Abstract
This entry is focused on description of material anisotropy in elastic and plastic ranges. Concise classification of anisotropic materials with respect to symmetry of elastic matrices as referred to the crystal lattice symmetry is given, and extended analogy between symmetries of constitutive material matrices (elastic and yield/failure) is also discussed. In this entry basic features of anisotropic initial yield criteria are discussed. Two ways to account for anisotropy are presented: the explicit vs. implicit formulations. The explicit description of anisotropy is rigorously based on well established theory of common invariants (Sayir, Goldenblat–Kopnov, von Mises, Hill). The implicit approach involves linear transformation tensor of the Cauchy stress that accounts for anisotropy to enhance the known isotropic criteria to be able to capture anisotropy, hydrostatic pressure insensitivity and asymmetry of the yield surface (Barlat, Plunckett, Cazacu, Khan). The advantages and differences of both formulations are critically presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Altenbach H, Kolupaev V (2015) Classical and non-classical failure criteria. In: Altenbach H, Sadowski T (eds) Failure and Damage Analysis of Advanced Materials, Springer, Wien, Heidelberg, New York, Dordrecht, London, CISM International Centre for Mechanical Sciences Courses and Lectures, vol 560, pp 1–66
Altenbach H, Altenbach J, Zolochevsky A (1995) A generalized constitutive equation for creep of polymers at multiaxial loading. Mechanics of Composite Materials 31(6):511–518
Altenbach H, Bolchoun A, Kolupaev VA (2014) Phenomenological yield and failure criteria. In: Altenbach H, Öchsner A (eds) Plasticity of Pressure-Sensitive Materials, Springer, Heidelberg, New York, Dordrecht, London, Engineering Materials, pp 49–152
Barlat F, Brem JC, Yoon JW, Chung K, Dick RE, Lege DJ, Pourboghrat F, Choi SH, Chu E (2003) Plane stress function for aluminium alloy sheets – part I: theory. Int J Plast 19:1297–1319
Berryman G (2005) Bounds and self-consistent estimates for elastic constants of random polycrystals with hexagonal, trigonal, and tetragonal symmetries. J Mech Phy Solids 53:2141–2173
Betten J (1988) Applications of tensor functions to the formulation of yield criteria for anisotropic materials. Int J Plast 4:29–46
Boehler JP, Sawczuk A (1970) Équilibre limite des sols anisotropes. J Mécanique 9:5–33
Cazacu O, Barlat F (2004) A criterion for description of anisotropy and yield differential effects in pressure-insensitive materials. Int J Plast 20:2027–2045
Cazacu O, Planckett B, Barlat F (2006) Orthotropic yield criterion for hexagonal close packed metals. Int J Plast 22:1171–1194
Desmorat R, Marull R (2011) Non-quadratic Kelvin modes based plasticity criteria for anisotropic materials. Int J Plast 27:327–351
Dunand M, Maertens AP, Luo M, Mohr D (2012) Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading - part I: Plasticity. Int J Plast 36:34–49
Gan H, Orozco CE, Herkovich CT (2000) A strain-compatible method for micromechanical analysis of multi-phase composites. Int J Solids Struct 37:5097–5122
Ganczarski A, Lenczowski J (1997) On the convexity of the Goldenblatt-Kopnov yield condition. Arch Mech 49:461–475
Ganczarski A, Skrzypek J (2013) Mechanics of Novel Materials. Iss. Cracow Univ. Technol., Cracow
Ganczarski AW, Skrzypek JJ (2014) Constraints on the applicability range of Hill’s criterion: strong orthotropy or transverse isotropy. Acta Mechanica 225(9):2563–2582
Goldenblat II, Kopnov VA (1966) Obobshchennaya teoriya plasticheskogo techeniya anizotropnyh sred. Sbornik Stroitelnaya Mehanika pp 307–319
Herakovich CT, Aboudi J (1999) Thermal effects in composites. In: Hetnarski RB (ed) Thermal Stresses V, Lastran Corp. Publ. Division, Rochester
Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc Roy Soc London A193:281–297
