Dual‐horizon peridynamics

Summary In this paper, we develop a dual-horizon peridynamics (DH-PD) formulation that naturally includes varying horizon sizes and completely solves the ‘ghost force’ issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly. Neither the ‘partial stress tensor’ nor the ‘slice’ technique is needed to ameliorate the ghost force issue. We will show that the traditional peridynamics can be derived as a special case of the present DH-PD. All three peridynamic formulations, namely, bond-based, ordinary state-based, and non-ordinary state-based peridynamics, can be implemented within the DH-PD framework. Our DH-PD formulation allows for h-adaptivity and can be implemented in any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed, reducing the computational cost. Both two-dimensional and three-dimensional examples including the Kalthoff–Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method. Copyright © 2016 John Wiley & Sons, Ltd.

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

[2]  F. Bobaru,et al.  Studies of dynamic crack propagation and crack branching with peridynamics , 2010 .

[3]  T. Rabczuk,et al.  T-spline based XIGA for fracture analysis of orthotropic media , 2015 .

[4]  T. Belytschko,et al.  Non‐planar 3D crack growth by the extended finite element and level sets—Part II: Level set update , 2002 .

[5]  R. Batra,et al.  Three-dimensional numerical simulation of the Kalthoff experiment , 2000 .

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

[7]  K. Ravi-Chandar,et al.  Dynamic Fracture of Nominally Brittle Materials , 1998 .

[8]  Timon Rabczuk,et al.  Damage and fracture algorithm using the screened Poisson equation and local remeshing , 2016 .

[9]  Youn Doh Ha,et al.  ADAPTIVE REFINEMENT AND MULTISCALEMODELING IN 2D PERIDYNAMICS , 2011 .

[10]  Ted Belytschko,et al.  Mesh-free Galerkin simulations of dynamic shear band propagation and failure mode transition , 2002 .

[11]  T. L. Warren,et al.  A non-ordinary state-based peridynamic method to model solid material deformation and fracture , 2009 .

[12]  N. Nguyen-Thanh,et al.  An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics , 2014 .

[13]  P. Areias,et al.  Element-wise algorithm for modeling ductile fracture with the Rousselier yield function , 2013 .

[14]  K. Lease,et al.  A new adaptive integration method for the peridynamic theory , 2011 .

[15]  Mirco Zaccariotto,et al.  Crack propagation with adaptive grid refinement in 2D peridynamics , 2014, International Journal of Fracture.

[16]  Richard A. Regueiro,et al.  Peridynamics simulations of geomaterial fragmentation by impulse loads , 2015 .

[17]  Thomas-Peter Fries,et al.  Higher‐order XFEM for curved strong and weak discontinuities , 2009 .

[18]  T. Rabczuk,et al.  XLME interpolants, a seamless bridge between XFEM and enriched meshless methods , 2014 .

[19]  E. Moyer,et al.  Peridynamic Solutions for Timoshenko Beams , 2014 .

[20]  I. Babuska,et al.  The partition of unity finite element method , 1996 .

[21]  T. Rabczuk,et al.  On three-dimensional modelling of crack growth using partition of unity methods , 2010 .

[22]  Charles E. Augarde,et al.  A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields , 2014 .

[23]  T. Belytschko,et al.  Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment , 2003 .

[24]  Stewart Andrew Silling,et al.  Dynamic fracture modeling with a meshfree peridynamic code , 2003 .

[25]  T. Belytschko,et al.  A simplified mesh‐free method for shear bands with cohesive surfaces , 2007 .

[26]  S. Silling Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces , 2000 .

[27]  S. Silling,et al.  Peridynamic States and Constitutive Modeling , 2007 .

[28]  Timon Rabczuk,et al.  A computational library for multiscale modeling of material failure , 2013, Computational Mechanics.

[29]  Gross,et al.  Local crack branching as a mechanism for instability in dynamic fracture. , 1995, Physical review letters.

[30]  H. Nguyen-Xuan,et al.  An extended isogeometric thin shell analysis based on Kirchhoff-Love theory , 2015 .

[31]  Erdogan Madenci,et al.  Combined finite element and peridynamic analyses for predicting failure in a stiffened composite curved panel with a central slot , 2012 .

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

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

[34]  Timon Rabczuk,et al.  Element-wise fracture algorithm based on rotation of edges , 2013 .

[35]  David John Littlewood,et al.  Variable Horizon in a Peridynamic Medium , 2015 .

[36]  R. Lehoucq,et al.  Convergence of Peridynamics to Classical Elasticity Theory , 2008 .

[37]  H. Nguyen-Xuan,et al.  A simple and robust three-dimensional cracking-particle method without enrichment , 2010 .

[38]  X. Zhuang,et al.  A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture modeling , 2013 .

[39]  S. Silling,et al.  A meshfree method based on the peridynamic model of solid mechanics , 2005 .

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

[41]  Tianhong Yang,et al.  Characterization on jointed rock masses based on PFC2D , 2013 .

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

[43]  R. Lehoucq,et al.  Peridynamic Theory of Solid Mechanics , 2010 .

[44]  John T. Foster,et al.  Peridynamic Plates and Flat Shells: A non-ordinary, state-based model , 2014 .

[45]  Timon Rabczuk,et al.  Finite strain fracture of 2D problems with injected anisotropic softening elements , 2014 .

[46]  Peridynamic Modeling of the Kalthoff-Winkler Experiment , 2001 .

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

[48]  S. Silling,et al.  Convergence, adaptive refinement, and scaling in 1D peridynamics , 2009 .

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

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

[51]  Nicolas Sau,et al.  Peridynamic modeling of concrete structures , 2007 .

[52]  R. Lehoucq,et al.  Peridynamics for multiscale materials modeling , 2008 .