Dynamics of chains with non-monotone stress-strain relations. I. Model and numerical experiments

Journal of the Mechanics and Physics of Solids

Volumn 49, Issue 1, 2001, Pages 131-148

  Balk, Alexander M ^a   Cherkaev, Andrej V ^a   Slepyan, Leonid I ^b  

^a UNIVERSITY OF UTAH   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

HYSTERESIS; MASS TRANSFER; MATHEMATICAL MODELS; PHASE TRANSITIONS; STRAIN; STRESS ANALYSIS; VARIATIONAL TECHNIQUES; VIBRATIONS (MECHANICAL);

NONMONOTONE STRESS-STRAIN RELATIONS;

STRUCTURAL ANALYSIS;

EID: 0035202323     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(00)00025-9     Document Type: Article

References (18)

1. Ball J., James R. Finite phase mixtures as minimizers of energy. Arch. Rat. Mech. Anal. 100:1987;13-52.
2. Ball J., James R. Proposed experimental tests of a theory of fine microstructure and two-well problem. Phil. Trans. Roy. Soc. Lon. 338A:1992;389-450.
3. Bhattacharya K., Kohn R.V. Elastic energy minimization and the recoverable strains of polycrystalline shape-memory materials. Arch. Rat. Mech. Anal. 139:1997;99-180.
4. Bruno O. Quasistatic dynamics and pseudoelasticity in polycrystalline shape memory wires. Smart Mater. Struct. 4:1995;7-13.
5. Cherkaev A.V. Relaxation of problems of optimal structural design. Int. J. Solids Struct. 31:1994;2251-2280.
6. Ericksen J. Some phase transitions in crystals. Arch. Rat. Mech. Anal. 73:1980;99-124.
7. Ericksen J. Constitutive theory for some constrained elastic crystals. J. Solids and Struct. 22:1986;951-964.
8. Faciu C., Suliciu I. A Maxwellian model for pseudoelastic materials. Scripta Metallurgica et Materialia. 31:1994;1399-1404.
9. Kaganova I., Roitburd A. Equilibrium shape of an inclusion in a solid. Sov. Phys. Dokl. 32:1987;925-927.
10. Khachaturyan A.G. Theory of Structural Transformations in Solids. 1983;Wiley.
11. Kohn R.V. The relaxation of a double-well energy. Continuum Mech. Thermodyn. 3:1991;193-236.
12. Luskin, M., 1996. On the computation of crystalline microstructure. Acta Numerica.
13. Rogers R.C., Truskinovsky L. Discretization and hysteresis. Physica B. 233:1997;370-375.
14. Rosakis P., Knowles J. Unstable kinetic relations and the dynamics of solid-solid phase transitions. J. Mech. Phys. Solids. 45:1997;2055-2081.
15. Suliciu I. Some stability-instability problems in phase transitions modelled by piecewise linear elastic or viscoelastic constitutive equations. Int. J. Engng. Sci. 30:1992;483-494.
16. Truskinovsky L. Nucleolion and growth in elasticity. Duxbury P., Pence T. Dynamics of Crystal Surfaces and Interfaces. 1997;185-197 Plenum, New York.
17. Truskinovsky L., Zanzotto G. Ericksen's bar revisited: energy wiggles. J. Mech. Phys. Solids. 44:1996;1371-1408.
18. Vainshtein, A., Healey, T., Rosakis, P., Truskinovsky, L., 1997. The role of the spinodal region in one-dimensional martensitic phase transitions. Physica D.