Mechanical Anisotropy

Oller, Sergio

doi:10.1007/978-3-319-04933-5_2

Sergio Oller

Part of the book series: Lecture Notes on Numerical Methods in Engineering and Sciences ((LNNMES))

2556 Accesses

Abstract

The constitutive models developed for the behavior simulation of simple isotropic materials are not suitable for the analysis of composite materials due to the strong anisotropy of these latters. There are different reasons and degrees of importance. The composite representation by a single orthotropic material having properties of the whole set has not been satisfactory either. Therefore, the mixing theory will also be presented in this chapter.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 39.99; Price excludes VAT (USA)

Hardcover Book: USD 54.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

1.
Hill. R (1971). The Mathematical Theory of Plasticity. Oxford University Press.
2.
Bassani J. L. (1977). Yield characterization of metals with transversely isotropic plastic properties. Int. J. Mech. Si vol 19, pp. 651.
3.
Barlat F. and Lian J. (1989). Plastic behavior and stretchability of sheet metals. Part I: A yield function for othotropic sheet under plane stress conditions. Int. Journal of Plasticity, vol. 5, pp. 51.
4.
Barlat F. and Lege D. J. and Brem J. C. (1991). A six-component yield function for anisotropic materials. Int. Journal of Plasticity, vol. 7, pp. 693.
5.
NOTE: A non proportional material is the material in which the relationship among the material elastic modules in any two directions is not equal to the relation among the strength in the same directions.
6.
Hull D. (1987). An Introduction to Composite Materials. Cambridge University Press.
7.
Matthews F. L. and Rawlings R. D. (1994). Composite Materials: Engineering and Science. Chapman and Hall.
8.
Pendleton R.L. and Tuttle M.E. (1989). Manual on Experimental Methods for Mechanical Testing of Composites. Elsevier Applied Science Publishers.
9.
Malvern L.E. (1969). Introduction to the Mechanics of a Continuous Medium. Prentice-Hall.
10.
Gurtin M. E. (1981). An introduction to continuum mechanics. Academic Press. New York.
11.
Chen W. F. and Han D. J. (1988). Plasticity for structural engineers. Springer-Verlag. New York.
12.
NOTA: Dado un estado de tensiones principales σ₁, σ₂, σ₃, la función de fluencia resulta simétrica si se cumple f (σ₁, σ₂, σ₃) ≡ f (σ₃, σ₁, σ₂).
13.
Hill R. (1948). A theory of the yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. London. Ser. A. Vol. 193, pp. 281–297.
14.
Hill R. (1965). Micro mechanics of elastoplastic materials. J. Mech. Phis. Solids. Vol. 13, pp. 89–101.
15.
Hill R. (1979). Theoretical plasticity of textured aggregates. Math. Proc. Cambridge Philos. Soc.. Vol. 85, pp. 179–191, No 1.
16.
Hill R. (1990). Constitutive modelling of orthotropic plasticity in sheet metals. J. Mech. Phys. Solids. Vol. 38, pp. 405–417, No. 3.
17.
Karafillis A. P. and Boyce M. C. (1993). A general anisotropic yield criterion using bounds and a transformation weighting tensor. J. Mech. Phys. Solids. Vol. 41, pp. 1859–1886. number = 12
18.
Dvorak G. J. and Bahei-El-Din Y. A. (1982). Plasticity analysis of fibrous composites. J. App. Mech. Vol. 49, pp. 327–335.
19.
Shih C. F. and Lee D. (1978). Further developments in anisotropic plasticity. J. Engng Mater. Technol. Vol. 105, pp. 242
20.
Eisenberg M. A. and Yen C. F. (1984). The anisotropic deformation of yield surfaces. J. Engng. Mater. Technol. Vol. 106, pp. 355
21.
Voyiadjis G. Z. and Foroozesh M. (1990). Anisotropic distortional yield model. J. Appl. Mech. Vol. 57, pp. 537.
22.
Voyiadjis G.Z. and Thiagarajan G. (1995). A damage ciclic plasticity model for metal matrix composites. Constitutive Laws, Experiments and Numerical Implementation.
23.
Eggleston H. G. (1969). Convexity. Cambridge University Press.
24.
Betten J. (1981). Creep theory of anisotropic solids. J. Rheol. Vol. 25, pp. 565–581.
25.
Betten J. (1988). Application of tensor functions to the formulation of yield criteria for anisotropic materials. Int. J. Plasticity, Vol. 4, pp. 29–46.
26.
Oller S., Onate E., Miquel J. and Botello S. (1993). A finite element model for analysis of multiphase composite materials. Ninth International Conferences on Composite Materials. Ed. A. Miravete. Zaragoza - Spain.
27.
Oller S., Onate E. and Miquel J. (1993). Simulation of anisotropic elastic–plastic behaviour of materials by means of an isotropic formulation. 2nd. US Nat. Congr. Comput. Mech. Washington DC.
28.
