Sciences de l'ingénieur; Damage; Internal length; Strain localization
Abstract :
[en] Classical finite element method including strain-softening materials suffers from a mesh-dependency solution. The thickness of the bands in which strains are localized is arbitrarily narrow and may lead to a rupture without energy consumption. This is the case in quasi-static as well as in dynamics problems. The present paper uses a two-scale dynamic damage law that is based on an intrinsic length at micro-scale, corresponding to the inter-distance between two adjacent micro-cracks, that regularizes the strain localization problem in dynamics. The material response is time-dependent due to the inertial effect of the micro-crack propagation. This produces a natural, microstructurally-based, delayed response of the material that, in turn, removes the mesh-sensitivity in dynamics. As a consequence, the size of the strain localization band is controlled by the internal length of the material.
Disciplines :
Civil engineering
Author, co-author :
François, Bertrand ; Université de Liège - ULiège > Urban and Environmental Engineering
Keita, Oumar
Language :
French
Title :
A microstructurally-based internal length for strain localization problems in dynamics.
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
E.C. Aifantis On the microstructural origin of certain inelastic models J. Eng. Mater. Technol. 106 4 1984 326 330
M.F. Ashby, and S.D. Hallam The failure of brittle solids containing small cracks under compressive stress states Acta Metall. 34 1986 497 510
H. Bhatt, A. Rosakis, and G. Sammis A micro-mechanics based constitutive model for brittle failure at high strain rates J. Appl. Mech. 79 3 2011 1016 1028
Z.P. Bazant, T. Belytschko, and T. Chang Continuum theory for strain softening J. Eng. Mech. 110 12 1984 1666 1692
Z.P. Bazant Instability, ductility, and size effect in strain-softening concrete J. Eng. Mech. Div. 102 2 1976 331 344
Z.P. Bazant Scaling of Structural Strength 2002 Hermes Penton Science London
Z.P. Bazant, and T.B. Belytschko Wave propagation in a strain-softening bar: exact solution ASCE J. Eng. Mech. 111 3 1985 381 389
Z.P. Bazant, and G. Pijaudier-Cabot Nonlocal continuum damage, localization instability and convergence J. Appl. Mech. ASME 55 1998 287 294
T. Belytschko, Z.P. Bazant, Y.W. Hyun, and T.P. Chang Strain-softening materials and finite-element solutions Comput. Struct. 23 2 1986 163 180
A. Benssousan, J. Lions, and G. Papanicolaou Asymptotic Analysis for Periodic Structures 1978 Kluwer Academic Publisher Amsterdam
W.F. Brace, and E.G. Bombolakis A note on brittle crack growth in compression J. Geophys. Res. 68 1963 3709 3713
R. Chambon, D. Caillerie, and T. Matsushima Plastic continuum with microstructure, local second gradient theories for geomaterials: localization studies Int. J. Solids Struct. 38 2001 8503 8527
R. Charlier Approche unifiée de quelques problèmes non linéaires de mécanique des milieux continus par la méthode des éléments finis PhD Thesis 1987 Université de Liège
F. Collin, R. Chambon, and R. Charlier A finite element method for poro mechanical modelling of geotechnical problems using local second gradient models Int. J. Numer. Method Eng. 65 2006 1749 1772
C. Dascalu, G. Bilbie, and E. Agiasofitou Damage and size effect in elastic solids:A homogenization approach Int. J. Solid Struct. 45 2008 409 430
R. De Borst, and L.J. Sluys Localisation in a Cosserat continuum under static and dynamic loading conditions Comput. Methods Appl. Mech. Eng. 90 1 1991 805 827
R. De Borst, L.J. Sluys, H.B. Muhlhaus, and J. Pamin Fundamental issues in finite element analyses of localization of deformation Eng. Comput. 10 2 1993 99 121
R. Desmorat, M. Chambart, F. Gatuingt, and D. Guilbaud Delay-active damage versus non-local enhancement for anisotropic damage dynamics computations with alternated loading Eng. Fract. Mech. 77 12 2010 2294 2315
B. François, and C. Dascalu A two-scale time-dependent damage model based on non-planar growth of micro-cracks J. Mech. Phys. Solids 58 11 2010 1928 1946
L.B. Freund Dynamic Fracture Mechanics 1998 Cambridge University Press
A. Glema, T. Lodygowski, and P. Perzyna Interaction of deformation waves and localization phenomena in inelastic solids Comput. Methods Appl. Mech. Eng. 183 2000 123 140
