On general isotropic tensor functions of one tensor

International Journal for Numerical Methods in Engineering

Volumn 61, Issue 6, 2004, Pages 880-895

  de Souza Neto, E A ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Isotropic tensor functions; Spectral representation; Tensor function derivatives

Indexed keywords

ALGORITHMS; CONTINUUM MECHANICS; EIGENVALUES AND EIGENFUNCTIONS; TENSORS;

COMPUTATIONAL MECHANICS; EIGENPROJECTION; FUNCTION DERIVATIVES; TENSOR FUNCTIONS;

FUNCTIONS;

MATHEMATICAL METHOD;

EID: 4644233289     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1094     Document Type: Article

References (13)

1. Chadwick P, Ogden RW. A theorem in tensor calculus and its application to isotropic elasticity. Archive for Rational Mechanics and Analysis 1971; 44:54-68.
2. Miehe C, Lambrecht M. Algorithms for computation of stresses and elasticity moduli in terms of Seth-Hill's family of generalized strain tensors. Communications in Numerical Methods in Engineering 2001; 17(5):337-353.
3. Carlson DE, Hoger A. The derivative of a tensor-valued function of a tensor. Quarterly of Applied Mathematics 1986; 44(3):409-423.
4. Miehe C. Computation of isotropic tensor functions. Communications in Numerical Methods in Engineering 1993; 9:889-896.
5. Hoger A. The material time derivative of the logarithmic strain. International Journal of Solids and Structures 1986; 22(9):1019-1032.
6. de Souza Neto EA. The exact derivative of the exponential of an unsymmetric tensor. Computer Methods in Applied Mechanics and Engineering 2001; 190:2377-2383.
7. Ortiz M, Radovitzky RA, Repetto EA. The computation of the exponential and logarithmic mappings and their first and second linearizations. International Journal for Numerical Methods in Engineering 2001; 52(12):1431-1441.
8. Miehe C, Shotte J. Lambrecht M. Homogenization of inelastic solid materials at finite strains based on incremental minimization principles. Application to the texture analysis of polycrystals. Journal of the Mechanics and Physics of Solids 2002; 50(10):2123-2167.
9. Itskov M. Application of the Dunford-Taylor integral to isotropic tensor functions and their derivatives. Proceedings of the Royal Society of London Series A 2003; 459:1449-1457.
10. Ogden RW. Non-linear Elastic Deformations. Ellis Horwood: Chichester, 1984.
11. de Souza Neto EA, Perić D, Owen DRJ. A phenomenological three-dimensional rate-independent continuum damage model for highly filled polymers: formulation and computational aspects. Journal of the Mechanics and Physics of Solids 1994; 42(10):1533-1550.
12. de Souza Neto EA, Perić D, Owen DRJ. Continuum modelling and numerical simulation of material damage at finite strains. Archives of Computational Methods in Engineering 1998; 5:311-384.
13. Perić D, de Souza Neto EA. A new computational model for tresca plasticity at finite strains with an optimal parameterization in the principal space. Computer Methods in Applied Mechanics and Engineering 1999; 171:463-489.