Self-similar voiding solutions of a single layered model of folding rocks

SIAM Journal on Applied Mathematics

Volumn 72, Issue 1, 2012, Pages 444-463

  Dodwell, T J ^a   Peletier, M A ^b   Budd, C J ^a   Hunt, G W ^a  

^a UNIVERSITY OF BATH   (United Kingdom)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Geological folding; Kuhn Tucker theorem; Nonlinear bending; Obstacle problem; Saddle reef; Voiding

Indexed keywords

GEOLOGICAL FOLDING; KUHN- TUCKER THEOREM; NON-LINEAR BENDING; OBSTACLE PROBLEMS; VOIDING;

MATHEMATICAL TECHNIQUES;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 84859905931     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/110822499     Document Type: Article

References (17)

1. J. A. Boon, C. J. Budd, and G. W. Hunt, Level set methods for the displacement of layered materials, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 463 (2007), pp. 1447-1466.
2. C. J. Budd, R. Edmunds, and G. W. Hunt, A nonlinear model for parallel folding with friction, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 459 (2003), pp. 2097-2119.
3. E. A. Coddington and N. Levinson, Theory of Differential Equations, McGraw-Hill, New York, 1955.
4. T. J. Dodwell, G. W. Hunt, M. A. Peletier, and C. J. Budd, Multilayered folding with voids, Phil. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., to appear.
5. R. Edmunds, G. W. Hunt, and M. A. Wadee, Parallel folding in multilayered structures, J. Mech. Phys. Solids, 54 (2006), pp. 384-400.
6. C. M. Elliot and J. R. Ockendon, Weak and Variational Methods for Free and Moving Boundary Problems, Pitman, Boston, 1982.
7. A. Griewank and P. J. Rabier, On the smoothness of convex envelopes, Trans. Amer. Math. Soc., 322 (1990), pp. 691-709.
8. G. W. Hunt, M. A. Peletier, and M. A. Wadee, The Maxwell stability criterion in pseudoenergy models of kink banding, J. Structural Geology, 22 (2000), pp. 669-681.
9. G. W. Hunt, M. A. Wadee, and M. A. Peletier, Friction models of kink-banding in compressed layered structures, in Proceedings of the 5th International Workshop on Bifurcation and Localization Theory in Geomechanics, Lisse, The Netherlands, Swets & Zeitlinger, 2001, pp. 249-256.
10. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, 1980.
11. J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, Convergence properties of the Nelder-Mead simplex method in low dimensions, SIAM J. Optim., 9 (1998), pp. 112-147.
12. D. G. Luenberger, Optimization by Vector Space Methods, Wiley-Interscience, New York, 1968.
13. A. Mielke, Hamiltonian and Lagrangian Flows on Center Manifolds (with Applications to Elliptic Variational Problems), Springer, New York, 1991.
14. J.G. Ramsay, Folding and Fracturing of Rocks, McGraw-Hill, New York, 1967.
15. W. Rudin, Real and Complex Analysis, 3rd ed., McGraw-Hill, New York, 1987.
16. J. M. T. Thompson and G. W. Hunt, A General Theory of Elastic Stability, Wiley, London, 1973.
17. M. A. Wadee, G. W. Hunt, and M. A. Peletier, Kink band instability in layered structures, J. Mech. Phys. Solids, 52 (2004), pp. 1071-1091.