Three-dimensional analysis of a cohesive crack coupled with heat flux through the crack

This paper presents an algorithm for coupling cohesive crack modeling with non-stationary heat flow. Firstly, the nonlinear system of equation, based on global formulations, for such a computational model is derived. The nonlinearity here comes from nonlinear relations in the crack. The relations refer to cohesion forces and to heat flux which both depend of crack opening and additionally are dependent of temperature difference between both sides of the crack. In the paper the discontinuities of displacement field and temperature field are both approximated using XFEM. All the analysis concerning crack surface is performed using local coordinate systems for each integration point. The local coordinate system is two-dimensional for both 2D and 3D analysis. The paper is illustrated with non-stationary thermo-mechanical examples for a domain with propagating crack.

[1]  T. Belytschko,et al.  The extended/generalized finite element method: An overview of the method and its applications , 2010 .

[2]  L. J. Sluys,et al.  A new method for modelling cohesive cracks using finite elements , 2001 .

[3]  M. Ortiz,et al.  FINITE-DEFORMATION IRREVERSIBLE COHESIVE ELEMENTS FOR THREE-DIMENSIONAL CRACK-PROPAGATION ANALYSIS , 1999 .

[4]  J. Jaśkowiec.  Analysis of cohesive crack coupled with thermoelasticity , 2014 .

[5]  Mark A Fleming,et al.  ENRICHED ELEMENT-FREE GALERKIN METHODS FOR CRACK TIP FIELDS , 1997 .

[6]  I. Singh,et al.  Simulation of 3-D thermo-elastic fracture problems using coupled FE-EFG approach , 2014 .

[7]  S. Belouettar,et al.  Thermal and thermo-mechanical influence on crack propagation using an extended mesh free method , 2012 .

[8]  M. Ortiz,et al.  Three‐dimensional cohesive modeling of dynamic mixed‐mode fracture , 2001 .

[9]  T. Belytschko,et al.  Extended finite element method for cohesive crack growth , 2002 .

[10]  Marco Paggi,et al.  A coupled cohesive zone model for transient analysis of thermoelastic interface debonding , 2014, 1410.0242.

[11]  Huang Yuan,et al.  Applications of normal stress dominated cohesive zone models for mixed-mode crack simulation based on extended finite element methods , 2011 .

[12]  J. Jaśkowiec,et al.  Coupling of FEM and EFGM with dynamic decomposition in 2D quasi-brittle crack growth analysis , 2004 .

[13]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[14]  Marc Duflot,et al.  The extended finite element method in thermoelastic fracture mechanics , 2008 .

[15]  Mgd Marc Geers,et al.  A Thermo-mechanical cohesive zone model , 2010 .

[16]  M. Ortiz,et al.  On the convergence of 3D free discontinuity models in variational fracture , 2010 .

[17]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[18]  Ares J. Rosakis,et al.  3D Modelling of Impact Failure in Sandwich Structures , 2003 .

[19]  M. Eslami,et al.  Higher order tip enrichment of eXtended Finite Element Method in thermoelasticity , 2010 .

[20]  T. Siegmund,et al.  A numerical study on interface crack growth under heat flux loading , 2005 .

[21]  M. Ortiz,et al.  Three-dimensional modeling of intersonic shear-crack growth in asymmetrically loaded unidirectional composite plates , 2002 .

[22]  Jan Jaśkowiec,et al.  A consistent iterative scheme for 2D and 3D cohesive crack analysis in XFEM , 2014 .

[23]  Michael Ortiz,et al.  Three‐dimensional finite‐element simulation of the dynamic Brazilian tests on concrete cylinders , 2000 .

[24]  R. Larsson,et al.  A thermo-mechanical cohesive zone formulation for ductile fracture , 2008 .

[25]  G. Maugin.  The Thermomechanics of Plasticity and Fracture , 1992 .

[26]  Xiaopeng Xu,et al.  Numerical simulations of fast crack growth in brittle solids , 1994 .

[27]  N. Chevaugeon,et al.  Improved crack tip enrichment functions and integration for crack modeling using the extended finite element method , 2013 .

[28]  Milan Jirásek,et al.  Inelastic Analysis of Structures , 2001 .

[29]  Application of the extended EFG method and cohesive crack model to the crack growth analysis of concrete structures , 2002 .

[30]  P. Bouchard,et al.  Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria , 2003 .

[31]  Hamouine Abdelmadjid,et al.  A state-of-the-art review of the X-FEM for computational fracture mechanics , 2009 .

[32]  J. Chaboche,et al.  Mechanics of Solid Materials , 1990 .

[33]  Jesper L. Asferg,et al.  A consistent partly cracked XFEM element for cohesive crack growth , 2007 .

[34]  Paul A. Wawrzynek,et al.  An algorithm to generate quadrilateral or triangular element surface meshes in arbitrary domains with applications to crack propagation , 1995 .

[35]  Cheng Zhu,et al.  A thermo-mechanical damage model for rock stiffness during anisotropic crack opening and closure , 2014 .