On micro-to-macro transitions for multi-scale analysis of non-linear heterogeneous materials: Unified variational basis and finite element implementation

International Journal for Numerical Methods in Engineering

Volumn 87, Issue 1-5, 2011, Pages 149-170

  Peric D ^a   De Souza Neto, E A ^a   Feijoo R A ^b   Partovi, M ^a   Molina, A J Carneiro ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

^b LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

Author keywords

Finite element; Homogenization; Micro to macro transitions; Multi scale analysis

Indexed keywords

BOUNDARY DISPLACEMENTS; BOUNDARY TRACTION; COMPUTATIONAL STRATEGY; COMPUTER MODELLING; ELASTOPLASTIC MATERIALS; FINITE ELEMENT; FINITE ELEMENT IMPLEMENTATION; FINITE ELEMENT SIMULATIONS; HETEROGENEOUS MATERIALS; HOMOGENIZATION; KINEMATICAL CONSTRAINTS; LENGTH SCALE; MACROSCALES; MACROSCOPIC STRESS; MATERIAL RESPONSE; MICRO-SCALES; MICRO-TO-MACRO TRANSITIONS; MULTI SCALE ANALYSIS; MULTISCALES; NON-LINEAR; NUMERICAL EXAMPLE; PERIODIC BOUNDARIES; REPRESENTATIVE VOLUME ELEMENTS; SMALL STRAINS; VARIATIONAL FORMULATION;

STATISTICS; STRAIN;

FINITE ELEMENT METHOD;

EID: 79958752343     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.3014     Document Type: Article

References (51)

