Skip to main content
SpringerLink
Log in

Anisotropic Damage for Extreme Dynamics

  • Reference work entry
  • First Online:
Handbook of Damage Mechanics

Abstract

Within this document, recent achievements of the Perzyna-type viscoplasticity theory for metallic materials subjected to extreme loading are considered. The complexity of the subject of matter lays in fact that for robust modelling the number of important phenomena included in the description is high. In consequence, the number of material parameters in the model is considerable. Thus, very detailed experimental examination of a particular material, under vast range of strain rates, temperatures, and scales of observations, is needed for applications.

The important features of the presented theory, which assure reliability of the extreme dynamics modelling, in its qualitative and quantitative meaning, can be summarized as follows: (i) the description is invariant with respect to any diffeomorphism (covariant material model); (ii) the obtained evolution problem is well posed; (iii) sensitivity to the rate of deformation; (iv) finite elasto-viscoplastic deformations; (v) plastic non-normality; (vi) dissipation effects (anisotropic description of damage); (vii) thermomechanical couplings; and (viii) length-scale sensitivity are included.

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)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 649.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Abaqus, Abaqus Version 6.12 Theory Manual, 2012, SIMULIA Worldwide, Headquarters, Providence, RI.

    Google Scholar 

  • R.K. Abu Al-Rub, G.Z. Voyiadjis, A finite strain plastic-damage model for high velocity impact using combined viscosity and gradient localization limiters: part I – theoretical formulation. Int. J. Damage Mech. 15(4), 293–334 (2006)

    Article  Google Scholar 

  • X. Boidin, P. Chevrier, J.R. Klepaczko, H. Sabar, Identification of damage mechanism and validation of a fracture model based on mesoscale approach in spalling of titanium alloy. Int. J. Solids Struct. 43(14–15), 4029–4630 (2006)

    Google Scholar 

  • J.D. Campbell, The dynamic yielding of mild steel. Acta Metall. 1(6), 706–710 (1953)

    Article  Google Scholar 

  • S. Cochran, D. Banner, Spall studies in uranium. J. Appl. Phys. 48(7), 2729–2737 (1988)

    Article  Google Scholar 

  • D.R. Curran, L. Seaman, D.A. Shockey, Dynamic failure of solids. Phys. Rep. 147(5-6), 253–388 (1987)

    Article  Google Scholar 

  • J.K. Dienes, On the analysis of rotation and stress rate in deforming bodies. Acta Mech. 32, 217–232 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  • W. Dornowski, Influence of finite deformations on the growth mechanism of microvoids contained in structural metals. Arch. Mech. 51(1), 71–86 (1999)

    MATH  Google Scholar 

  • W. Dornowski, P. Perzyna, Analysis of the influence of various effects on cycle fatigue damage in dynamic process. Arch. Appl. Mech. 72, 418–438 (2002a)

    Article  MATH  Google Scholar 

  • W. Dornowski, P. Perzyna, Localized fracture phenomena in thermo-viscoplastic flow process under cyclic dynamic loadings. Acta Mech. 155, 233–255 (2002b)

    Article  MATH  Google Scholar 

  • W. Dornowski, P. Perzyna, Numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes. Int. J. Solids Struct. 39, 4949–4977 (2002c)

    Article  MATH  Google Scholar 

  • W. Dornowski, P. Perzyna, Numerical investigation of localized fracture phenomena in inelastic solids. Found. Civil Environ. Eng. 7, 79–116 (2006)

    Google Scholar 

  • M.K. Duszek–Perzyna, P. Perzyna, Material instabilities: theory and applications, in Analysis of the Influence of Different Effects on Criteria for Adiabatic Shear Band Localization in Inelastic Solids, eds. by R.C. Batra and H.M. Zbib, vol. 50 (ASME, New York, 1994)

    Google Scholar 

  • A. Glema, Analysis of wave nature in plastic strain localization in solids, in Rozprawy, vol 379 (Publishing House of Poznan University of Technology, Poznan, Poland, 2004, in Polish)

