[en] This paper aims at presenting a general versatile time integration scheme applicable to anisotropic damage coupled to elastoplasticity, considering any damage rate and isotropic hardening formulations. For this purpose a staggered time integration scheme in a finite strain framework is presented, together with an analytical consistent tangent operator. The only restrictive hypothesis is to work with an undamaged isotropic material, assumed here to follow a J2 plasticity model. The only anisotropy considered is thus a damage-induced anisotropy. The possibility to couple any damage rate law with the present algorithm is illustrated with a classical ductile damage model for aluminium, and a biological damage-like application. The later proposes an original bone remodelling law coupled to trabecular bone plasticity for the simulation of orthodontic tooth movements. All the developments have been considered in the framework of the implicit non-linear finite element code Metafor (developed at the LTAS/MN2L,
University of Liège, Belgium - www.metafor.ltas.ulg.ac.be).
Disciplines :
Mechanical engineering
Author, co-author :
Mengoni, Marlène ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Département d'aérospatiale et mécanique
Ponthot, Jean-Philippe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire
Language :
English
Title :
A generic anisotropic continuum damage model integration scheme adaptable to both ductile damage and biological damage-like situations
Publication date :
2015
Journal title :
International Journal of Plasticity
ISSN :
0749-6419
Publisher :
Pergamon Press - An Imprint of Elsevier Science, Oxford, United Kingdom
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
J. Aboudi The effect of anisotropic damage evolution on the behavior of ductile and brittle matrix composites Int. J. Solids Struct. 48 2011 2102 2119
R.K. Abu Al Rub, and M.K. Darabi A thermodynamic framework for constitutive modeling of time- and rate-dependent materials. Part I: Theory Int. J. Plast. 34 2012 61 92
R.K. Abu Al-Rub, and G.Z. Voyiadjis On the coupling of anisotropic damage and plasticity models for ductile materials Int. J. Solids Struct. 40 2003 2611 2643
R.K. Abu Al Rub, and 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 2006 293 334
H. Badreddine, K. Saanouni, and A. Dogui On non-associative anisotropic finite plasticity fully coupled with isotropic ductile damage for metal forming Int. J. Plast. 26 2010 1541 1575
D. Balzani, S. Brinkhues, and G.A. Holzapfel Constitutive framework for the modeling of damage in collagenous soft tissues with application to arterial walls Comput. Methods Appl. Mech. Eng. 2012 139 151
H.H. Bayraktar, and T.M. Keaveny Mechanisms of uniformity of yield strains for trabecular bone J. Biomech. 37 2004 1671 1678
G.S. Beaupré, T.E. Orr, and D.R. Carter An approach for time-dependent bone modeling and remodeling-theoretical development J. Orthop. Res. 8 1990 651 661
K.B. Bernick, T.P. Prevost, S. Suresh, and S. Socrate Biomechanics of single cortical neurons Acta Biomater. 7 2011 1210 1219
J. Besson Damage of ductile materials deforming under multiple plastic or viscoplastic mechanisms Int. J. Plast. 25 2009 2204 2221
J. Besson Continuum models of ductile fracture: a review Int. J. Damage Mech. 19 2010 3 52
S. Boers, P. Schreurs, and M. Geers Operator-split damage-plasticity applied to groove forming in food can lids Int. J. Solids Struct. 42 2005 4154 4178
N. Bonora, A. Ruggiero, L. Esposito, and D. Gentile CDM modeling of ductile failure in ferritic steels: assessment of the geometry transferability of model parameters Int. J. Plast. 22 2006 2015 2047
E. Borgqvist, and M. Wallin Numerical integration of elasto-plasticity coupled to damage using a diagonal implicit Runge-Kutta integration scheme Int. J. Damage Mech. 22 2013 68 94
A. Boryor, A. Hohmann, M. Geiger, U. Wolfram, C. Sander, and F.G. Sander A downloadable meshed human canine tooth model with PDL and bone for finite element simulations Dental Mater. 25 2009 e57 e62
C. Bourauel, D. Vollmer, and A. Jäger Application of bone remodeling theories in the simulation of orthodontic tooth movements J. Orofac. Orthop. 61 2000 266 279
G.W. Brodland, D.I.L. Chen, and J.H. Veldhuis A cell-based constitutive model for embryonic epithelia and other planar aggregates of biological cells Int. J. Plast. 22 2006 965 995
