A class of exact solutions for a 3D filamentary continuous medium

Computers and Mathematics with Applications

Volumn 53, Issue 2, 2007, Pages 317-323

  Baesu, Eveline ^a  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

Author keywords

Elastic; Fiber; Networks

Indexed keywords

COMPUTER NETWORKS; CONSTITUTIVE EQUATIONS; DEFORMATION; DIFFERENTIAL EQUATIONS; ELASTIC CONSTANTS; FIBERS;

CONVEXITY CONDITIONS; HOMOGENEOUS DEFORMATIONS; UNIQUE SOLUTION;

KINEMATICS;

EID: 34247488305     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.02.052     Document Type: Article

References (25)

1. Tchebychev P.L. Sur la coupe des vetements. Assoc. Franc. pour. l'avancement des sci., CongrPes des Paris 154 (1878)
2. Stoker J.J. Differential Geometry (1969), Wiley-Interscience, New York
3. Rivlin R.S. Plane strain of a net formed by inextensible rods. J. Ration. Mech. Anal. 4 (1955) 951
4. Adkins J.E. Finite plane deformation of thin elastic sheets reinforced with inextensible cords. Philos. Trans. R. Soc. Lond. Ser. A 249 (1956) 125
5. Green A.E., and Adkins J.E. Large Elastic Deformations. 2nd edition (1970), Clarendon Press, Oxford
6. Rivlin R.S. The deformation of a membrane formed by inextensible rods. Arch. Ration. Mech. Anal. 2 (1959) 447
7. Kuznetsov E.N. Theory of instantaneously rigid nets. Appl. Math. Mech. (PMM) 29 (1965) 654
8. Kuznetsov E.N. Introduction to the Theory of Cable Systems (1969), Publishing House of Construction Literature, Moscow (in Russian)
9. Kuznetsov E.N. Axisymmetric static nets. Internat. J. Solids Structures 18 (1982) 1103
10. Pipkin A.C. Some developments in the theory of inextensible networks. Quart. Appl. Math. 38 (1980) 343
11. Pipkin A.C. Plane traction problems for inextensible networks. Quart. J. Mech. Appl. Math. 34 (1981) 415
12. Pipkin A.C. Equilibrium of Tchebychev nets. Arch. Ration. Mech. Anal. 85 (1984) 81
13. Green W.A., and Shi J. Plane deformations of membranes formed with elastic cords. Quart. J. Mech. Appl. Math. 43 (1990) 317
14. Steigmann D.J., and Pipkin A.C. Equilibrium of elastic nets. Philos. Trans. R. Soc. Lond. Ser. A 335 (1991) 419
15. Steigmann D.J. Equilibrium of pre-stressed networks. IMA J. Appl. Math. 48 (1992) 195
16. McLaughlin P.V. Plastic limit behavior and failure of filament reinforced materials. Internat. J. Solids Structures 8 (1972) 1299
17. McLaughlin P.V., and Batterman S.C. Limit behavior of fibrous materials. Internat. J. Solids Structures 6 (1970) 1357
18. McLaughlin P.V., Majumdar S., and Phillips J.W. Elastic behavior, brittle fracture and plastic flow of filamentary networks. Internat. J. Solids Structures 9 (1973) 951
19. E. Baesu, Elastic-plastic behavior of filamentary networks, in: Proceedings of the ASME Winter Annual Meeting, Orlando, FL, 2000
20. Baesu E. Finite deformations of elastic-plastic filamentary networks. J. Nonlinear. Mech. 38 (2003) 1473
21. E. Baesu, M. Zheng, D. Beljic, A continuum model of 2D fiber networks, in: C. Viney, et al. (Eds.), Symposium on Mechanical Properties of Bioinspired and Biological Materials (MRS Proceedings Volume 844Y), 2004
22. Hill R. On uniqueness and stability in the theory of finite elastic strain. J. Mech. Phys. Solids 5 (1957) 229
23. Graves L.M. The Weierstrass condition for multiple integral variation problems. Duke Math. J. 5 (1939) 656
24. Gao D. Duality Principles in Nonconvex Systems (1999), Kluwer Academic Publishers, Dordrecht
25. van Tiel J. Convex Analysis - An Introduction (1984), Wiley, New York