    Google Scholar 

  • A. Glema, T. Łodygowski, W. Sumelka, P. Perzyna, The numerical analysis of the intrinsic anisotropic microdamage evolution in elasto-viscoplastic solids. Int. J. Damage Mech. 18(3), 205–231 (2009)

    Article  Google Scholar 

  • A. Glema, T. Łodygowski, W. Sumelka, Nowacki’s double shear test in the framework of the anisotropic thermo-elasto-vicsoplastic material model. J. Theor. Appl. Mech. 48(4), 973–1001 (2010a)

    Google Scholar 

  • A. Glema, T. Łodygowski, W. Sumelka, Towards the modelling of an anisotropic solids. Comput. Methods Sci. Technol. 16(1), 73–84 (2010b)

    Article  Google Scholar 

  • H.A. Grebe, H.-R. Pak, M.A. Meyers, Adiabatic shear localization in titanium and Ti-6 pct Al-4 pct V alloy. Metall. Mater. Trans. A 16(5), 761–775 (1985)

    Article  Google Scholar 

  • A.E. Green, P.M. Naghdi, A general theory of an elastic–plastic continuum. Arch. Ration. Mech. Anal. 18, 251–281 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  • S. Hanim, J.R. Klepaczko, Numerical study of spalling in an aluminum alloy 7020–T6. Int. J. Impact Eng. 22, 649–673 (1999)

    Article  Google Scholar 

  • R. Hill, Aspects of invariance in solid mechanics. Adv. Appl. Mech. 18, 1–75 (1978)

    Article  MATH  Google Scholar 

  • G.A. Holzapfel, Nonlinear Solid Mechanics – A Continuum Approach for Engineering (Wiley, New York, 2000)

    MATH  Google Scholar 

  • J.R. Klepaczko, Behavior of rock like materials at high strain rates in compression. Int. J. Plast. 6, 415–432 (1990a)

    Article  Google Scholar 

  • J.R. Klepaczko, Dynamic crack initiation, some experimental methods and modelling, in Crack dynamics in metallic materials, ed. by J.R. Klepaczko (Springer, Vienna, 1990b), pp. 255–453

    Chapter  Google Scholar 

  • J.R. Klepaczko, Constitutive relations in dynamic plasticity, pure metals and alloys, in Advances in Constitutive Relations Applied in Computer Codes (CISM, Udine, 2007). 23–27 July

    Google Scholar 

  • T. Lehmann, Anisotrope plastische Formänderungen. Rom. J. Tech. Sci. Appl. Mech. 17, 1077–1086 (1972)

    Google Scholar 

  • T. Łodygowski, P. Perzyna, Localized fracture of inelastic polycrystalline solids under dynamic loading process. Int. J. Damage Mech. 6, 364–407 (1997a)

    Article  Google Scholar 

  • T. Łodygowski, P. Perzyna, Numerical modelling of localized fracture of inelastic solids in dynamic loading process. Int. J. Numer. Methods Eng. 40, 4137–4158 (1997b)

    Article  MATH  Google Scholar 

  • T. Łodygowski, W. Sumelka, Damage induced by viscoplastic waves interaction. Vib. Phys. Syst. 25, 23–32 (2012)

    Google Scholar 

  • T. Łodygowski, A. Rusinek, T. Jankowiak, W. Sumelka, Selected topics of high speed machining analysis. Eng. Trans. 60(1), 69–96 (2012)

    Google Scholar 

  • P. Longere, A. Dragon, H. Trumel, X. Deprince, Adiabatic shear banding-induced degradation in thermo-elastic/viscoplastic material under dynamic loading. Int. J. Impact Eng. 32, 285–320 (2005)

    Article  Google Scholar 

  • J.E. Marsden, T.J.H. Hughes, Mathematical Foundations of Elasticity (Prentice-Hall, New Jersey, 1983)

    MATH  Google Scholar 

  • M.A. Meyers, C.T. Aimone, Dynamic Fracture (Spalling) of Materials. Progress in Material Science, vol. 28 (Pergamon, New York, 1983)

