A higher-order stress-based gradient-enhanced damage model based on isogeometric analysis

Abstract The micro-damage associated with diffuse fracture processes in quasi-brittle materials can be described by continuum damage mechanics. In order to overcome the mesh dependence of local damage formulations, non-local and gradient-enhanced approaches are often employed. In this manuscript, a higher-order stress-based gradient-enhanced formulation is proposed, which exploits the higher-order continuity of B-spline functions in isogeometric analysis (IGA). The proposed formulation does not require the decomposition of the fourth-order model into two second-order models. Two numerical examples are presented to demonstrate the performance of the formulation and to compare the obtained solutions with results from conventional gradient-enhanced damage formulation.

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

[2]  Thomas J. R. Hughes,et al.  A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework , 2014 .

[3]  Hehua Zhu,et al.  An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function , 2014 .

[4]  Mgd Marc Geers,et al.  Strain-based transient-gradient damage model for failure analyses , 1998 .

[5]  Ted Belytschko,et al.  Bridging domain methods for coupled atomistic–continuum models with L2 or H1 couplings , 2009 .

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

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

[8]  Nicolas Triantafyllidis,et al.  A gradient approach to localization of deformation. I. Hyperelastic materials , 1986 .

[9]  Ted Belytschko,et al.  Concurrently coupled atomistic and XFEM models for dislocations and cracks , 2009 .

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

[11]  T. Belytschko,et al.  Localization limiters in transient problems , 1988 .

[12]  T. Rabczuk,et al.  Molecular dynamics/xfem coupling by a three-dimensional extended bridging domain with applications to dynamic brittle fracture , 2013 .

[13]  Timon Rabczuk,et al.  Finite strain fracture of plates and shells with configurational forces and edge rotations , 2013 .

[14]  Ted Belytschko,et al.  An adaptive concurrent multiscale method for the dynamic simulation of dislocations , 2011 .

[15]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[16]  Ted Belytschko,et al.  Cracking particles: a simplified meshfree method for arbitrary evolving cracks , 2004 .

[17]  T. Hughes,et al.  Isogeometric analysis of the Cahn–Hilliard phase-field model , 2008 .

[18]  Charles E. Augarde,et al.  Fracture modeling using meshless methods and level sets in 3D: Framework and modeling , 2012 .

[19]  L. J. Sluys,et al.  Incorrect initiation and propagation of failure in non-local and gradient-enhanced media , 2004 .

[20]  Gilles Pijaudier-Cabot,et al.  Measurement of Characteristic Length of Nonlocal Continuum , 1989 .

[21]  Rhj Ron Peerlings,et al.  Gradient‐enhanced damage modelling of concrete fracture , 1998 .

[22]  Jerzy Pamin,et al.  Dispersion analysis and element‐free Galerkin solutions of second‐ and fourth‐order gradient‐enhanced damage models , 2000 .

[23]  Yuri Bazilevs,et al.  Rotation free isogeometric thin shell analysis using PHT-splines , 2011 .

[24]  Antonio Huerta,et al.  Discretization Influence on Regularization by Two Localization Limiters , 1994 .

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

[26]  Antolino Gallego,et al.  NURBS-based analysis of higher-order composite shells , 2013 .

[27]  F. Dufour,et al.  Stress‐based Non‐local Damage Model , 2013 .

[28]  G. Bongers.  A stress-based gradient-enhanced damage model , 2011 .

[29]  T. Belytschko,et al.  A three dimensional large deformation meshfree method for arbitrary evolving cracks , 2007 .

[30]  A. C. Eringen,et al.  Crack-tip problem in non-local elasticity , 1977 .

[31]  M. Crisfield.  A FAST INCREMENTAL/ITERATIVE SOLUTION PROCEDURE THAT HANDLES "SNAP-THROUGH" , 1981 .

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

[33]  Milan Jirásek,et al.  Size effect on fracture energy induced by non‐locality , 2004 .

[34]  Timon Rabczuk,et al.  An adaptive multiscale method for quasi-static crack growth , 2014 .

[35]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[36]  Gouri Dhatt,et al.  Incremental displacement algorithms for nonlinear problems , 1979 .

[37]  Hehua Zhu,et al.  A nonlinear semi-concurrent multiscale method for fractures , 2016 .

[38]  Wam Marcel Brekelmans,et al.  Comparison of nonlocal approaches in continuum damage mechanics , 1995 .

[39]  G. Meschke,et al.  Numerical modeling of concrete cracking , 2011 .

[40]  Timon Rabczuk,et al.  Efficient coarse graining in multiscale modeling of fracture , 2014 .

[41]  Thomas J. R. Hughes,et al.  An isogeometric analysis approach to gradient damage models , 2011 .

[42]  Ted Belytschko,et al.  Coupling Methods for Continuum Model with Molecular Model , 2003 .

[43]  P. Steinmann,et al.  A finite element method for the computational modelling of cohesive cracks , 2005 .

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

[45]  Mgd Marc Geers,et al.  Enhanced damage modelling of quasi-brittle and fatigue fracture : computational aspects , 2000 .

[46]  Zhen Chen,et al.  One-Dimensional Softening With Localization , 1986 .

[47]  R. Desmorat,et al.  Nonstandard Thermodynamics Framework for Robust Computations with Induced Anisotropic Damage , 2010 .

[48]  T. Belytschko,et al.  A bridging domain method for coupling continua with molecular dynamics , 2004 .

[49]  Ted Belytschko,et al.  A method for dynamic crack and shear band propagation with phantom nodes , 2006 .

[50]  T. Rabczuk,et al.  Phase-field modeling of fracture in linear thin shells , 2014 .

[51]  Stéphane Bordas,et al.  A meshless adaptive multiscale method for fracture , 2015 .

[52]  Z. Bažant,et al.  Nonlocal Continuum Damage, Localization Instability and Convergence , 1988 .

[53]  Timon Rabczuk,et al.  Initially rigid cohesive laws and fracture based on edge rotations , 2013 .

[54]  Timon Rabczuk,et al.  Concurrent multiscale modeling of three dimensional crack and dislocation propagation , 2015, Adv. Eng. Softw..