Oller S., Botello S., Miquel J. and Onate E. (1995). An anisotropic elastoplastic model based on an isotropic formulation. Engineering Computations, Vol. 12, No. 3, pp. 245–262.
29.
Green A. E. and Nagdhi P. M. (1971). Some remarks on elastic–plastic deformation at finite strains. Int. J. of Eng. Sc., Vol 9, pp. 1219–1229.
30.
Lubliner J. (1990). Plasticity Theory. Macmillan Publishing, U.S.A.
31.
Garcia Garino G. and Oliver J. (1992). A numerical model for elastoplastic large strain problems. Fundamentals and applications. Computational Plasticity III. Ed. D.R.J. Owen and E. Onate and E. Hinton. Vol. 1, pp. 117–129, CIMNE, Barcelona, Spain.
32.
NOTE: The condition of plastic incompressibility is verified when the yield function is not affected by the spheric part of the stresses tensor.
33.
Sobotka, Z. (1969). Theorie des plastischen Fließens von ainsotropen Körpern. Z. Angew. Math. Mech., vol. 49, pp. 25–32.
34.
Boehler, J. P., and Sawczuk, A. (1970). Équilibre limite des sols anisotropes. J. Méc., Vol. 9,pp. 5–32.
35.
Oller, S., Onate, E., Miquel Canet, J., and Botello, S. (1996-a). A plastic damage constitutive model for composite materials. Int. Jour. Solids Struct., Vol. 33, No. 17, pp. 2501–2518.
36.
Oller, S., Onate, E., and Miquel Canet, J. (1996-b). A mixing anisotropic formulation for analysis of composites. Communications in Numerical Methods in Engineering, Vol. 12, 471–482.
37.
Oller, S., Rubert, J., Las Casas, E., Onate, E., and Proença, S. (1998). Large Strains Elastoplastic Formulation For Anisotropic Materials. First Esaform Conference on Material Forminged. by J. Chenot, J. Agassant, P. Montnitinnet, B. Bergnes, N. Billon. pp. 191194. Sophia Antipolis (France) March. 1998.
38.
Car, E., Oller, S. and Onate, E. (1999-a). Numerical Constitutive Model For Laminated Composite Materials. Second ESAFORM Conference on Material Forming. Minho, Portugal, Ed. J. A. Covas, pp. 147–150.
39.
Car, E., Oller, S., and Onate, E. (1999-b). A Large Strain Plasticity Model for Anisotropic Material - Composite Material Application. Int. J. Plastiaty, Vol.17, No. 11, pp. 1437–1463.
40.
Las Casas E., Oller S., Rubert J., Proença and Onate E. (1998). A Large Strain Explicit Formulation for Composites. Proceedings of the Fourth World Congress on Computational Mechanics. Ed. S. Idelsohn, E. Onate and E. Dvorkin. CIMNE, Barcelona, Spain.
41.
Oller S., Car E. and Lubliner J. (2001). Definition of a general implicit orthotropic yield criterion. Submitted in Computer Methods in Applied Mechanics and Engineering.
42.
Press, W. H., Teulosky, S. A., Vetterling, W. T. and Flannery, B. P. (1992). Numerical recipes in Fortran 77. The art of scientific computing. Volume I. Cambridge University Press.
43.
Car E. (2000). Modelo constitutivo continuo para el estudio del comportamiento mecânico de los materiales compuestos. PhD thesis, Universidad Politécnica de Cataluna. Barcelona, España.
44.
NOTE: The additivity of the strains is defined as Ė ^e = Ė - Ė ^p, and being A^E a linear elastic application from one space to another, the elastic part of the Green-Lagrange strain result: A^È :Ė ^e = A^È :Ė - A^E : Ė ^p, from which \( {\dot{\overline{E}}}^e=\dot{\overline{E}}-{\dot{\overline{E}}}^p \) is obtained in the fictitious space, where the evolution of plastic law of starin in isotropic space is obtained as, \( {\dot{\overline{E}}}^p={\mathrm{A}}^E:{\dot{E}}^p \).
45.
NOTE: Consider the validity of the following tensorial product operation of configuration transformation: (A B):C = B:(A^T C) = A:(C B^T).
46.
Simo J. and Taylor R. (1985). Consistent tangent operators for rate-dependent elastoplasticity. Computer Methods in Applied Mechanics and Engineering. 48, 101–118.
47.
Cris field M. (1991). Non linearfinite element analysis of solids and structures. John Wiley & Sons Ltd.
48.
Ortiz M. and Popov E. (1985). Accuracy and stability of integration algorithms for elastoplastic constitutive relations. International Journal of Numerical Methods in Engineering.. Vol. 21, pp. 1561–1576.

Authors

Prof. Dr. Sergio Oller
View author publications
You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Oller, S. (2014). Mechanical Anisotropy. In: Numerical Simulation of Mechanical Behavior of Composite Materials. Lecture Notes on Numerical Methods in Engineering and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-04933-5_2

Download citation

DOI: https://doi.org/10.1007/978-3-319-04933-5_2
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04932-8
Online ISBN: 978-3-319-04933-5
eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics