Minimal rotationally invariant bases for hyperelasticity

SIAM Journal on Applied Mathematics

Volumn 64, Issue 6, 2004, Pages 2050-2075

  Miller, Gregory H ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

Elasticity; Gr bner bases; Hyperelasticity; Integrity basis; Symmetry

Indexed keywords

GRODIE;BNER BASES; HYPERELASTICITY; INTEGRITY BASIS; SYMMETRY;

ALGORITHMS; FUNCTIONS; INVARIANCE; LAGRANGE MULTIPLIERS; POLYNOMIALS; PROBLEM SOLVING; TENSORS;

ELASTICITY;

EID: 11044230458     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139903438776     Document Type: Article

References (25)

1. E. A. ARNOLD, Modular algorithms for computing Gröbner bases, J. Symbolic Comput., 35 (2003), pp. 403-419.
2. D. BAYER AND M. STILLMAN, A theorem on refining division orders by the reverse lexicographical order, Duke Math. J., 55 (1987), pp. 321-328.
3. T. BECKER AND V. WEISPFENNING, Gröbner Bases: A Computational Approach to Commutative Algebra, Graduate Texts in Math. 141, Springer-Verlag, New York, 1993.
4. G. BIRKHOFF AND S. MACLANE, A Survey of Modern Algebra, 5th ed., A. K. Peters, Natick, MA, 1997.
5. B. BUCHBERGER, Gröbner bases: An algorithmic method in polynomial ideal theory, in Multi-dimensional Systems Theory, N. K. Bose, ed., D. Reidel, Boston, 1985, pp. 184-232.
6. F. A. COTTON, Chemical Applications of Group Theory, Wiley-Interscience, New York, 1990.
7. 4), J. Pure Appl. Algebra, 139 (1999), pp. 61-88.
8. S. FORTE AND M. VIANELLO, Symmetry classes for elasticity tensors, J. Elasticity, 43 (1996), pp. 81-108.
9. K. GATERMANN, Computer Algebra Methods for Equivariant Dynamical Systems, Springer-Verlag, Berlin, 2000.
10. R. GEBAUER AND H. M. MÖLLER, On an installation of Buchberger's algorithm, J. Symbolic Comput., 6 (1988), pp. 275-286.
11. A. GIOVINI, T. MORA, G. NIESI, L. ROBBIANO, AND C. TRAVERSO, "One sugar cube, please" or Selection strategies in the Buchberger algorithm, in Proceedings of the International Symposium on Algorithms and Computation, ACM, New York, 1991, pp. 49-54.
12. T. GRANLUND, GNU MP: The GNU Multiple Precision Arithmetic Library, edition 4.1.2, Tech. report, Swox AB, Stockholm, Sweden, 2002.
13. E. MAYR AND A. MEYER, The complexity of the word problem for commutative semigroups and polynomial ideals, Adv. Math., 46 (1982), pp. 305-329.
14. G. H. MILLER, An iterative Riemann solver for systems of hyperbolic conservation laws, with application to hyperelastic solid mechanics, J. Comput. Phys., 193 (2003), pp. 198-225.
15. G. H. MILLER AND P. COLELLA, A high-order Eulerian Godunov method for elastic-plastic flow in solids, J. Comput. Phys., 167 (2001), pp. 131-176.
16. G. H. MILLER AND P. COLELLA, A conservative three-dimensional Eulerian method for coupled fluid-solid shock capturing, J. Comput. Phys., 183 (2002), pp. 26-82.
17. T. MOLIEN, Über die invarianten der linearen Substitutionsgruppe, Sitzungsber. Königl. Preuss. Akad. Wiss., (1897), pp. 1152-1156.
18. F. D. MURNAGHAN, The Theory of Group Representations, Dover, New York, 1963.
19. N. SLOANE, Error-correcting codes and invariant theory: New applications of a nineteenth-century technique, Amer. Math. Monthly, 84 (1977), pp. 82-107.
20. G. F. SMITH AND R. S. RIVLIN, The strain-energy function for anisotropic elastic materials, Trans. Amer. Math. Soc., 88 (1958), pp. 175-193.
21. A. J. M. SPENCER, On generating functions for the number of invariants of orthogonal tensors, Mathematika, 17 (1970), pp. 275-286.
22. A. J. M. SPENCER, Theory of invariants, in Continuum Physics, Vol. 1, A. Eringen, ed., Academic Press, New York, 1971, pp. 239-353.
23. R. STANLEY, Invariants of finite groups and their applications to combinatorics, Bull. Amer. Math. Soc. (N.S.), 1 (1979), pp. 475-511.
24. B. STURMFELS, Algorithms in Invariant Theory, Springer-Verlag, New York, 1993.
25. H. WEYL, The Classical Groups, Their Invariants and Representations, Princeton University Press, Princeton, NJ, 1946.