Regularised crack behaviour effects on continuum modelling of quasi-brittle materials under cyclic loading

Abstract A continuum model for quasi-brittle materials able to reproduce mechanical phenomena related to cyclic loading is proposed. Specific care is taken to reproduce progressive stiffness recovery and hysteresis effects caused respectively by crack closure and friction. A virtual testing approach is set up to analyse the evolution of microscopic quantities during uni-axial cyclic tests and to justify an original and efficient modelling of these phenomena. Thus, a regularised formulation of the homogenised multiple contact problem induced by the non-simultaneous closure of microscopic cracks is presented. The proposed continuum model is validated by means of member-scale simulations of reversely loaded reinforced concrete shear walls.

[1]  Anthony Duncan Jefferson,et al.  Smoothed contact in a micromechanical model for cement bound materials , 2013 .

[2]  K. Gylltoft,et al.  A fracture mechanics model for fatigue in concrete , 1984 .

[3]  Gilles Pijaudier-Cabot,et al.  Failure and size effect for notched and unnotched concrete beams , 2013 .

[4]  Benjamin Richard,et al.  A three-dimensional steel/concrete interface model including corrosion effects , 2010 .

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

[6]  Ludovic Jason,et al.  Bond slip model for the simulation of reinforced concrete structures , 2012 .

[7]  Alain Sellier,et al.  Orthotropic damage coupled with localized crack reclosure processing. Part I: Constitutive laws , 2013 .

[8]  M. Tabbara,et al.  RANDOM PARTICLE MODEL FOR FRACTURE OF AGGREGATE OR FIBER COMPOSITES , 1990 .

[9]  A. Hillerborg,et al.  Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements , 1976 .

[10]  Farid Benboudjema,et al.  Creep Consideration Effect on Meso-Scale Modeling of Concrete Hydration Process and Consequences on the Mechanical Behavior , 2013 .

[11]  Roux,et al.  Fracture of disordered, elastic lattices in two dimensions. , 1989, Physical review. B, Condensed matter.

[12]  McCall,et al.  Hysteresis, Discrete Memory, and Nonlinear Wave Propagation in Rock: A New Paradigm. , 1995, Physical review letters.

[13]  H. Reinhardt,et al.  Uniaxial behavior of concrete in cyclic tension , 1989 .

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

[15]  M. Matallah,et al.  A practical method to estimate crack openings in concrete structures , 2009 .

[16]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—I. Formulation , 1987 .

[17]  Benjamin Richard,et al.  Compressive behavior of a lattice discrete element model for quasi-brittle materials , 2014 .

[18]  Kimiro Meguro,et al.  FRACTURE ANALYSES OF CONCRETE STRUCTURES BY THE MODIFIED DISTINCT ELEMENT METHOD , 1989 .

[19]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[20]  Benjamin Richard,et al.  Beam-particle approach to model cracking and energy dissipation in concrete: Identification strategy and validation , 2016 .

[21]  René de Borst,et al.  Gradient-dependent plasticity: formulation and algorithmic aspects , 1992 .

[22]  Bhushan Lal Karihaloo,et al.  Lattice modelling of the failure of particle composites , 2003 .

[23]  Roman Lackner,et al.  An anisotropic elastoplastic‐damage model for plain concrete , 1998 .

[24]  Danièle Chauvel,et al.  CEOS.fr experimental programme and reference specimen tests results , 2014 .

[25]  P. Rivard,et al.  Experimental Study of Crack Closure on Heterogeneous Quasi-Brittle Material , 2015 .

[26]  F. Dufour,et al.  Stress-based nonlocal damage model , 2011 .

[27]  F. Ragueneau,et al.  Continuum damage mechanics based model for quasi brittle materials subjected to cyclic loadings: Formulation, numerical implementation and applications , 2013 .

[28]  H. Reinhardt,et al.  Post-peak cyclic behaviour of concrete in uniaxial tensile and alternating tensile and compressive loading , 1984 .

[29]  Benjamin Richard,et al.  Lattice models applied to cyclic behavior description of quasi‐brittle materials: advantages of implicit integration , 2015 .

[30]  Hans W. Reinhardt,et al.  Tensile Tests and Failure Analysis of Concrete , 1986 .

[31]  M. Matallah,et al.  Inelasticity–damage-based model for numerical modeling of concrete cracking , 2009 .

[32]  P. H. Feenstra,et al.  A composite plasticity model for concrete , 1996 .

[33]  Anthony Duncan Jefferson,et al.  The simulation of crack opening–closing and aggregate interlock behaviour in finite element concrete models , 2015 .

[34]  Erik Schlangen,et al.  Experimental and numerical analysis of micromechanisms of fracture of cement-based composites , 1992 .

[35]  Luc Dormieux,et al.  Micromechanical Analysis of Anisotropic Damage in Brittle Materials , 2002 .

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

[37]  D. Hordijk Local approach to fatigue of concrete , 1991 .