The explicit determination of the logarithm of a tensor and its derivatives

Journal of Elasticity

Volumn 93, Issue 2, 2008, Pages 141-148

  Jog, C S ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Derivatives; Logarithm of a tensor

Indexed keywords

TENSORS;

DERIVATIVES; ELASTIC MATERIALS; LOGARITHM OF A TENSOR; NON-LINEAR CONSTITUTIVE RELATIONS; SPACE DIMENSIONS;

ALGEBRA;

EID: 52549121977     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10659-008-9169-x     Document Type: Article

References (10)

1. L. Anand 1979 On H. Hencky's approximate strain energy function for moderate deformations ASME J. Appl. Mech. 46 78 82
2. L. Anand 1986 Moderate deformations in extension-torsion of incompressible isotropic elastic materials J. Mech. Phys. Solids 34 293 304
3. J.R. Cardoso 2005 An explicit formula for the matrix logarithm S. Afr. Optom. 64 3 80 83
4. S.H. Cheng N.J. Higham C.S. Kenney A.L. Laub 2001 Approximating the logarithm of a matrix to specified accuracy SIAM J. Matrix Anal. Appl. 22 4 1112 1125
5. Gurtin, M.E.: An Introduction to Continuum Mechanics. Academic Press, New York (1981)
6. Hoffman, K.M., Kunze, R.: Linear Algebra. Prentice Hall, New York (1971)
7. Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, Cambridge (1991)
8. H. Xiao 1995 Unified explicit basis-free expressions for time rate and conjugate stress of an arbitrary Hill's strain Int. J. Solids Struct. 32 22 3327 3340
9. E.M.E. Wermuth 1989 Two remarks on matrix exponentials Linear Algebra Appl. 117 127 132
10. J.A. Wood 2004 The chain rule for matrix exponential functions Coll. Math. J. 35 3 220 222