A finite element framework for continua with boundary energies. Part I: The two-dimensional case

Computer Methods in Applied Mechanics and Engineering

Volumn 198, Issue 27-29, 2009, Pages 2198-2208

  Javili, A ^a   Steinmann, P ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Boundary potentials; Surface tension

Indexed keywords

BOUNDARY EFFECTS; BOUNDARY ENERGIES; BOUNDARY POTENTIALS; CONVECTED COORDINATES; DEFORMATION GRADIENTS; DISCRETIZATION; FINITE ELEMENT IMPLEMENTATIONS; FINITE ELEMENTS; MATERIAL BEHAVIORS; MATERIAL MODELS; NUMERICAL EXAMPLES; WEAK FORMULATIONS;

CAPILLARITY; CONTINUUM MECHANICS; DEFORMATION; ELASTICITY; FINITE ELEMENT METHOD; SURFACE CHEMISTRY; SURFACE PROPERTIES; SURFACE TENSION; SURFACE WAVES; TWO DIMENSIONAL; WETTING;

BOUNDARY ELEMENT METHOD;

EID: 64749094700     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2009.02.008     Document Type: Article

References (39)

1. Adam N.K. The Physics and Chemistry of Surfaces (1941), Oxford University Press, London
2. Gurtin M.E. A continuum theory for elastic material surfaces. Arch. Ration. Mech. Anal. 112 (1975) 97-160
3. Gurtin M.E., and Murdoch A. A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57 (1975) 291-323
4. Lifshitz E.M., and Landau L.D. Fluid Mechanics. Course of Theoretical Physics. second ed. vol. 6 (1987), Butterworth-Heinemann
5. Leo P.H., and Sekerka R.F. The effect of surface stress on crystal-melt and crystal-crystal equilibrium. Acta Metall. 37 (1989) 3119-3138
6. Leo P.H., and Sekerka R.F. The effect of elastic fields on the morphological stability of a precipitate grown from solid solution. Acta Metall. 37 (1989) 3139-3149
7. Kreyszig E. Differential Geometry (1991), Dover Publications
8. Gruttmann F., and Taylor R.L. Theory and finite element formulation of rubberlike membrane shells using principal stretches. Int. J. Numer. Methods Engrg. 35 (1992) 1111-1126
9. Marsden J.E., and Hughes T.J.R. Mathematical Foundations of Elasticity (1994), Dover Publications
10. Olson L., and Kock E. A variational approach for modelling surface tension effects in inviscid fluids. Comput. Mech. 14 2 (1994) 140-153
11. Bathe K.J. Finite Element Procedures (Part 1-2). second ed. (1995), Prentice Hall
12. Adamson W., and Gast A.P. Physical Chemistry of Surfaces (1997), Wiley-Interscience
13. Navti S.E., Ravindran K., Taylor C., and Lewis R.W. Finite element modelling of surface tension effects using a Lagrangian-Eulerian kinematic description. Comput. Methods Appl. Mech. Engrg. 147 (1997) 41-60
14. Simha N.K., and Bhattacharya K. Equilibrium conditions at corners and edges of an interface in a multiphase solid. Mater. Sci. Eng. A238 (1997) 32-41
15. Simha N.K., and Bhattacharya K. Kinetics of phase boundaries with edges and junctions. J. Mech. Phys. Solids 46 (1998) 2323-2359
16. Simha N.K., and Bhattacharya K. Kinetics of phase boundaries with edges and junctions in a three-dimensional multiphase body. J. Mech. Phys. Solids 48 (2000) 2619-2641
17. Johnson WC. Superficial stress and strain at coherent interfaces. Acta Mater. 48 (2000) 433-444
18. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (2000), Dover Publications
19. Bellet M. Implementation of surface tension with wall adhesion effects in a three-dimensional finite element model for fluid flow. Commun. Numer. Methods Engrg. 17 8 (2001) 563-579
20. Haiss W. Surface stress of clean and adsorbate-covered solids. Rep. Prog. Phys. 64 (2001) 591-648
21. Dettmer W., Saksono P.H., and Perić D. On a finite element formulation for incompressible newtonian fluid flows on moving domains in the presence of surface tension. Commun. Numer. Methods Engrg. 19 9 (2003) 659-668
22. Fischer F.D., Simha N.K., and Svoboda J. Kinetics of diffusional phase transformation in multicomponent elastic-plastic materials. ASME J. Eng. Mater. Technol. 125 (2003) 266-276
23. Kuhl E., Askes H., and Steinmann P. An ale formulation based on spatial and material settings of continuum mechanics. Part 1: Generic hyperelastic formulation. Comput. Methods Appl. Mech. Engrg. 193 (2004) 4207-4222
24. E. Fried, M.E. Gurtin, AA unified treatment of evolving interfaces accounting for small deformations and atomic transport with emphasis on grain-boundaries and epitaxy, in: H. Aref, E. Van der Giessen (Eds.), Advances in Applied Mechanics, 40 (2004) 1-177.
25. Kaptay G. Classification and general derivation of interfacial forces, acting on phases, situated in the bulk, or at the interface of other phases. J. Mater. Sci. 40 (2005) 2125-2131
26. Steinmann P., and Häsner O. On material interfaces in thermomechanical solids. Arch. Appl. Mech. 75 (2005) 31-41
27. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method for Solid and Structural Mechanics. sixth ed. (2005), Butterworth-Heinemann
28. Ciarlet P.G. An Introduction to Differential Geometry with Applications to Elasticity (2006), Springer
29. Dettmer W., and Perić D. A computational framework for free surface fluid flows accounting for surface tension. Comput. Methods Appl. Mech. Engrg. 195 23-24 (2006) 3038-3071
30. Saksono P.H., and Perić D. On finite element modelling of surface tension. Variational formulation and applications-Part I: quasistatic problems. Comput. Mech. 38 (2006) 265-281
31. Saksono P.H., and Perić D. On finite element modelling of surface tension. Variational formulation and applications-Part II: dynamic problems. Comput. Mech. 38 (2006) 251-263
32. Yang F. Effect of interfacial stresses on the elastic behavior of nanocomposite materials. J. Appl. Phys. 99 (2006) 054306
33. Kramer D., and Weissmüller J. A note on surface stress and surface tension and their interrelation via Shuttleworth's equation and the Lippmann equation. Surf. Sci. 601 (2007) 3042-3051
34. Mosler J., and Ortiz M. Variational h-adaption in finite deformation elasticity and plasticity. Int. J. Numer. Methods Engrg. 72 5 (2007) 505-523
35. Mosler J. A novel variational algorithmic formulation for wrinkling at finite strains based on energy minimization: application to mesh adaption. Comput. Methods Appl. Mech. Engrg. 197 (2007) 1131-1146
36. Bonet J., and Wood R.D. Nonlinear Continuum Mechanics for Finite Element Analysis. second ed. (2008), Cambridge University Press
37. Fischer F.D., Waitz T., Vollath D., and Simha N.K. On the role of surface energy and surface stress in phase-transforming nanoparticles. Prog. Mater. Sci. 53 (2008) 481-527
38. Steinmann P. On boundary potential energies in deformational and configurational mechanics. J. Mech. Phys. Solids 56 3 (2008) 772-800
39. Yun G., and Park H.S. A multiscale, finite deformation formulation for surface stress effects on the coupled thermomechanical behavior of nanomaterials. Comput. Methods Appl. Mech. Engrg. 197 (2008) 3337-3350