    Google Scholar 

  • J.C. Nagtegaal, J.E. de Jong, Some aspects of non-isotropic work-hardening in finite strain plasticity, in Proceedings of the workshop on plasticity of metals at finite strain: theory, experiment and computation, ed. by E.H. Lee, R.L. Mallet (Stanford University, New York, 1982), pp. 65–102

    Google Scholar 

  • R. Narayanasamy, N.L. Parthasarathi, C.S. Narayanan, Effect of microstructure on void nucleation and coalescence during forming of three different HSLA steel sheets under different stress conditions. Mater. Des. 30, 1310–1324 (2009)

    Article  Google Scholar 

  • S. Nemat-Nasser, W.-G. Guo, Thermomechanical response of HSLA-65 steel plates: experiments and modeling. Mech. Mater. 37, 379–405 (2005)

    Article  Google Scholar 

  • J.A. Nemes, J. Eftis, Several features of a viscoplastic study of plate-impact spallation with multidimensional strain. Comput. Struct. 38(3), 317–328 (1991)

    Article  MATH  Google Scholar 

  • J.A. Nemes, J. Eftis, Constitutive modelling of the dynamic fracture of smooth tensile bars. Int. J. Plast. 9(2), 243–270 (1993)

    Article  MATH  Google Scholar 

  • R.B. Pęcherski, W.K. Nowacki, Z. Nowak, P Perzyna, Effect of strain rate on ductile fracture. a new methodology, in Workshop, Dynamic Behaviour of Materials, In memory of our Friend and Colleague Prof. J.R. Klepaczko, Metz, 13–15 May 2009, pp. 65–73

    Google Scholar 

  • P. Perzyna, The constitutive equations for rate sensitive plastic materials. Quart. Appl. Math. 20, 321–332 (1963)

    MathSciNet  MATH  Google Scholar 

  • P. Perzyna, Fundamental problems in viscoplasticity. Adv. Appl. Mech. 9, 243–377 (1966)

    Article  Google Scholar 

  • P. Perzyna, Termodynamika materiałów niesprężystych (PWN, Warszawa, 1978) (in Polish)

    Google Scholar 

  • P. Perzyna, Constitutive modelling for brittle dynamic fracture in dissipative solids. Arch. Mech. 38, 725–738 (1986a)

    MathSciNet  MATH  Google Scholar 

  • P. Perzyna, Internal state variable description of dynamic fracture of ductile solids. Int. J. Solids Struct. 22, 797–818 (1986b)

    Article  Google Scholar 

  • P. Perzyna, Instability phenomena and adiabatic shear band localization in thermoplastic flow process. Acta Mech. 106, 173–205 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • P. Perzyna, Constitutive modelling of dissipative solids for localization and fracture, chapter 3, in Localization and Fracture Phenomena in Inelastic Solids, ed. by P. Perzyna. CISM Course and Lectures, vol. 386 (Springer, New York, 1998), pp. 99–241

    Chapter  Google Scholar 

  • P. Perzyna, The thermodynamical theory of elasto-viscoplasticity. Eng. Trans. 53, 235–316 (2005)

    MathSciNet  MATH  Google Scholar 

  • P. Perzyna, The thermodynamical theory of elasto-viscoplasticity accounting for microshear banding and induced anisotropy effects. Mech. Mater. 27(1), 25–42 (2008)

    Google Scholar 

  • A. Rusinek, J.R. Klepaczko, Experiments on heat generated during plastic deformation and stored energy for trip steels. Mater. Des. 30(1), 35–48 (2009)

    Article  Google Scholar 

  • C. Rymarz, Mechanika ośrodków ciągłych (PWN, Warszawa, 1993) (in Polish)

    Google Scholar 

  • L. Seaman, D.R. Curran, D.A. Shockey, Computational models for ductile and brittle fracture. J. Appl. Phys. 47(11), 4814–4826 (1976)

    Article  Google Scholar 

  • S. Shima, M. Oyane, Plasticity for porous solids. Int. J. Mech. Sci. 18, 285–291 (1976)

    Article  Google Scholar 

  • J.-H. Song, H. Wang, T. Belytschko, A comparative study on finite element methods for dynamic fracture. Comput. Mech. 42, 239–250 (2008)

