Modelling of reinforced‐concrete structures providing crack‐spacing based on X‐FEM, ED‐FEM and novel operator split solution procedure

In this work, we present a novel approach to the finite element modelling of reinforced-concrete (RC) structures that provides the details of the constitutive behavior of each constituent (concrete, steel and bond-slip), while keeping formally the same appearance as the classical finite element model. Each component constitutive behavior can be brought to fully non-linear range, where we can consider cracking (or localized failure) of concrete, the plastic yielding and failure of steel bars and bond-slip at concrete steel interface accounting for confining pressure effects. The standard finite element code architecture is preserved by using embedded discontinuity (ED-FEM) and extended (X-FEM) finite element strain representation for concrete and slip, respectively, along with the operator split solution method that separates the problem into computing the deformations of RC (with frozen slip) and the current value of the bond-slip. Several numerical examples are presented in order to illustrate very satisfying performance of the proposed methodology. Copyright © 2010 John Wiley & Sons, Ltd.

[1]  Milan Jirásek,et al.  Embedded crack model. Part II: combination with smeared cracks , 2001 .

[2]  Edward L. Wilson,et al.  Unified computational model for static and dynamic frictional contact analysis , 1992 .

[3]  Ted Belytschko,et al.  Arbitrary discontinuities in finite elements , 2001 .

[4]  Adnan Ibrahimbegovic,et al.  Thermodynamic-based interface model for cohesive brittle materials : Application to bond slip in RC structures , 2006 .

[5]  A. Ibrahimbegovic.  Nonlinear Solid Mechanics , 2009 .

[6]  Delphine Brancherie,et al.  Prediction of crack pattern distribution in reinforced concrete by coupling a strong discontinuity model of concrete cracking and a bond‐slip of reinforcement model , 2005 .

[7]  J. Oliver.  On the discrete constitutive models induced by strong discontinuity kinematics and continuum constitutive equations , 2000 .

[8]  Delphine Brancherie,et al.  Combined hardening and softening constitutive model of plasticity: precursor to shear slip line failure , 2003 .

[9]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[10]  A. Huespe,et al.  A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM , 2006 .

[11]  Anna Kucerová,et al.  Novel anisotropic continuum-discrete damage model capable of representing localized failure of massive structures. Part II: identification from tests under heterogeneous stress field , 2009, ArXiv.

[12]  Adnan Ibrahimbegovic,et al.  An efficient implementation of stress resultant plasticity in analysis of Reissner‐Mindlin plates , 1993 .

[13]  Adnan Ibrahimbegovic,et al.  Saint‐Venant multi‐surface plasticity model in strain space and in stress resultants , 2005 .

[14]  Z. Bažant.  Mechanics of Distributed Cracking , 1986 .

[15]  Francisco Armero,et al.  Numerical modeling of softening hinges in thin Euler-Bernoulli beams , 2006 .

[16]  Ted Belytschko,et al.  Structured extended finite element methods for solids defined by implicit surfaces , 2002 .

[17]  Adnan Ibrahimbegovic,et al.  STRESS RESULTANT FINITE ELEMENT ANALYSIS OF REINFORCED CONCRETE PLATES , 1993 .

[18]  Tod A. Laursen,et al.  A finite element formulation for rod/continuum interactions: The one-dimensional slideline , 1994 .