M. Brünig Numerical analysis and elastic-plastic deformation behavior of anisotropically damaged solids Int. J. Plast. 18 2002 1237 1270
M. Brünig An anisotropic ductile damage model based on irreversible thermodynamics Int. J. Plast. 19 2003 1679 1713
M. Brünig Numerical analysis of anisotropic ductile continuum damage Comput. Methods Appl. Mech. Eng. 192 2003 2949 2976
M. Brünig, and S. Gerke Simulation of damage evolution in ductile metals undergoing dynamic loading conditions Int. J. Plast. 27 2011 1598 1617
M. Brünig, O. Chyra, D. Albrecht, L. Driemeier, and M. Alves A ductile damage criterion at various stress triaxialities Int. J. Plast. 24 2008 1731 1755
B. Calvo, E. Pea, P. Martins, T. Mascarenhas, M. Doblar, R.N. Jorge, and A. Ferreira On modelling damage process in vaginal tissue J. Biomech. 42 2009 642 651
S.C. Cowin Wolff's law of trabecular architecture at remodelling equilibrium J. Biomech. Eng. 108 1986 83 88
R. Desmorat, and S. Otin Cross-identification isotropic/anisotropic damage and application to anisothermal structural failure Eng. Fract. Mech. 75 2008 3446 3463
E. de Souza Neto, and D. Perić A computational framework for a class of fully coupled models for elastoplastic damage at finite strains with reference to the linearization aspects Comput. Methods Appl. Mech. Eng. 130 1996 179 193
E. de Souza Neto, D. Perić, and D. Owen A model for elastoplastic damage at finite strains: algorithmic issues and applications Eng. Comput. 11 1994 257 281
E.A. de Souza Neto, D. Peric, and D.R.J. Owen Computational Methods for Plasticity: Theory and Applications 2011 John Wiley & Sons
M. Doblaré, and J.M. García Anisotropic bone remodelling model based on a continuum damage-repair theory J. Biomech. 35 2002 1 17
I. Doghri Numerical implementation and analysis of a class of metal plasticity models coupled with ductile damage Int. J. Numer. Methods Eng. 38 1995 3403 3431
V. d'Otreppe, R. Boman, and J.P. Ponthot Generating smooth surface meshes from multi-region medical images Int. J. Numer. Methods Biomed. Eng. 28 2012 646 660
R. Duddu, and H. Waisman A nonlocal continuum damage mechanics approach to simulation of creep fracture in ice sheets Comput. Mech. 51 2013 961 974
M. Dunand, A.P. Maertens, M. Luo, and D. Mohr Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading - part I: plasticity Int. J. Plast. 36 2012 34 49
M. Ekh, R. Lillbacka, and K. Runesson A model framework for anisotropic damage coupled to crystal (visco)plasticity Int. J. Plast. 20 2004 2143 2159
R. El khaoulani, and P.O. Bouchard Efficient numerical integration of an elastic-plastic damage law within a mixed velocity-pressure formulation Math. Comput. Simul. 94 2013 145 158
H. Frost The Laws of Bone Structure 1964 Henry Ford Hospital Surgical Monographs
H. Frost Bone mass and the mechanostat: a proposal Anat. Rec. 219 1987 1 9
J.M. García, M. Doblaré, and J. Cegonino Bone remodelling simulation: a tool for implant design Comput. Mater. Sci. 25 2002 100 114
D. Garcia, P.K. Zysset, M. Charlebois, and A. Curnier A three-dimensional elastic plastic damage constitutive law for bone tissue Biomech. Model. Mechanobiol. 8 2009 149 165
S. Guo, G. Kang, and J. Zhang A cyclic visco-plastic constitutive model for time-dependent ratchetting of particle-reinforced metal matrix composites Int. J. Plast. 40 2013 101 125
A. Gurson Continuum theory of ductile rupture by void nucleation and growth I. Yield criteria and flow rules for porous ductile media Trans. ASME Ser. H, J. Eng. Mater. Technol. 99 1977 2 15
Y. Hammi, and M. Horstemeyer A physically motivated anisotropic tensorial representation of damage with separate functions for void nucleation, growth, and coalescence Int. J. Plast. 23 2007 1641 1678
M.F. Horstemeyer, and D.J. Bammann Historical review of internal state variable theory for inelasticity Int. J. Plast. 26 2010 1310 1334
M. Horstemeyer, M. Matalanis, A. Sieber, and M. Botos Micromechanical finite element calculations of temperature and void configuration effects on void growth and coalescence Int. J. Plast. 16 2000 979 1015
S. Hosseini, W. Wilson, K. Ito, and C. van Donkelaar A numerical model to study mechanically induced initiation and progression of damage in articular cartilage Osteoarthr. Cartilage 22 2014 95 103
Jacobs, C.R., 1994. Numerical Simulation of Bone Adaptation to Mechanical Loading. Ph.D. Thesis, Department of Mechanical Engineering - Stanford University.
