A multiscale approach for modeling progressive damage of composite materials using fast Fourier transforms

Computer Methods in Applied Mechanics and Engineering

Volumn 268, Issue , 2014, Pages 871-883

  Spahn, J ^a,b   Andra H ^a   Kabel, M ^a   Muller R ^b  

^a FRAUNHOFER INSTITUTE FOR INDUSTRIAL MATHEMATICS ITWM   (Germany)

^b University of Koblenz Landau   (Germany)

Author keywords

Composite materials; Computational homogenization; Continuum damage mechanics; Fast Fourier transforms; Multiscale analysis

Indexed keywords

ADVANCED SIMULATION TECHNIQUES; COMPUTATIONAL HOMOGENIZATION; CONVERGENCE BEHAVIORS; FAST FOURIER TRANSFORMATION (FFT); MACROSCOPIC RESPONSE; MULTI SCALE ANALYSIS; MULTI-SCALE APPROACHES; STANDARD FINITE ELEMENT;

COMPOSITE MATERIALS; CONTINUUM DAMAGE MECHANICS; FAST FOURIER TRANSFORMS; NUMERICAL METHODS;

LOADING;

EID: 84890119800     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2013.10.017     Document Type: Article

References (55)

1. Aboudi J. Micromechanical analysis of composites by the method of cells-update. Applied Mechanics Reviews 1996, 49:83.
2. Belytschko T., Loehnert S., Song J.-H. Multiscale aggregating discontinuities: a method for circumventing loss of material stability. International Journal for Numerical Methods in Engineering 2008, 73(6):869-894.
3. Belytschko T., Song J. Coarse-graining of multiscale crack propagation. International journal for numerical methods in engineering 2010, 81(5):537-563.
4. Brisard S., Dormieux L. FFT-based methods for the mechanics of composites: a general variational framework. Computational Materials Science 2010, 49(3):663-671.
5. Castañeda P. The effective mechanical properties of nonlinear isotropic composites. Journal of the Mechanics and Physics of Solids 1991, 39(1):45-71.
6. Castañeda P. Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. Journal of the Mechanics and Physics of Solids 1996, 44(6):827-862.
7. Castañeda P., Suquet P. Nonlinear composites. Advances in Applied Mechanics 1997, 34:171-302.
8. Chaboche J., Kruch S., Maire J., Pottier T. Towards a micromechanics based inelastic and damage modeling of composites. International Journal of Plasticity 2001, 17(4):411-439.
9. Coenen E., Kouznetsova V., Geers M. Multi-scale continuous-discontinuous framework for computational-homogenization-localization. Journal of Mechanics Physics of Solids 2012, 60:1486-1507.
10. Cuntze R. Efficient 3D and 2D failure conditions for UD laminae and their application within the verification of the laminate design. Composites Science and Technology 2006, 66(7):1081-1096.
11. De Borst R., Sluys L., Muhlhaus H.-B., Pamin J. Fundamental issues in finite element analyses of localization of deformation. Engineering Computations 1993, 10(2):99-121.
12. Dennis J.E., Schnabel R.B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations 1987, vol. 16. Society for Industrial and Applied Mathematics.
13. Dvorak G.J. Transformation field analysis of inelastic composite materials. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 1992, 437(1900):311-327.
14. Eshelby J.D. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1957, 241(1226):376-396.
15. Eyre D., Milton G. A fast numerical scheme for computing the response of composites using grid refinement. EPJ Applied Physics 1999, 6:41-48.
16. Feyel F., Chaboche J. FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials. Computer Methods in Applied Mechanics and Engineering 2000, 183(3):309-330.
17. Fish J., Shek K., Pandheeradi M., Shephard M.S. Computational plasticity for composite structures based on mathematical homogenization: theory and practice. Computer Methods in Applied Mechanics and Engineering 1997, 148(1):53-73.
18. Hashin Z., Shtrikman S. A variational approach to the theory of the elastic behaviour of multiphase materials. Journal of the Mechanics and Physics of Solids 1963, 11(2):127-140.
19. Hill R. Acceleration waves in solids. Journal of the Mechanics and Physics of Solids 1962, 10(1):1-16.
20. Hill R. Elastic properties of reinforced solids: some theoretical principles. Journal of the Mechanics and Physics of Solids 1963, 11(5):357-372.
21. Hill R. A self-consistent mechanics of composite materials. Journal of the Mechanics and Physics of Solids 1965, 13(4):213-222.
22. Hill R. The mathematical theory of plasticity 1998, Vol. 11. Oxford university press.
23. Kabel M., Andrä H. Numerical bounds of effective elastic moduli. Berichte des Fraunhofer ITWM 2012, 224(1):1-13.
24. Kachanov L. Introduction to Continuum Damage Mechanics 1986, vol. 10. Springer.
25. Kanouté P., Boso D., Chaboche J., Schrefler B. Multiscale methods for composites: a review. Archives of Computational Methods in Engineering 2009, 16(1):31-75.
