Theory and finite element computations of a unified cyclic phase transformation model for monocrystalline materials at small strains

Computational Mechanics

Volumn 40, Issue 3, 2007, Pages 429-445

  Stein, Erwin ^a   Zwickert, Ole ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

Finite elements; Monocrystals; Numerical methods; Phase transformation; Shape memory

Indexed keywords

COMPUTATIONAL METHODS; CRYSTALLINE MATERIALS; ENERGY BARRIERS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; STRAIN MEASUREMENT;

MONOCRYSTALS; QUASIPLASTIC TEMPERATURE; SHAPE MEMORY;

PHASE TRANSITIONS;

EID: 34250796422     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-006-0118-x     Document Type: Article

References (14)

1. Ball JM, James RD (1987) Fine phase mixtures and minimizers of energy. Arch Rat Mech Anal 100:13-52
2. Bhattacharya K (2003) Microstructure of martensite : why it forms and how it gives rise to the shape-memory effect. Oxford University Press, Oxford
3. Carstensen C (2005) Ten remarks on nonconvex minimisation for phase transition simulations. Comput Methods Appl Mech Engrg 194:169-193
4. Govindjee S, Miehe C (2001) A multi-variant martensitic phase transformation model: formulation and numerical implementation. Comput Methods Appl Mech Engrg 191:215-238
5. Govindjee S, Mielke A, Hall GJ (2003) The free-energy of mixing for n-variant martensitic phase transformations using qausi-convex analysis. J Mech Phys Solids 52:I-XXVI
6. Hall GJ, Govindjee S (2002) Application of the relaxed free energy of mixing to problems in shape memory alloy simulation. J Intell Material Syst Struct 13:773-782
7. Howard G, Shield TW (1995) Orientation dependence of the pseudoelastic behavior of single crystals of Cu-Al-Ni in tension. J Mech Phys Solids 43:869-895
8. Levitas VI, Idesman AV, Stein E (1998) Finite element simulation of martensitic phase transitions in elastoplastic materials. Int J Solids Struct 35:855-887
9. Mielke A, Theil F, Levitas VI (2002) A variational formulation of rate-independent phase transformations using extremum principle. Arch Rational Mech Anal 162:137-177
10. Patoor E, Eberhardt A, Berveiller M (1995) Micromechanical modelling of superelasticity in shape memory alloys. J Phys IV C8-5:277-292
11. Stein E (ed) (2003) Error-controlled adaptive finite elements in solid mechanics. Chichester [u.a]: Wiley, New York
12. Uebel A (2002) Untersuchung des thermischen und Mechanischen Hystereseverhaltens von einkristallinen Cu82Al14Ni4- Formgedächtnislegierungen. Dissertation an der Fakultät III - Prozesswissenschaften der Universität Berlin
13. Winzek B (2000) Entwicklung, Herstellung und Charakterisierung von Mikroaktoren mit Formgedaechtnisschichten auf der Basis von TiNi. Dr.-Ing. thesis at Institut fuer Materialforschung, Programm Mikrosystemtechnik, Forschungszentrum Karlsruhe GmbH, Wissenschaftliche Berichte FZKA 6467
14. Xiangyang Z, Qingping S, Shouwen Y (2000) A non-invariant plane model for the interface in cualni single crystal shape memory alloys. J Mech Phy Solids 48:2163-2182