Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

     

Higher derivatives and the inverse derivative of a tensor-valued function of a tensor

Author(s): Andrew N. Norris
Journal: Quart. Appl. Math. 66 (2008), 725-741.
MSC (2000): Primary 15-XX, 15A24
Posted: September 11, 2008
MathSciNet review: 2465142
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: The $ n^{th}$ derivative of a tensor-valued function of a tensor is defined by a finite number of coefficients each with closed form expression.


References:

1.
D. E. Carlson and A. Hoger, The derivative of a tensor-valued function of a tensor, Q. Appl. Math. 44 (1986), 409-423. MR 860894 (87j:53024)

2.
P. Chadwick and R. W. Ogden, A theorem of tensor calculus and its application to isotropic elasticity, Arch. Rat. Mech. Anal. 44 (1971), no. 1, 54-68. MR 0334656 (48:12975)

3.
Y-C. Chen and G-S. Dui, The derivative of isotropic tensor functions, elastic moduli and stress rate: I. Eigenvalue formulation, Math. Mech. Solids 9 (2004), no. 5, 493-511. MR 2094142 (2005e:74001)

4.
W. F. Donoghue, Jr., Monotone matrix functions and analytic continuation, Springer-Verlag, New York, 1974. MR 0486556 (58:6279)

5.
Guan-Suo Dui, Some basis-free formulae for the time rate and conjugate stress of logarithmic strain tensor, J. Elasticity 83 (2006), no. 2, 113-151. MR 2242836

6.
R. Hill, Aspects of invariance in solid mechanics, Adv. Appl. Mech. 18 (1978), 1-75. MR 564892 (84f:73002)

7.
M. Itskov and N. Aksel, A closed-form representation for the derivative of non-symmetric tensor power series, Int. J. Solids Struct. 39 (2002), no. 24, 5963-5978. MR 2123747 (2005i:74003)

8.
C. S. Jog, Derivatives of the stretch, rotation and exponential tensors in n-dimensional vector spaces, J. Elasticity 82 (2006), no. 2, 175-192. MR 2230236 (2006m:74015)

9.
O. Kintzel and Y. Bascedilar, Fourth-order tensors - tensor differentiation with applications to continuum mechanics. I: Classical tensor analysis, Z. Angew. Math. Mech. 86 (2006), no. 4, 291-311. MR 2216494 (2007d:53018)

10.
R. W. Ogden, Non-linear elastic deformations, Ellis Horwood, 1984.

11.
L. Rosati, A novel approach to the solution of the tensor equation AX+XA=H, Int. J. Solids Struct. 37 (2000), no. 25, 3457-3477. MR 1751369 (2000m:74006)

12.
M. Scheidler, Time rates of generalized strain tensors. Part I: Component formulas, Mech. Materials 11 (1991), 199-210.

13.
-, The tensor equation $ {AX+XA=F(A,H)}$, with applications to kinematics of continua, J. Elasticity 36 (1994), no. 2, 117-153. MR 1314315 (96e:73019)

14.
H. Xiao, O. T. Bruhns, and A. Meyers, Strain rates and material spins, J. Elasticity 52 (1998), no. 1, 1-41. MR 1673216 (99m:73021)


Similar Articles:

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 15-XX, 15A24

Retrieve articles in all Journals with MSC (2000): 15-XX, 15A24


Additional Information:

Andrew N. Norris
Affiliation: Mechanical and Aerospace Engineering, Rutgers University, Piscataway, New Jersey 08854-8058
Email: norris@rutgers.edu
PII: S0033-569X-08-01108-2
Received by editor(s): June 28, 2007
Posted: September 11, 2008
Copyright of article: Copyright 2008, Brown University
The copyright for this article reverts to public domain after 28 years from publication.



Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2012 Brown University
Comments: qam-query@ams.org
AMS Website