A nested dynamic multi-scale approach for 3D problems accounting for micro-scale multi-physics

Computer Methods in Applied Mechanics and Engineering

Volumn 199, Issue 21-22, 2010, Pages 1342-1351

  Wiechert, L ^a   Wall, W A ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Biomechanics; Computational homogenization; Dynamics; Interfacial phenomena; Multi scale method; Surfactant

Indexed keywords

3-D PROBLEMS; COMPUTATIONAL HOMOGENIZATION; CONSTITUTIVE ASSUMPTION; DYNAMIC SIMULATION; FINITE ELEMENT ANALYSIS; FIRST-ORDER; INTERFACIAL PHENOMENA; LARGE DEFORMATIONS; LOCAL SCALE; MACRO SCALE; MICRO-SCALES; MICRO-STRUCTURAL; MULTI-PHYSICS; MULTI-SCALE APPROACHES; MULTISCALE METHOD; QUASI-STATIC; SOLUTION TECHNIQUES; STRESS-STRAIN RELATIONSHIPS; STRUCTURAL PROBLEMS; SURFACTANT FILMS; TIME INTEGRATION; TRANSFER OF INFORMATION; TRANSIENT EFFECT;

BIOMECHANICS; HOMOGENIZATION METHOD; STRESS-STRAIN CURVES; SURFACE ACTIVE AGENTS; THREE DIMENSIONAL;

DYNAMICS;

EID: 76549118221     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2009.09.017     Document Type: Article

References (40)

