MATHEMATICAL MODELS; MEASUREMENT THEORY; PROBLEM SOLVING;

EID: 33645812768     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10659-005-9035-z     Document Type: Article
Times cited : (156)

References (28)
  • 1
    • 0000940684 scopus 로고
    • A method of calculating the physical constants of polycrystalline materials
    • K. Aleksandrov and L. Aisenberg, A method of calculating the physical constants of polycrystalline materials. Sov. Phys. Dokl. 11 (1966) 323-325.
    • (1966) Sov. Phys. Dokl. , vol.11 , pp. 323-325
    • Aleksandrov, K.1    Aisenberg, L.2
  • 4
    • 0004151496 scopus 로고    scopus 로고
    • Springer, Berlin Heidelberg New York
    • R. Bhatia, Matrix Analysis. Springer, Berlin Heidelberg New York (1997).
    • (1997) Matrix Analysis
    • Bhatia, R.1
  • 5
    • 44049110894 scopus 로고
    • On the structure of the linear anisotropic symmetries
    • S.C. Cowin and M.M. Mehrabadi, On the structure of the linear anisotropic symmetries. J. Mech. Phys. Solids 40 (1992) 1459-1472.
    • (1992) J. Mech. Phys. Solids , vol.40 , pp. 1459-1472
    • Cowin, S.C.1    Mehrabadi, M.M.2
  • 6
    • 0031072752 scopus 로고    scopus 로고
    • Averaging anisotropic elastic constant data
    • S.C. Cowin and G. Yang, Averaging anisotropic elastic constant data. J. Elast. 46 (1999) 151-180.
    • (1999) J. Elast. , vol.46 , pp. 151-180
    • Cowin, S.C.1    Yang, G.2
  • 7
    • 33645804325 scopus 로고
    • The elastic constants of piesoelectric crystals
    • R.F.S. Hearmon, The elastic constants of piesoelectric crystals. J. Appl. Phys. 3 (1952) 120123.
    • (1952) J. Appl. Phys. , vol.3 , pp. 120123
    • Hearmon, R.F.S.1
  • 9
    • 33144479510 scopus 로고
    • The elastic properties of crystalline aggregate
    • R. Hill, The elastic properties of crystalline aggregate. Proc. Phys. Soc. A 65 (1952) 349-354.
    • (1952) Proc. Phys. Soc. A , vol.65 , pp. 349-354
    • Hill, R.1
  • 11
    • 0000831926 scopus 로고
    • Condition estimates for matrix functions
    • C.S. Kenney and A.J. Laub, Condition estimates for matrix functions. SIAM J. Matrix Anal. Appl. 10(1989) 191-209.
    • (1989) SIAM J. Matrix Anal. Appl. , vol.10 , pp. 191-209
    • Kenney, C.S.1    Laub, A.J.2
  • 12
  • 14
    • 0000419561 scopus 로고
    • On the principle of a geometric mean of even-rank symmetric tensors for textured polycrystals
    • S. Matthies and M Humbert, On the principle of a geometric mean of even-rank symmetric tensors for textured polycrystals. J. Appl. Crystallogr. 28 (1995) 254-266.
    • (1995) J. Appl. Crystallogr , vol.28 , pp. 254-266
    • Matthies, S.1    Humbert, M.2
  • 15
    • 0029255185 scopus 로고
    • Six-dimensional orthogonal tensor representation of the rotation about an axis in three dimensions
    • M.M. Mehrabadi, S.C. Cowin and J. Jaric, Six-dimensional orthogonal tensor representation of the rotation about an axis in three dimensions. Int. J. Solids Struct. 32 (1995) 439-449.
    • (1995) Int. J. Solids Struct. , vol.32 , pp. 439-449
    • Mehrabadi, M.M.1    Cowin, S.C.2    Jaric, J.3
  • 16
    • 0025387418 scopus 로고
    • Eigentensors of linear anisotropic elastic materials
    • M.M. Mehrabadi and S.C. Cowin, Eigentensors of linear anisotropic elastic materials. Quart. J. Mech. Appl. Math. 43(1) (1990) 15-41.