    Article  MATH  Google Scholar 

  • W. Sumelka, The Constitutive Model of the Anisotropy Evolution for Metals with Microstructural Defects (Publishing House of Poznan University of Technology, Poznań, 2009)

    Google Scholar 

  • W. Sumelka, The role of the covariance in continuum damage mechanics. ASCE J. Eng. Mech. (2013). doi:10.1061/(ASCE)EM.1943-7889.0000600

    MATH  Google Scholar 

  • W. Sumelka, T. Łodygowski, The influence of the initial microdamage anisotropy on macrodamage mode during extremely fast thermomechanical processes. Arch. Appl. Mech. 81(12), 1973–1992 (2011)

    Article  MATH  Google Scholar 

  • W. Sumelka, T. Łodygowski, Reduction of the number of material parameters by an approximation. Comput. Mech. 52, 287–300 (2013)

    Article  MATH  Google Scholar 

  • W. Sumelka, T. Łodygowski, Thermal stresses in metallic materials due to extreme loading conditions. ASME J. Eng. Mater. Technol. 135, 021009–1–8 (2013)

    Google Scholar 

  • W. Sumelka, A. Glema, The evolution of microvoids in elastic solids, in 17th International Conference on Computer Methods in Mechanics CMM-2007, Łódź-Spała, 19–22 June 2007, pp. 347–348

    Google Scholar 

  • T. Łodygowski, Theoretical and Numerical Aspects of Plastic Strain Localization, vol 312, D.Sc. Thesis, Publishing House of Poznan University of Technology, 1996

    Google Scholar 

  • T. Łodygowski, A. Glema, W. Sumelka, Anisotropy induced by evolution of microstructure in ductile material, in The 8th World Congress on Computational Mechanics (WCCM8), 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008), Venice, 30 June–5 July 2008

    Google Scholar 

  • W. Thomson, On six principal strains of an elastic solid. Philos. Trans. R. Soc. 166, 495–498 (1856)

    Google Scholar 

  • D. Tikhomirov, R. Niekamp, E. Stein, On three-dimensional microcrack density distribution. ZAMM J. Appl. Math. Mech. 81(1), 3–16 (2001)

    Article  MATH  Google Scholar 

  • G.Z. Voyiadjis, R.K. Abu Al-Rub, A finite strain plastic-damage model for high velocity impacts using combined viscosity and gradient localization limiters: part II – numerical aspects and simulations. Int. J. Damage Mech. 15(4), 335–373 (2006)

    Article  Google Scholar 

  • H. Xiao, O.T. Bruhns, A. Meyers, Hypo-elasticity model based upon the logarithmic stress rate. J. Elast. 47, 51–68 (1997a)

    Article  MathSciNet  MATH  Google Scholar 

  • H. Xiao, O.T. Bruhns, A. Meyers, Logarithmic strain, logarithmic spin and logarithmic rare. Acta Mech. 124, 89–105 (1997b)

    Article  MathSciNet  MATH  Google Scholar 

  • H. Xiao, O.T. Bruhns, A. Meyers, Strain rates and material spin. J. Elast. 52, 1–41 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  • S. Zaremba, Sur une forme perfectiońée de la théorie de la relaxation. Bull. Int. Acad. Sci. Crac. 8, 594–614 (1903)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Computer Aided Design, Institute of Structural Engineering, Poznan University of Technology, 5 M. Skłodowskiej-Curie, 60-965, Poznań, Poland

    Tomasz Łodygowski & Wojciech Sumelka

Authors
  1. Tomasz Łodygowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wojciech Sumelka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tomasz Łodygowski .

Editor information

Editors and Affiliations

  1. Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, Louisiana, USA

    George Z. Voyiadjis

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media New York

About this entry

Cite this entry

Łodygowski, T., Sumelka, W. (2015). Anisotropic Damage for Extreme Dynamics. In: Voyiadjis, G. (eds) Handbook of Damage Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5589-9_32

Download citation

Publish with us

Policies and ethics

Search

Navigation