1. C. Bayreuther, Mehrskalenmodelle in der Festkörpermechanik und Kopplung von Mehrgittermethoden mit Homogenisierungsverfahren, Ph.D. Thesis, Universität Stuttgart.
2. Chung J., and Hulbert G.M. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-alpha method. J. Appl. Mech. 60 (1993) 371-375
3. Denny E., and Schroter R.C. A model of non-uniform lung parenchyma distortion. J. Biomech. 39 4 (2006) 652-663
4. 2) to describe the response of highly non-linear structures using generalized continua. Comput. Methods Appl. Mech. Engrg. 192 (2003) 3233-3244
5. 2 multiscale approach for modelling the elastoviscoplastic behaviour of long fiber sic/ti composite materials. Comput. Methods Appl. Mech. Engrg. 183 (2000) 309-330
6. Gee M., Hu J., and Tuminaro R. A new smoothed aggregation multigrid method for anisotropic problems. Numer. Linear Algebr. Appl. 16 (2009) 19-37
7. Gefen A., Halpern P., Shiner R.J., Schroter R.C., and Elad D. Analysis of mechanical stresses within the alveolar septa leading to pulmonary edema. Technol. Health Care 9 3 (2001) 257-267
8. Ghosh S., Lee K., and Moorthy S. Multiple scale analysis of heterogeneous elastic structures using homogenisation theory and voronoi cell finite element method. Int. J. Solid Struct. 32 (1995) 27-62
9. Ghosh S., Lee K., and Raghavan P. A multi-level computational model for multi-scale damage analysis in composite and porous materials. Int. J. Solid Struct. 38 (2001) 2335-2385
10. Gitman I.M., Gitman M.B., and Askes H. Quantification of stochastically stable representative volumes for random heterogeneous materials. Arch. Appl. Mech. 75 (2006) 79-92
11. Gravemeier V., Lenz S., and Wall W. Towards a taxonomy for multiscale methods on computational mechanics: building blocks of existing methods. Comput. Mech. 41 (2008) 279-291
12. Hauptmann R., Schweizerhof K., and Doll S. Extension of the 'solid-shell' concept for application to large elastic and large elastoplastic deformations. Int. J. Numer. Meth. Engrg. 49 (2000) 1121-1141
13. Hill R. Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 11 (1963) 357-372
14. Hund A., and Ramm E. Locality constraints within multiscale model for non-linear material behavior. Int. J. Numer. Meth. Engrg. 70 (2007) 1613-1632
15. Ibrahimbegovic A., and Markovic D. Strong coupling methods in multi-phase and multi-scale modeling of inelastic behavior of heterogeneous structures. Comput. Methods Appl. Mech. Engrg. 192 (2003) 3089-3107
16. V.G. Kouznetsova, Computational homogenization for the multi-scale analysis of multi-phase materials, Ph.D. Thesis, Technische Universiteit Eindhoven.
17. V.G. Kouznetsova, W.A.M. Brekelmans, F.P.T. Baaijens, An approach to micro-macro modeling of heterogeneous materials, Comput. Mech. 27 (2001) 37-48.
18. Kouznetsova V.G., Geers M.G.D., and Brekelmans W.A.M. Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy. Comput. Methods Appl. Mech. Engrg. 193 (2004) 5525-5550
19. Kowe R., Schroter R.C., Matthews F.L., and Hitchings D. Analysis of elastic and surface tension effects in the lung alveolus using finite element methods. J. Biomech. 19 7 (1986) 541-549
20. U. Kuettler, M.W. Gee, Ch. Foerster, A. Comerford, W.A. Wall, Coupling strategies for biomedical fluid-structure interaction problems, Int. J. Num. Meth. Biomed. Engrg. (2009), accepted for publication.
21. Mead J., Takishima T., and Leith D. Stress distribution in lungs: a model of pulmonary elasticity. J. Appl. Physiol. 28 (1970) 596-608
22. Michel J.C., Moulinec H., and Suquet P. Effective properties of composite materials with periodic microstructure: a computational approach. Comput. Methods Appl. Mech. Engrg. 172 (1999) 109-143
23. Miehe C. Computational micro-to-macro transitions for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy. Comput. Methods Appl. Mech. Engrg. 192 (2003) 559-591
24. Miehe C., and Bayreuther C.G. On multiscale FE analyses of heterogeneous structures: from homogenization to multigrid solvers. Int. J. Numer. Meth. Engrg. 71 (2007) 1135-1180
25. Miehe C., Schröder J., and Schotte J. Computational homogenization analysis in finite plasticity. simulation of texture development in polycrystalline materials. Comput. Methods Appl. Mech. Engrg. 171 (1999) 387-418
26. Nemat-Nasser S., and Hori M. Micromechanics: Overall Properties of Heterogeneous Materials (1993), Elsevier, Amsterdam
27. Otis D.R., Ingenito E.P., Kamm R.D., and Johnson M. Dynamic surface tension of surfactant TA: experiments and theory. J. Appl. Physiol. 77 6 (1994) 2681-2688
28. Shan Z., and Gokhale A.M. Representative volume element for non-uniform micro-structure. Comput. Mater. Sci. 24 (2002) 361-379
29. Smit R.J.M., Brekelmans W.A.M., and Meijer H.E.H. Prediction of the mechanical behavior of non-linear heterogeneous systems by multi-level finite element modeling. Comput. Methods Appl. Mech. Engrg. 155 (1998) 181-192
30. Suquet P.M. Plasticity Today: Modelling, Methods and Applications, Chapter Local and Global aspects in the Mathematical Theory of Plasticity (1985), Elsevier Applied Science Publishers, London pp. 279-310
31. Temizer I., and Zohdi T.I. A numerical method for homogenization in non-linear elasticity. Comput. Mech. 40 2 (2006) 281-298
32. Terada K., and Kikuchi N. Computational Methods in Micromechanics, AMD-212/MD-22, Chapter Non-linear Homogenization Method for Practical Applications (1995), ASME Press pp. 1-16
33. Terada K., and Kikuchi N. A class of general algorithms for multi-scale analysis of heterogeneous media. Comput. Methods Appl. Mech. Engrg. 190 (2001) 5427-5464
34. Wall W.A., and Rabczuk T. Fluid-structure interaction in lower airways of CT-based lung geometries. Int. J. Numer. Meth. Fluids 57 5 (2008) 653-675
35. W.A. Wall, L. Wiechert, A. Comerford, S. Rausch, Towards a comprehensive computational model for the respiratory system, Int. J. Num. Meth. Biomed. Engrg. (2009), submitted for publication.
36. Wiechert L., Metzke R., and Wall W.A. Modeling the mechanical behavior of lung tissue at the micro-level. J. Engrg. Mech. 135 (2009) 434-438
37. Wiechert L., Rabczuk T., Comerford A., Metzke R., and Wall W.A. Towards stresses and strains in the respiratory system. ESAIM Proc. 23 (2008) 98-113
38. Wiechert L., Rabczuk T., Gee M.W., Metzke R., and Wall W.A. High Performance Computing on Vector Systems 2007, Chapter Coupled Problems in Computational Modeling of the Respiratory System (2007), Springer, Berlin pp. 145-166
39. Yvonnet J., and He Q.-C. The reduced model multi-scale method (r3m) for the non-linear homogenization of hyperelastic media at finite strains. J. Comput. Phys. 223 (2007) 341-368
40. Zohdi T., and Wriggers P. Introduction to Computational Micromechanics (2005), Springer