Material forces and phase transitions in elasticity

Archive of Applied Mechanics

Volumn 77, Issue 2-3, 2007, Pages 135-146

  Kalpakides, V K ^a   Balassas, K G ^a   Massalas, C V ^a  

^a UNIVERSITY OF IOANNINA   (Greece)

Author keywords

Inverse deformation function; Martensitic materials; Material force; Two phase elastic body

Indexed keywords

COMPUTATION THEORY; ELASTICITY; MARTENSITIC TRANSFORMATIONS; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS; NUMERICAL ANALYSIS; PHASE TRANSITIONS;

INVERSE DEFORMATION FUNCTION; MARTENSITIC MATERIALS; MATERIAL FORCE; TWO-PHASE ELASTIC BODY;

FORCE CONTROL;

EID: 33846794192     PISSN: 09391533     EISSN: 14320681     Source Type: Journal    
DOI: 10.1007/s00419-006-0071-3     Document Type: Conference Paper

References (24)

1. Abeyaratne, R., Knowles, J.K. (1990) On the driving traction acting on a surface of strain discontinuity in a continuum. J. Mech. Phys. Solid 38, 345-360
2. Abeyaratne, R., Bhattacharya, K., Knowles, J.K. (2001) Strain-Energy functions with multiple local minima: Modeling phase transformations using finite thermoelasticity. In: Fu, Y., Ogden, R.W. (eds.) Nonlinear Elasticity: Theory and Applications, pp. 433-490. Cambridge Univ. Press, Cambridge
3. Askes, J., Kuhl, E., Steinmann, P. (2004) An ALE formulation based on spatial and material settings of continuum mechanics. Part 2: classification and applications. Comput. Methods Appl. Mech. Eng. 193, 4223-4245
4. Balassas, K.G., Kalpakides, V.K.: The use of material forces in a phase transition problem (submitted for publication to Comput. Methods Appl. Mech. Eng.)
5. Balassas, K.G., Kalpakides, V.K., Stavroulakis, G.E. (2005) The use of material forces to improve the finite element solution in elasticity. J. Mech. Behav. Mat. 16, 269-278
6. Braun, M. (1997) Configurational forces induced by finite-element discretization. Proc. Estonian Acad. Sci. Phys. Math. 46, 24-31
7. Edelen, D.J.D. (1981) Aspects of variational arguments in the theory of elasticity - fact and folklore. Int. J. Solids Struct. 17, 729-740
8. Ericksen, J.L. (1975) Equilibrium of bars. J. Elast. 5, 191-201
9. Gurtin, M.E. (2000) Configurational Forces as Basic Concepts of Continuum Physics. In: Applied Mathematical Sciences, vol. 37, Springer, Berlin Heidelberg New York
10. Kalpakides, V.K., Balassas, K.G. (2005) The Inverse deformation mapping in the finite element method. Phil. Mag. 85, 4257-4275
11. Kienzler, R., Herrmann, G. (2000) Mechanics in Material Space with applications to defect and Fracture Mechanics. Springer, Berlin Heidelberg New York
12. Kienzler, R., Herrmann, G. (2002) Fracture criteria based on local properties of the Eshelby tensor. Mech. Res. Commun. 29, 521-527
13. Kuhl, E., Steinmann, P. (2004) On the impact of Configurational mechanics on computational mechanics. In: Kalpakides, V.K., Maugin, G.A. (eds.), Configurational Mechanics, pp. 15-29. Balkema, Leiden
14. Kuhl, E., Denzer, R., Barth, F.J., Steinmann, P. (2004) Application of the material force method to thermo-hyperelasticity. Comput. Methods Appl. Eng. 193, 3303-3325
15. Maugin, G.A. (1993) Material Inhomogeneities in Elasticity. Chapman and Hall, London
16. Maugin, G.A. (2000) Geometry of material space: its consequences in modern computational means. Tech. Mech. 20, 95-104
17. Maugin, G.A., Kalpakides, V.K. (2002) A Hamiltonian formulation of elasticity and thermoelasticity. J. Phys. A: Math. Gen. 35, 10775-10788
18. Mueller, R., Maugin, G.A. (2002) On material forces and finite element discretization. Comp. Mech. 29, 52-60
19. Mueller, R., Kolling, S., Gross D. (2002) On configurational forces in the context of the finite element method. Int. J. Numer. Methods Eng. 53, 1557-1574
20. Mueller, R., Gross D., Maugin, G.A. (2004) Use of material forces in adaptive finite element methods. Comp. Mech. 33, 421-434
21. Oden, J.T. (1972) Finite Elements of Nonlinear Continua. McGraw-Hill, New York, pp. 284-292
22. Steinmann, P. (2002) On spatial and material settings of hyperelastostatic crystal defects. J. Mech. Phys. Solids 50, 1743-1766
23. Steinmann, P., Ackermann, D., Barth, F.J. (2001) Applications of material forces to hyperelastic fracture mechanics. Part II. Computational setting. Int. J. Solids Struct. 38, 5509-5526
24. Thoutireddy, P. (2003) Variational arbitrary Lagrangian-Eulerian method. Ph.D. Thesis, California Institute of Technology, Pasadena, California