Computation of the exponential and other isotropic tensor functions and their derivatives

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 35-36, 2003, Pages 3985-3999

  Itskov, Mikhail ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

Closed form representation; Derivative of tensor function; Exponential tensor function; Isotropic tensor functions; Numerical accuracy; Recurrent procedure

Indexed keywords

ALGORITHMS; FUNCTIONS; INTEGRAL EQUATIONS;

ISOTROPIC TENSOR FUNCTIONS;

TENSORS;

MATHEMATICAL METHOD;

EID: 0042925510     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(03)00397-9     Document Type: Article

References (17)

1. Carlson D.E. Hoger A. The derivative of a tensor-valued function of a tensor Quart. Appl. Math. 44 1986 409-423
2. Chadwick P. Ogden R.W. A theorem of tensor calculus and its application to isotropic elasticity Arch. Ration. Mech. Anal. 44 1971 54-68
3. Hill R. Constitutive inequalities for isotropic elastic solids under finite strain Proc. R. Soc. Lond. A 314 1970 457-472
4. Itskov M. Application of the Dunford-Taylor integral to isotropic tensor functions and their derivatives Proc. R. Soc. Lond. A 459 2003 1449-1457
5. Itskov M. The derivative with respect to a tensor: Some theoretical aspects and applications Z. Angew. Math. Mech. (ZAMM) 82 2002 535-544
6. Itskov M. Aksel N. A closed-form representation for the derivative of non-symmetric tensor power series Int. J. Solids Struct. 39 2002 5963-5978
7. Kato T. Perturbation Theory for Linear Operators 1966 Springer New York
8. Miehe C. Exponential map algorithm for stress updates in anisotropic multiplicative elasto-plasticity for single crystals Int. J. Numer. Meth. Engrg. 39 1996 3367-3390
9. Miehe C. Lambrecht M. Algorithms for computation of stresses and elasticity moduli in terms of Seth-Hill's family of generalized strain tensors Commun. Numer. Meth. Engrg. 17 2001 337-353
10. Ortiz M. Radovitzky R.A. Repetto E.A The computation of the exponential and logarithmic mappings and their first and second linearizations Int. J. Numer. Meth. Engrg. 52 2001 1431-1441
11. Papadopoulos P. Lu J. A general framework for the numerical solution of problems in finite elasto-plasticity Comput. Methods Appl. Mech. Engrg. 159 1998 1-18
12. Rinehart R.F. The equivalence of definitions of a matric function Am. Math. Mon. 62 1955 395-414
13. Sansour C. Kollmann F.G. Large viscoplastic deformations of shells. Theory and finite element formulation Comput. Mech. 21 1998 512-525
14. Steinmann P. Stein E. On the numerical treatment and analysis of finite deformation ductile single crystal plasticity Comput. Methods Appl. Mech. Engrg. 129 1996 235-254
15. Truesdell C. Noll W. The Nonlinear Field Theories of Mechanics Flügge S. Handbuch der Physik, vol. III/3 1965 Springer Berlin
16. Xiao H. Unified explicit basis-free expressions for time rate and conjugate stress of an arbitrary Hill's strain Int. J. Solids Struct. 32 1995 3327-3340
17. Xiao H. Bruhns O.T. Meyers A.T.M. Strain rates and material spins J. Elasticity 52 1998 1-41