Local second gradient models and damage mechanics: application to concrete

The non linear behaviour of concrete is often simulated using local constitutive models based on the continuous damage mechanics theory. This approach however is not adequate for post-localisation studies with strain softening. It is well known that spurious mesh dependence appears in computations and cases of failure without energy dissipation. In order to improve computational performance second grade local models are chosen to include a meso scale in the continuous damage model. This approach differs from the nonlocal one in the sense that it is a local theory with higher order stresses depending only on the local cinematic history. 1D numerical computations with concrete specimens are presented. Using a random initialisation of the iterative solver of the equilibrium equation we search the existence of various solutions for the boundary value study and also to see if the second grade term regularise the problem giving results that are mesh insensitive and objective.

[1]  Gilles Pijaudier-Cabot,et al.  Isotropic and anisotropic descriptions of damage in concrete structures , 1999 .

[2]  Dusan Krajcinovic,et al.  Constitutive Equations for Damaging Materials , 1983 .

[3]  Rhj Ron Peerlings,et al.  Gradient enhanced damage for quasi-brittle materials , 1996 .

[4]  C. Borderie.  Phénomènes unilatéraux dans un matériau endommageable : Modélisation et application à l'analyse de structures en béton. , 1991 .

[5]  J. Mazars.  A description of micro- and macroscale damage of concrete structures , 1986 .

[6]  Z. Bažant,et al.  Nonlocal damage theory , 1987 .

[7]  Zenon Mróz,et al.  A continuum model for plastic-brittle behaviour of rock and concrete , 1979 .

[8]  R. Chambon,et al.  Etude de la localisation unidimensionnelle à l'aide d'un modèle de second gradient , 1996 .

[9]  P. Germain,et al.  The Method of Virtual Power in Continuum Mechanics. Part 2: Microstructure , 1973 .

[10]  J Mazars,et al.  APPLICATION DE LA THEORIE DE L'ENDOMMAGEMENT AU COMPORTEMENT NON LINEAIRE ET A LA RUPTURE DU BETON DE STRUCTURE , 1982 .

[11]  René Chambon,et al.  Plastic continuum with microstructure, Local Second Gradient Theories for Geomaterials : Localization Studies , 2001 .

[12]  N. Burlion,et al.  Damage and localisation in elastic materials with voids , 1996 .

[13]  Jacky Mazars,et al.  Damage model for concrete‐like materials coupling cracking and friction, contribution towards structural damping: first uniaxial applications , 2000 .

[14]  M. Frémond,et al.  Damage, gradient of damage and principle of virtual power , 1996 .

[15]  René Chambon,et al.  Second gradient models as a particular case of microstructured models: a large strain finite elements analysis , 2000 .

[16]  Gilles Pijaudier-Cabot,et al.  Continuum damage modelling: Approximation of crack induced anisotropy , 1997 .

[17]  J. Lemaitre,et al.  Mécanique des matériaux solides , 1996 .

[18]  D. Caillerie,et al.  One-dimensional localisation studied with a second grade model , 1998 .

[19]  J. Mazars.  APPLICATION DE LA MECANIQUE DE L'ENDOMMAGEMENT AU COMPORTEMENT NON LINEAIRE ET A LA RUPTURE DU BETON DE STRUCTURE , 1984 .

[20]  Mgd Marc Geers,et al.  A critical comparison of nonlocal and gradient-enhanced softening continua , 2001 .

[21]  E. Aifantis.  On the Microstructural Origin of Certain Inelastic Models , 1984 .

[22]  Zdenek P. Bazant,et al.  Instability, Ductility, and Size Effect in Strain-Softening Concrete , 1978 .

[23]  Gilles Pijaudier-Cabot,et al.  Coupled diffusion-damage modelling and the implications on failure due to strain localisation , 1998 .

[24]  R. D. Mindlin.  Micro-structure in linear elasticity , 1964 .

[25]  Robert Charlier,et al.  An algorithm and a method to search bifurcation points in non‐linear problems , 2001 .

[26]  Gilles Pijaudier-Cabot,et al.  CONTINUUM DAMAGE THEORY - APPLICATION TO CONCRETE , 1989 .