1. Sanchez-Palencia E. Comportement local et macroscopique d'un type de milieux physique hétérogènes. International Journal of Engineering Science 1974; 12:231-251.
2. Suquet PM. Local and global aspects in the mathematical theory of plasticity. In Plasticity Today: Modelling Methods and Applications, Sawczuk A (ed.). Elsevier Applied Science Publishers: Amsterdam, 1985.
3. Suquet PM. Elements of homogenization for inelastic solid mechanics. In Homogenization Techniques for Composite Media, Sanchez-Palencia E, Zaoui A (eds). Springer: Berlin, 1987.
4. Oden JT, Vemaganti K, Moes N. Hierarchical modelling of heterogenous solids. Computer Methods in Applied Mechanics and Engineering 1999; 172:2-25.
5. Zohdi TI, Oden JT, Rodin GJ. Hierarchical modeling of heterogeneous bodies. Computer Methods in Applied Mechanics and Engineering 1996; 138:273-298.
6. Ghosh S, Lee K, Murthy S. Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element method. Computer Methods in Applied Mechanics and Engineering 1996; 132:63-116.
7. Moulinec H, Suquet P. A numerical method for computing the overall response of nonlinear composites with complex microstructure. Computer Methods in Applied Mechanics and Engineering 1998; 157:69-94.
8. Michel JC, Moulinec H, Suquet P. Effective properties of composite materials with periodic microstructure: a computational approach. Computer Methods in Applied Mechanics and Engineering 1999; 172:109-143.
9. Fish J, Shek K, Pandheeradi M, Shephard MS. Computational plasticity for composite structures based on mathematical homogenization: theory and practice. Computer Methods in Applied Mechanics and Engineering 1997; 148:53-73.
10. Fish J, Zheng Y. Multiscale enrichment based on partition of unity. International Journal for Numerical Methods in Engineering 2005; 62:1341-1359.
11. Yuan Z, Fish J. Toward realization of computational homogenization in practice. International Journal for Numerical Methods in Engineering 2008; 73:361-380.
12. Smit RJM, Brekelmans WAM, Meijer HEH. Prediction of the mechanical behaviour of nonlinear heterogeneous systems by multi-level finite element modeling. Computer Methods in Applied Mechanics and Engineering 1998; 155:181-192.
13. 2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials. Computer Methods in Applied Mechanics and Engineering 2000; 183:309-330.
14. Miehe C, Schotte J, Schröder J. Computational micro-macro transitions and overall tangent moduli in the analysis of polycrystals at large strains. Computational Materials Science 1999; 16:372-382.
15. Miehe C, Schröder J, Schotte J. Computational homogenization analysis in finite plasticity. Simulation of texture development in polycrystalline materials. Computer Methods in Applied Mechanics and Engineering 1999; 171:387-418.
16. Miehe C, Koch A. Computational micro-macro transitions of discretized microstructures undergoing small strains. Archives of Applied Mechanics 2002; 72:300-317.
17. Pellegrino C, Galvanetto U, Schrefler BA. Numerical homogenization of periodic composite materials with non-linear material components. International Journal for Numerical Methods in Engineering 1999; 46:1609-1637.
18. Kouznetsova VG, Brekelmans WAM, Baaijens FPT. An approach to micro-macro modelling of heterogeneous materials. Computational Mechanics 2001; 27:37-48.
19. Kouznetsova VG. Computational homogenization for multiscale analysis of multi-phase materials. Ph.D. Thesis, TU University Eindhoven, Eindhoven, 2002.
20. Ladevèze P, Loiseau O, Dureisseix D. A micro-macro and parallel computational strategy for highly heterogeneous structures. International Journal for Numerical Methods in Engineering 2001; 52:121-138.
21. Ladevèze P. Multiscale modelling and computational strategies for composites. International Journal for Numerical Methods in Engineering 2004; 60:233-253.
22. Terada K, Kikuchi N. A class of general algorithms for multi-scale analyses of heterogeneous media. Computer Methods in Applied Mechanics and Engineering 2001; 190:5427-5464.
23. Matsui K, Terada K, Yuge K. Two-scale finite element analysis of heterogeneous solids with periodic microstructures. Computers and Structures 2004; 82:593-606.
24. Watanabe I, Terada K, de Souza Neto EA, Peric D. Characterization of macroscopic tensile strength of polycrystalline metals with two-scale finite element analysis. Journal of the Mechanics and Physics of Solids 2008; 56:1105-1125.
25. Markovič D, Ibrahimbegović A. On micro-macro interface conditions for micro-scale based FEM for inelastic behaviour of heterogeneous materials. Computer Methods in Applied Mechanics and Engineering 2004; 193:5503-5523.
26. Zohdi TI, Wriggers P. Introduction to Computational Micromechanics. Springer: Berlin, 2005.
27. Belytschko T, Loehnert S, Song JH. Multiscale aggregating discontinuities: a method for circumventing loss of material stability. International Journal for Numerical Methods in Engineering 2008; 73:869-894.
28. Belytschko T, Song JH. Coarse-graining of multiscale crack propagation. International Journal for Numerical Methods in Engineering 2010; 81:537-563.
29. Hund A, Ramm E. Locality constraints within multiscale model for non-linear material behaviour. International Journal for Numerical Methods in Engineering 2007; 70:1613-1632.
30. Swan CC. Techniques for stress- and strain-controlled homogenization of inelastic periodic composites. Computer Methods in Applied Mechanics and Engineering 1994; 117:249-267.
31. Mandel J. Plasticité Classique et Viscoplasticité. CISM Courses and Lectures No. 97. Springer: Udine, Italy, 1971.
32. Hill R. On constitutive macro-variables for heterogeneous solids at finite strain. Proceedings of the Royal Society of London, Series A 1972; 326:131-147.
33. Willis JR. Variational and related methods for the overall properties of composites. Advances in Applied Mechanics 1981; 21:1-78.
34. Nemat-Nasser S, Hori M. Micromechanics: Overall Properties of Heterogeneous Materials. North-Holland: Amsterdam, 1993.
35. de Souza Neto EA, Feijóo RA. Variational foundations of multi-scale constitutive models of solid: small and large strain kinematical formulation. National Laboratory for Scientific Computing (LNCC/MCT), Brazil, Internal Research & Development Report No. 16/2006, 2006.
36. Hill R. A self-consistent mechanics of composite materials. Journal of the Mechanics and Physics of Solids 1965; 13(4):213-222.
37. Taylor GI. Plastic strains in metals. Journal Institute of Metals 1938; 62:307-324.
38. Simo JC, Hughes TJR. Computational inelasticity. Springer: New York, 1998.
39. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures. Wiley: New York, 2000.
40. de Souza Neto EA, Perić D, Owen DRJ. Computational Methods for Plasticity: Theory and Applications. Wiley: Chichester, 2008.
41. Wriggers P. Nonlinear Finite Element Methods. Springer: Berlin, 2008.
42. de Souza Neto EA, Perić D. A computational framework for a class of fully coupled models for elastoplastic damage at finite strains with reference to the linearization aspects. Computer Methods in Applied Mechanics and Engineering 1996; 130:179-193.
43. de Souza Neto EA, Perić D, Owen DRJ. Continuum modelling and numerical simulation of material damage at finite strains. Archives of Computational Methods in Engineering 1998; 5:311-384.
44. Dutko M, Peric D, Owen DRJ. Universal anisotropic yield criterion based on superquadric functional representation-1: algorithmic issues and accuracy analysis. Computer Methods in Applied Mechanics and Engineering 1993; 109:73-93.
45. Perić D. On a class of constitutive equations in viscoplasticity: formulation and computational issues. International Journal for Numerical Methods in Engineering 1993; 36:1365-1393.
46. Perić D, de Souza Neto EA. A new computational model for Tresca plasticity at finite strains with an optimal parametrization in the principal space. Computer Methods in Applied Mechanics and Engineering 1999; 171:463-489.
47. Somer DD, de Souza Neto EA, Dettmer WG, Perić D. A sub-stepping scheme for multi-scale analysis of solids. Computer Methods in Applied Mechanics and Engineering 2009; 198:1006-1016.
48. Speirs DCD, de Souza Neto EA, Perić D. An approach to the mechanical constitutive modelling of arterial tissue based on homogenization and optimization. Journal of Biomechanics 2008; 41:2673-2680.
49. Giusti SM, Novotny AA, de Souza Neto EA, Feijóo RA. Sensitivity of the macroscopic elasticity tensor to topological microstructural changes. Journal of the Mechanics and Physics of Solids 2009; 57:555-570.
50. Giusti SM, Novotny AA, de Souza Neto EA, Feijóo RA. Sensitivity of the macroscopic thermal conductivity tensor to topological microstructural changes. Computer Methods in Applied Mechanics and Engineering 2009; 198:727-739.
51. Giusti SM, Novotny AA, de Souza Neto EA. Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions. Proceedings of the Royal Society A 2010; 466:1703-1723.