A computational framework for G/XFEM material nonlinear analysis

Abstract The Generalized/eXtended Finite Element Method (G/XFEM) has been developed with the purpose of overcoming some limitations inherent to the Finite Element Method (FEM). Different kinds of functions can be used to enrich the original FEM approximation, building a solution specially tailored to problem. Certain obstacles related to the nonlinear analysis can be mitigated with the use of such strategy and the damage and plasticity fronts can be precisely represented. A FEM computational environment has been previously enclosed the G/XFEM formulation to linear analysis with minimum impact in the code structure and with requirements for extensibility and robustness. An expansion of the G/XFEM implementation to physically nonlinear analysis under the approach of an Unified Framework for constitutive models based on elastic degradation is firstly presented here. The flexibility of the proposed framework is illustrated by several examples with different constitutive models, enrichment functions and analysis models.

[1]  I. Babuska,et al.  The design and analysis of the Generalized Finite Element Method , 2000 .

[2]  J. Lemaître.  A CONTINUOUS DAMAGE MECHANICS MODEL FOR DUCTILE FRACTURE , 1985 .

[3]  Jeong-Ho Kim,et al.  A new generalized finite element method for two‐scale simulations of propagating cohesive fractures in 3‐D , 2015 .

[4]  Phillipe D. Alves,et al.  An object-oriented approach to the Generalized Finite Element Method , 2013, Adv. Eng. Softw..

[5]  I. Babuska,et al.  Special finite element methods for a class of second order elliptic problems with rough coefficients , 1994 .

[6]  C. S. de Barcellos,et al.  On error estimator and p‐adaptivity in the generalized finite element method , 2004 .

[7]  T. Belytschko,et al.  A review of extended/generalized finite element methods for material modeling , 2009 .

[8]  D. Owen,et al.  Computational methods for plasticity : theory and applications , 2008 .

[9]  Egidio Rizzi,et al.  A unified theory of elastic degradation and damage based on a loading surface , 1994 .

[10]  O. C. Zienkiewicz,et al.  A new cloud-based hp finite element method , 1998 .

[11]  S ZijlstraEeuwe,et al.  Goedecker‐Teter‐Hutter擬ポテンシャルに対し最適なGauss基底系 , 2009 .

[12]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[13]  R. M. Natal Jorge,et al.  Numerical modelling of ductile plastic damage in bulk metal forming , 2003 .

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

[15]  Alain Combescure,et al.  Cohesive laws X-FEM association for simulation of damage fracture transition and tensile shear switch in dynamic crack propagation , 2012 .

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

[17]  A. Combescure,et al.  A mixed augmented Lagrangian‐extended finite element method for modelling elastic–plastic fatigue crack growth with unilateral contact , 2007 .

[18]  Roque Luiz da Silva Pitangueira,et al.  A computational framework for constitutive modelling , 2017 .

[19]  Alain Combescure,et al.  Appropriate extended functions for X-FEM simulation of plastic fracture mechanics , 2006 .

[20]  Ivo Babuška,et al.  Generalized finite element methods for three-dimensional structural mechanics problems , 2000 .

[21]  S. Eckardt,et al.  Modelling of cohesive crack growth in concrete structures with the extended finite element method , 2007 .

[22]  Saeed Ziaei-Rad,et al.  Numerical Analysis of Damage Evolution in Ductile Solids , 2005 .

[23]  C. S. Barcellos,et al.  COMPARATIVE ANALYSIS OF CK- AND C0-GFEM APPLIED TO TWO-DIMENSIONAL PROBLEMS OF CONFINED PLASTICITY , 2015 .

[24]  Ivan Francisco Ruiz Torres.  Desenvolvimento e aplicação do método dos elementos finitos generalizados em análise tridimensional não-linear de sólidos , 2003 .

[25]  A. Khoei,et al.  X-FEM modeling of dynamic ductile fracture problems with a nonlocal damage-viscoplasticity model , 2015 .

[26]  Dorival Piedade Neto,et al.  AN OBJECT-ORIENTED CLASS DESIGN FOR THE GENERALIZED FINITE ELEMENT METHOD PROGRAMMING , 2013 .

[27]  Ekkehard Ramm,et al.  Identification and Interpretation of Microplane Material Laws , 2006 .

[28]  I. Babuska,et al.  The Partition of Unity Method , 1997 .

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

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

[31]  Stefano Mariani,et al.  Extended finite element method for quasi‐brittle fracture , 2003 .

[32]  Leszek Demkowicz,et al.  Toward a universal h-p adaptive finite element strategy , 1989 .

[33]  David R. Owen,et al.  Aspects of ductile fracture and adaptive mesh refinement in damaged elasto‐plastic materials , 2001 .

[34]  J. Mazars.  A description of micro- and macroscale damage of concrete structures , 1986 .

[35]  Oden,et al.  An h-p adaptive method using clouds , 1996 .

[36]  Kuang-Han Chu,et al.  STRESS-STRAIN RELATIONSHIP FOR PLAIN CONCRETE IN COMPRESSION , 1985 .

[37]  Jean Lemaitre,et al.  Coupled elasto-plasticity and damage constitutive equations , 1985 .

[38]  P. Petersson.  Crack growth and development of fracture zones in plain concrete and similar materials , 1981 .

[39]  J. Crété,et al.  Numerical modelling of crack propagation in ductile materials combining the GTN model and X-FEM , 2014 .