26. Kouznetsova V., Brekelmans W., Baaijens F. An approach to micro-macro modeling of heterogeneous materials. Computational Mechanics 2001, 27(1):37-48.
27. Kröner E. Bounds for effective elastic moduli of disordered materials. Journal of the Mechanics and Physics of Solids 1977, 25(2):137-155.
28. Kuhl E. Numerische Modelle für kohäsive Reibungsmaterialien 2000, Inst. f. Baustatik d. Univ, Stuttgart.
29. Lemaitre J., Desmorat R. Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures 2005, Springer.
30. Lippmann B., Schwinger J. Variational principles for scattering processes. I. Physical Review 1950, 79(3):469.
31. Maimí P., Camanho P., Mayugo J., Dávila C. A continuum damage model for composite laminates: Part I. Constitutive model. Mechanics of Materials 2007, 39(10):897-908.
32. Mazars J., Pijaudier-Cabot G. Continuum damage theory-application to concrete. Journal of Engineering Mechanics 1989, 115(2):345-365.
33. Michel J., Moulinec H., Suquet P. Effective properties of composite materials with periodic microstructure: a computational approach. Computer Methods in Applied Mechanics and Engineering 1999, 172(1):109-143.
34. Michel J., Moulinec H., Suquet P. A computational method based on augmented Lagrangians and fast fourier transforms for composites with high contrast. CMES (Computer Modelling in Engineering & Sciences) 2000, 1(2):79-88.
35. Michel J., Moulinec H., Suquet P. A computational scheme for linear and non-linear composites with arbitrary phase contrast. International Journal for Numerical Methods in Engineering 2001, 52(1-2):139-160.
36. Michel J.-C., Suquet P. Nonuniform transformation field analysis. International Journal of Solids and Structures 2003, 40(25):6937-6955.
37. Miehe C. Numerical computation of algorithmic (consistent) tangent moduli in large-strain computational inelasticity. Computer Methods in Applied Mechanics and Engineering 1996, 134(3):223-240.
38. Miehe C., Koch A. Computational micro-to-macro transitions of discretized microstructures undergoing small strains. Archive of Applied Mechanics 2002, 72(4):300-317.
39. Mori T., Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica 1973, 21(5):571-574.
40. Moulinec H., Suquet P. A fast numerical method for computing the linear and nonlinear mechanical properties of composites. Comptes rendus de l'Académie des sciences. Série II, Mécanique, Physique, Chimie, Astronomie 1994, 318(11):1417-1423.
41. 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(1):69-94.
42. Mura T. Micromechanics of Defects in Solids 1987, vol. 3. Kluwer Academic Pub.
43. Nemat-Nasser S., Hori M. Micromechanics: Overall Properties of Heterogeneous Materials 1999, vol. 2. Elsevier Amsterdam.
44. Pinho S., Darvizeh R., Robinson P., Schuecker C., Camanho P., Material and structural response of polymer-matrix fibre-reinforced composites, Journal of Composite Materials 46, 19?20, (2012) 2313?2341.
45. Puck A., Schürmann H. Failure analysis of FRP laminates by means of physically based phenomenological models. Composites Science and Technology 1998, 58(7):1045-1067.
46. Rice J., Rudnicki J. A note on some features of the theory of localization of deformation. International Journal of Solids and Structures 1980, 16(7):597-605.
47. Simo J., Ju J. Strain-and stress-based continuum damage models. I. Formulation. International Journal of Solids and Structures 1987, 23(7):821-840.
48. Smit R., Brekelmans W., Meijer H. Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling. Computer Methods in Applied Mechanics and Engineering 1998, 155(1):181-192.
49. Temizer I., Wriggers P. On the computation of the macroscopic tangent for multiscale volumetric homogenization problems. Computer Methods in Applied Mechanics and Engineering 2008, 198(3):495-510.
50. Tsai S., Wu E. A general theory of strength for anisotropic materials. Journal of Composite Materials 1971, 5(1):58-80.
51. Weinan E., Engquist B., Li X., Ren W., Vanden-Eijnden E. Heterogeneous multiscale methods: a review. Communications in Computational Physics 2007, 2(3):367-450.
52. Zeller R., Dederichs P. Elastic constants of polycrystals. Physica Status Solidi (b) 1973, 55(2):831-842.
53. Zohdi T.I., Wriggers P. An Introduction to Computational Micromechanics 2008, vol. 20. Springer Science+Business Media.
54. Linder C., Arun R. A strong discontinuity approach on multiple levels to model solids at failure. Computer Methods in Applied Mechanics and Engineering 2012.
55. Linder C., Xiaoxuan Z. A marching cubes based failure surface propagation concept for three-dimensional finite elements with non-planar embedded strong discontinuities of higher-order kinematics. International Journal for Numerical Methods in Engineering 2013, 96.6:339-372.