Hill R (1950) The Mathematical Theory of Plasticity. Oxford University Press, Oxford
Jastrzebski ZD (1987) The Nature and Properties of Engineering Materials. John Wiley & Sons Inc., New York
Khan AS, Liu H (2012) Strain rate and temperature dependent fracture criteria for isotropic and anisotropic metals. Int J Plast 37:1–15
Khan AS, Kazmi R, Farrokh B (2007) Multiaxial and non-proportional loading responses, anisotropy and modeling of Ti-6Al-4V titanium alloy over wide ranges of strain rates and temperatures. Int J Plast 23:931–950
Khan AS, Yu S, Liu H (2012) Deformation enhanced anisotropic responses of Ti-6Al-4V alloy, Part II: A stress rate and temperature dependent anisotropic yield criterion. Int J Plast 38:14–26
Kolupaev VA (2018) Equivalent Stress Concept for Limit State Analysis, Advanced Structured Materials, vol 86. Springer, Cham
Korkolis YP, Kyriakides S (2008) Inflation and burst of aluminum tubes. Part II: An advanced yield function including deformation-induced anisotropy. Int J Plast 24:1625–1637
Kowalsky UK, Ahrens H, Dinkler D (1999) Distorted yield surfaces - modeling by higher order anisotropic hardening tensors. Comput Mat Sci 16:81–88
Lekhnitskii SG (1981) Theory of Elasticity of an Anisotropic Body. Mir Publishers, Moscow
Love AEH (1944) A Treatise on the Mathematical Theory of Elasticity. Dover Publ., New York
Luo M, Dunand M, Moth D (2012) Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading - Part II: Ductile fracture. Int J Plast 32–33:36–58
Malinin NN, Rzysko J (1981) Mechanics of Materials. PWN, Warsaw
von Mises R (1913) Mechanik der festen Körper im plastisch deformablen Zustand. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse 4:582–592
von Mises R (1928) Mechanik der plastischen Formänderung von Kristallen. ZAMM 8(13):161–185
Nixon ME, Cazacu O, Lebensohn RA (2010) Anisotropic response of high-purity _-titanium: experimental characterization and constitutive modeling. Int J Plast 26:516–532
Nye JF (1957) Physical Properties of Crystals: Their Representations by Tensors and Matrices. Clarendon Press, Oxford
Ottosen NS, Ristinmaa M (2005) The Mechanics of Constitutive Modeling. Elsevier, Amsterdam
Rogers TG (1990) Yield criteria, flow rules, and hardening in anisotropic plasticity. In Boehler J.P. (ed) Yielding, damage and failure of anisotropic solids. Mech. Eng. Publ., London
Rymarz C (1993) Continuum Mechanics. PWN, Warsaw
Sayir M (1970) Zur Fließbedingung der Plastizitätstheorie. Ingenierurarchiv 39:414–432
Sobotka Z (1969) Theorie des plastischen Fliessens von anisotropen Körpern. ZAMM 49:25–32
Spencer AJM (1971) Theory of invariants. In: Eringen C (ed) Continuum Physics, Academic Press, New York
Szczepinski W (1993) On deformation-induced plastic anisotropy of sheet metals. Arch Mech 45(1):3–38
Tamma KK, Avila A (1999) An integrated micro/macro modelling and computational methodology for high temperature composites. In Hetnarski RB (ed) Thermal Stresses V. Lastran Corp. Publ. Division, Rochester
Tsai ST, Wu EM (1971) general theory of strength for anisotropic materials. Int J Numer Methods Engng 38:2083–2088
Yoshida F, Hamasaki HM, Uemori T (2013) A user-friendly 3D yield function to describe anisotropy of steel sheets. Int J Plast 45:119–139
Zyczkowski M (2001) Anisotropic yield conditions. In: Lemaitre J (ed) Handbook of Materials Behavior Models, Academic Press, San Diego
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Ganczarski, A. (2019). Anisotropic Material Behavior. In: Altenbach, H., Öchsner, A. (eds) State of the Art and Future Trends in Material Modeling . Advanced Structured Materials, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-030-30355-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-30355-6_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-30354-9
Online ISBN: 978-3-030-30355-6
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)