From 3-D nonlinear elasticity theory to 1-D bars with nonconvex energy

Journal of Elasticity

Volumn 70, Issue 1-3, 2003, Pages 87-100

  Buonsanti, Michele ^a   Royer Carfagni, Gianni ^b  

^a UNIVERSITY MEDITERRANEA OF REGGIO CALABRIA   (Italy)

^b UNIVERSITY OF PARMA   (Italy)

Author keywords

Cold drawing; Necking; Nonconvex energy; Nonlinear elasticity; Nonsimple materials; Plasticity; Polyconvexity; Polymer

Indexed keywords

BARS (METAL); ELASTOPLASTICITY; INTERFACIAL ENERGY; KINEMATICS; MATHEMATICAL MODELS; METAL DRAWING; ONE DIMENSIONAL; POLYMERS; STRAIN; THREE DIMENSIONAL;

NONCONVEX ENERGY; NONLINEAR ELASTICITY THEORY; POLYCONVEXITY; STRAIN ENERGY;

ELASTICITY;

EID: 0346885675     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:ELAS.0000005633.22491.af     Document Type: Article

References (20)

1. I. Müller and P. Villaggio, A model for an elastic plastic Body. Arch. Rational Mech. Anal. 65 (1977) 25-56.
2. L. Truskinovsky, Fracture as a phase transition. In: R.C. Batra and M.F. Beatty (eds), Contemporary Research in the Mechanics and Mathematics of Materials, CINME, Barcellona (1996) pp. 322-332.
3. J.L. Ericksen, Equilibrium of bars. J. Elasticity 5 (1975) 191-201.
4. J.E. Dunn and R.L. Fosdick, The morphology and stability of material phases. Arch. Rational Mech. Anal. 74 (1980) 1-99.
5. J.W. Cahn and J.E. Hilliard, Free energy of a non uniform system. I. Interfacial free energy. J. Chem. Phys. 28 (1958) 258-267.
6. J. Carr, M. Gurtin, and M. Slemrod, One-dimensional structured phase transformations under prescribed loads. J. Elasticity 15 (1985) 133-142.
7. J. Carr, M. Gurtin, and M. Slemrod, Structured phase transition on a finite interval. Arch. Rational Mech. Anal. 86 (1984) 317-351.
8. B. Coleman, Necking and drawing in polymeric fibers under tension. Arch. Rational Mech. Anal. 83 (1983) 115-137.
9. P. Podio-Guidugli and M. Lembo, Internal constraints, reactive stresses and the Timoshenko beam theory. J. Elasticity 65 (2002) 131-148.
10. B. Coleman and D.C. Newman, Constitutive relations for elastic materials susceptible to drawing. In: V.K. Stokes and D. Krajcinovic (eds), Constitutive Modeling for Nontraditional Materials. ASME, New York (1987).
11. B. Coleman and D.C. Newman, On the rheology of cold drawing. I. Elastic materials. J. Polymer Sci. Part B Polymer Phys. 26 (1988) 1801-1822.
12. B. Coleman and D.C. Newman, Mechanics of neck formation in the cold drawing of elastic films. Polymer Engrg. Sci. 30 (1990) 1299-1302.
13. J. Ball, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 100 (1977) 337-403.
14. J.E. Marsden and T.J.R. Hughes, Mathematical Foundations of Elasticity. Dover, Mineola, NY (1994).
15. R. Fosdick and G. Royer-Carfagni, Multiple natural states for an elastic isotropic material with polyconvex stored energy. J. Elasticity 60 (2000) 223-231.
16. B. Dacorogna, Direct Methods in the Calculus of Variations. Springer, New York (1989).
17. G. Alberti, Variational models for phase transitions. An approach via Γ-convergence. In: Summer School on Differential Equations and Calculus of Variations, Pisa (16-28 September 1996) Lecture Notes.
18. A. Nadai, Theory of Flow and Fracture of Solids, Vol. I. McGraw-Hill, New York (1950).
19. M. Froli and G. Royer-Carfagni, Discontinuous deformation of tensile steel bars: Experimental results. J. Engrg. Mech. ASCE 125 (1999) 1243-1250.
20. M. Froli and G. Royer-Carfagni, A mechanical model for the elastic-plastic behavior of metallic bars. Internat. J. Solids Struct. 37 (2000) 3901-3918.