P.P. Jeunechamps, and J.P. Ponthot An efficient 3D implicit approach for the thermomechanical simulation of elastic-viscoplastic materials submitted to high strain rate and damage Int. J. Numer. Methods Eng. 94 2013 920 960
L. Kachanov Time of the rupture process under creep conditions TVZ Akad Nauk S.S.R. Otd. Tech. Nauk 8 1958 26 31
A.S. Khan, and H. Liu A new approach for ductile fracture prediction on al 2024-t351 alloy Int. J. Plast. 35 2012 1 12
M. Kitzig, and U. Häußler-Combe Modeling of plain concrete structures based on an anisotropic damage formulation Mater. Struct. 44 2011 1837 1853
V. Krishnan, and Z. Davidovitch On a path to unfolding the biological mechanisms of orthodontic tooth movement J. Dental Res. 88 2009 597 608
Y. Lai, L. Jin, and X. Chang Yield criterion and elasto-plastic damage constitutive model for frozen sandy soil Int. J. Plast. 25 2009 1177 1205
L. Lecarme, C. Tekoglu, and T. Pardoen Void growth and coalescence in ductile solids with stage III and stage IV strain hardening Int. J. Plast. 27 2011 1203 1223
J. Lemaitre A Course on Damage Mechanics Failures 1992 Springer-Verlag
J. Lemaitre, and R. Desmorat Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures 2005 Springer
J. Lemaitre, R. Desmorat, and M. Sauzay Anisotropic damage law of evolution Eur. J. Mech. - A/Solids 19 2000 187 208
A. Lennon, and P. Prendergast Modelling damage growth and failure in elastic materials with random defect distributions Math. Proc. Roy. Irish Acad. 104 2004 155 171
S. Lindauer The basics of orthodontic mechanics Sem. Orthod. 7 2001 2 15
M. Luo, M. Dunand, and D. Mohr Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading - part II: ductile fracture Int. J. Plast. 2012 36 58
R. Mahnken Theoretical, numerical and identification aspects of a new model class for ductile damage Int. J. Plast. 18 2002 801 831
R.S. Masella, and P.L. Chung Thinking beyond the wire: Emerging biologic relationships in orthodontics and periodontology Sem. Orthod. 14 2008 290 304 Emerging Concepts in Orthodontic Periodontal Interactions for the 21st Century
M. Mashayekhi, S. Ziaei-Rad, J. Parvizian, K. Nikbin, and H. Hadavinia Numerical analysis of damage evolution in ductile solids Struct. Integrity Durability 1 2005 67 82
B. Melsen Tissue reaction to orthodontic tooth movement - a new paradigm Eur. J. Orthod. 23 2001 671 681
Mengoni, M., 2012. On the Development of an Integrated Bone Remodeling Law for Orthodontic Tooth Movements Models using the Finite Element Method. PhD Thesis, School of Engineering, University of Liège, Belgium. http://orbi.ulg.ac.be/handle/2268/126082.