    • (1990) Quart. J. Mech. Appl. Math. , vol.43 , Issue.1 , pp. 15-41
    • Mehrabadi, M.M.1    Cowin, S.C.2
  • 17
    • 0037281553 scopus 로고    scopus 로고
    • Means and averaging in the group of rotations
    • M. Moakher, Means and averaging in the group of rotations. SIAM J. Matrix Anal. Appl. 24 (2002) 1-16.
    • (2002) SIAM J. Matrix Anal. Appl. , vol.24 , pp. 1-16
    • Moakher, M.1
  • 18
    • 22944439423 scopus 로고    scopus 로고
    • A differential geometric approach to the geometric mean of symmetric positivedefinite matrices
    • M. Moakher, A differential geometric approach to the geometric mean of symmetric positivedefinite matrices. SIAM J. Matrix Anal. Appl. 26 (2005) 735-747.
    • (2005) SIAM J. Matrix Anal. Appl. , vol.26 , pp. 735-747
    • Moakher, M.1
  • 19
    • 33645544879 scopus 로고    scopus 로고
    • Symmetric positive definite matrices: From geometry to applications and visualization
    • Chapter 17 J. Weickert and H. Hagen (eds.).Springer, Berlin Heidelberg New York
    • M. Moakher and P.O. Batchelor, Symmetric positive definite matrices: From geometry to applications and visualization. Chapter 17 In: J. Weickert and H. Hagen (eds.), Visualization and Image Processing of Tensor Fields. Springer, Berlin Heidelberg New York (2005).
    • (2005) Visualization and Image Processing of Tensor Fields
    • Moakher, M.1    Batchelor, P.O.2
  • 20
    • 84990678853 scopus 로고
    • Calculation of polycrystal elastic constants from single crystal data
    • A. Morawiec, Calculation of polycrystal elastic constants from single crystal data. Phys. Status Solidi, B 154 (1989) 535-541.
    • (1989) Phys. Status Solidi, B , vol.154 , pp. 535-541
    • Morawiec, A.1
  • 21
    • 0014467539 scopus 로고
    • Averaging fourth-rank tensors with weight functions
    • P.R. Morris, Averaging fourth-rank tensors with weight functions. J. Appl. Phys. 40 (1969) 447-448.
    • (1969) J. Appl. Phys. , vol.40 , pp. 447-448
    • Morris, P.R.1
  • 22
    • 0001438007 scopus 로고
    • Functional calculus for sesquilinear forms and the purification map
    • W. Pusz and S.L. Woronowicz, Functional calculus for sesquilinear forms and the purification map. Rep. Math. Phys. 8 (1975) 159-170.
    • (1975) Rep. Math. Phys. , vol.8 , pp. 159-170
    • Pusz, W.1    Woronowicz, S.L.2
  • 23
    • 84956078977 scopus 로고
    • Berechnung der Fliebgrenze von Mischkristallen auf grand der Plastizitätsbedingung für Einkristalle. Z
    • A. Reuss, Berechnung der Fliebgrenze von Mischkristallen auf grand der Plastizitätsbedingung für Einkristalle. Z. Angew. Math. Mech. 9 (1929) 49-58.
    • (1929) Angew. Math. Mech. , vol.9 , pp. 49-58
    • Reuss, A.1
  • 24
    • 0000188055 scopus 로고
    • Optimization techniques on riemannian manifolds
    • AMS
    • S. Smith, Optimization techniques on Riemannian manifolds. In: Fields institute Communications, Vol. 3, AMS (1994) pp. 113-146.
    • (1994) Fields Institute Communications , vol.3 , pp. 113-146
    • Smith, S.1
  • 26
    • 0013389128 scopus 로고
    • Hermitian semidefinite matrix means and related matrix inequalities-an introduction
    • G.E. Trapp, Hermitian semidefinite matrix means and related matrix inequalities-an introduction. Linear and Multilinear Algebra 16 (1984) 113-123.
    • (1984) Linear and Multilinear Algebra , vol.16 , pp. 113-123
    • Trapp, G.E.1
  • 27
    • 84901259698 scopus 로고
    • Ueber die Beziehung zwischen den beiden
    • Elasticitätconstanten isotroper Körper
    • W. Voigt, Ueber die Beziehung zwischen den beiden Elasticitä tconstanten isotroper Körper. Ann. Phys. (Leipzig). 38 (1889) 573-587.
    • (1889) Ann. Phys. (Leipzig) , vol.38 , pp. 573-587
    • Voigt, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.