S. Graff, S. Forest, J.L. Strudel, C. Prioul, P. Pilvin, and J.L. Béchade Strain localization phenomena associated with static and dynamic strain ageing in notched specimens: experiments and finite element simulations Mater. Sci. Eng. A 387 2004 181 185
R. Hill Acceleration waves in solids J. Mech. Phys. Solids 10 1 1962 1 16
C. Huang, G. Subhash, and S.J. Vitton A dynamic damage growth model for uniaxial compressive response of rock aggregates Mech. Mater. 34 2002 267 277
O. Keita, C. Dascalu, and B. François A two-scale model for dynamic damage evolution J. Mech. Phys. Solids 64 2014 170 183
V. Kouznetsova, M.G.D. Geers, and W.A.M. Brekelmans Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme Int. J. Numer. Methods Eng. 54 2002 1235 1260
D. Lasry, and T. Belytschko Localization limiters in transient problems Int. J. Solids Struct. 24 6 1988 581 597
R. Mindlin Second gradient of strain and surface-tension in linear elasticity Int. J. Solids Struct. 1 1965 417 438
H.B. Mühlhaus Application of Cosserat theory in numerical solutions of limit load problems Arch. Appl. Mech. 59 2 1989 124 137
H.B. Mühlhaus, and E.C. Aifantis A variational principle for gradient plasticity Int. J. Solids Struct. 28 1991 845 858
A. Needleman Material rate dependance and mesh sensitivity in localization problems Comput. Meth. Appl. Mech. Eng. 67 1988 69 85
S. Nemat-Nasser, and M. Horii Compression-induced nonplanar crack extension with application to splitting, exfoliation, and rockburst J. Geophys. Res. 87 1982 6805 7682
S. Nemat-Nasser, and H. Deng Strain-rate effect on brittle failure in compression Acta Metall. Mater. 42 1994 1013 1024
F. Nicot, and F. Darve Diffuse and localized failure modes: two competing mechanisms Int. J. Numer. Anal. Meth. Geomech. 35 5 2011 586 601
R.R. Pedersen, A. Simone, and L.J. Sluys An analysis of dynamic fracture in concrete with a continuum visco-elastic visco-plastic damage model Eng. Fract. Mech. 75 13 2008 3782 3805
R.H.J. Peerlings, R. De Borst, W.A.M. Brekelmans, and J.H.P. de Vree Gradient enhanced damage for quasi-brittle materials Int. J. Numer. Meth. Eng. 39 1996 937 953
R.H.J. Peerlings, R. De Borst, W.A.M. Brekelmans, and M.G.D. Geers Localisation issues in local and nonlocal continuum approaches to fracture Eur. J. Mech. A/Solids 21 2 2002 175 189
R.H.J. Peerlings, and N.A. Fleck Computational evaluation of strain gradient elasticity constants Int. J. Multiscale Comput. Eng. 2 2004 599 619
G. Pijaudier-Cabot, and Z.P. Bazant Nonlocal damage theory J. Eng. Mech. 113 10 1987 1512 1533
G. Ravichandran, and G. Subhash A micromechanical model for high strain rate behavior of ceramics Int. J. Solids Struct. 32 1995 2627 2646
E. Sanchez-Palencia Non-homogeneous Media and Vibration Theory. Lecture Notes in Physics vol. 127 1980 Springer Berlin
V.P. Smyshlyaev, and K.D. Cherednichenko On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media J. Mech. Phys. Solids 48 2000 1325 1357
L.J. Sluys, and R. De Borst Wave propagation and localization in a rate-dependent cracked medium-model formulation and one-dimensional examples Int. J. Solids Struct. 29 23 1992 2945 2958
L.J. Sluys, R. De Borst, and H.-B. Mühlhaus Wave propagation, localization and dispersion in a gradient-dependent medium Int. J. Solids Struct. 30 9 1993 1153 1171
J. Sulem Bifurcation theory and localization phenomena Eur. J. Environ. Civ. Eng. 14 8-9 2010 989 1009
T.-H. Tran, V. Monchiet, and G. Bonnet A micromechanics-based approach for the derivation of constitutive elastic coefficients of strain-gradient media Int. J. Solids Struct. 49 2012 783 792
W.M. Wang, L.J. Sluys, and R. De Borst Interaction between material length scale and imperfection size for localization phenomena in viscoplastic media Eur. J. Mech. A/Solids 15 1996 447 464
E.Z. Wang, and N.G. Shrive Brittle fracture in compression: mechanisms, models and criteria Eng. Fract. Mech. 52 1995 1107 1126
T.F. Wong A note on the propagation behaviour of a crack nucleated by a dislocation pile-up J. Geophys. Res. 95 1990 8639 8646
F.H. Wu, and L.B. Freund Deformation trapping due to thermoplastic instability in one-dimensional wave propagation J. Mech. Phys. Solids 32 2 1984 119 132
J.X. Zhang, T.F. Wong, and D.M. Davis Micromechanics of pressured-induced grain crushing in porous rocks J. Geophys. Res. 95 1990 341 351
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.