M. Mengoni, and J.P. Ponthot Isotropic continuum damage/repair model for alveolar bone remodeling J. Comput. Appl. Math. 234 2010 2036 2045
M. Mengoni, R. Voide, C. de Bien, H. Freichels, C. Jérôme, A. Léonard, D. Toye, G.H. van Lenthe, R. Müller, and J.P. Ponthot A non-linear homogeneous model for bone-like materials under compressive load Int. J. Numer. Methods Biomed. Eng. 28 2012 334 348
A. Menzel, and P. Steinmann A theoretical and computational framework for anisotropic continuum damage mechanics at large strains Int. J. Solids Struct. 38 2001 9505 9523
A. Menzel, M. Ekh, P. Steinmann, and K. Runesson Anisotropic damage coupled to plasticity: modelling based on the effective configuration concept Int. J. Numer. Methods Eng. 54 2002 1409 1430
A. Menzel, M. Ekh, K. Runesson, and P. Steinmann A framework for multiplicative elastoplasticity with kinematic hardening coupled to anisotropic damage Int. J. Plast. 21 2005 397 434
G.L. Niebur, M.J. Feldstein, J.C. Yuen, T.J. Chen, and T.M. Keaveny High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone J. Biomech. 33 2000 1575 1583
J.P. Ponthot Unified stress update algorithms for the numerical simulation of large deformation elasto-plastic and elasto-viscoplastic processes Int. J. Plast. 18 2002 91 126
M. Qasim, R.N. Natarajan, H.S. An, and G.B. Andersson Damage accumulation location under cyclic loading in the lumbar disc shifts from inner annulus lamellae to peripheral annulus with increasing disc degeneration J. Biomech. 47 2014 24 31
W. Qi, and A. Bertram Anisotropic continuum damage modeling for single crystals at high temperatures Int. J. Plast. 15 1999 1197 1215
W.E. Roberts Bone physiology of tooth movement, ankylosis, and osseointegration Sem. Orthod. 6 2000 173 182
Rabotnov, Y.N. Creep Rupture. In: Hetenyi, M., Vincenti, W.G. (Eds.), Proceedings of the 12th International Congress of Applied Mechanics, Stanford 1968, Springer, Berlin, pp. 342-349
G. Rousselier Ductile fracture models and their potential in local approach of fracture Nucl. Eng. Des. 105 1987 97 111
A. Shojaei, G.Z. Voyiadjis, and P. Tan Viscoplastic constitutive theory for brittle to ductile damage in polycrystalline materials under dynamic loading Int. J. Plast. 48 2013 125 151
J. Simo, and J. Ju Strain-and stress-based continuum damage models I. Formulation Int. J. Solids Struct. 23 1987 820 840
J. Simo, and J. Ju Strain-and stress-based continuum damage models II. Computational aspects Int. J. Solids Struct. 23 1987 841 869
F.V. Souza, and D.H. Allen Computation of homogenized constitutive tensor of elastic solids containing evolving cracks Int. J. Damage Mech. 21 2012 267 291
C.M. Stewart, A.P. Gordon, Y.W. Ma, and R.W. Neu An anisotropic tertiary creep damage constitutive model for anisotropic materials Int. J. Pressure Ves. Piping 88 2011 356 364
J. Stölken, and J. Kinney On the importance of geometric nonlinearity in finite-element simulations of trabecular bone failure Bone 33 2003 494 504
C. Tekoglu, and T. Pardoen A micromechanics based damage model for composite materials Int. J. Plast. 26 2010 549 569
V. Tvergaard, and A. Needleman Analysis of the cup-cone fracture in a round tensile bar Acta Metall. 32 1984 157 169
A. Van Schepdael, J. Vander Sloten, and L. Geris A mechanobiological model of orthodontic tooth movement Biomech. Model. Mechanobiol. 12 2013 249 265
M. Vaz, and D.R.J. Owen Aspects of ductile fracture and adaptive mesh refinement in damaged elasto-plastic materials Int. J. Numer. Methods Eng. 50 2001 29 54
E. Verhulp, B. van Rietbergen, R. Müller, and R. Huiskes Micro-finite element simulation of trabecular-bone post-yield behaviour - effects of material model, element size and type Comput. Methods Biomech. Biomed. Eng. 11 2008 389 395
C. Verna, M. Dalstra, T.C. Lee, P.M. Cattaneo, and B. Melsen Microcracks in the alveolar bone following orthodontic tooth movement: a morphological and morphometric study Eur. J. Orthod. 26 2004 459 467
G.Z. Voyiadjis, and P.I. Kattan Advances in Damage Mechanics: Metals and Metal Matrix Composites with an Introduction to Fabric Tensors second ed. 2006 Elsevier Science Ltd
G.Z. Voyiadjis, Z.N. Taqieddin, and P.I. Kattan Anisotropic damage-plasticity model for concrete Int. J. Plast. 24 2008 1946 1965
F. Zaïri, M. Naït-Abdelaziz, J. Gloaguen, and J. Lefebvre A physically-based constitutive model for anisotropic damage in rubber-toughened glassy polymers during finite deformation Int. J. Plast. 27 2011 25 51
M. Zapara, N. Tutyshkin, W.H. Müller, and R. Wille Constitutive equations of a tensorial model for ductile damage of metals Continuum Mech. Thermodyn. 24 2012 697 717
P. Zysset, and A. Curnier A 3D damage model for trabecular bone based on fabric tensors J. Biomech. 29 1996 1549 1558
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
