Modeling inclusion problems in viscoelastic materials with the extended finite element method

Mechanical responses of viscoelastic materials with inclusions are studied. First, the incremental equations are formulated in time domain in the framework of the extended finite element method (XFEM), in which the enhancement functions are inserted in the approximation for representing inclusions. Next, the integration schemes are investigated for different type of elements in the extended finite element method. The full integration scheme is used for the low Poisson ratio (e.g. 0.3) problem, and the selective integration scheme treating the volumetric locking problem in the conventional finite element method (FEM) is extended in the present method for the high Poisson ratio (e.g. 0.49999) problem often encountered in viscoelastic materials. Numerical results show that the extended finite element method is efficient for complex problems involving viscoelastic materials even if nearly incompressible.

[1]  K. Washizu.  Variational Methods in Elasticity and Plasticity , 1982 .

[2]  O. C. Zienkiewicz,et al.  The Finite Element Method: Its Basis and Fundamentals , 2005 .

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

[4]  T. Belytschko,et al.  MODELING HOLES AND INCLUSIONS BY LEVEL SETS IN THE EXTENDED FINITE-ELEMENT METHOD , 2001 .

[5]  Ted Belytschko,et al.  The extended finite element method for rigid particles in Stokes flow , 2001 .

[6]  Zihui Xia,et al.  Interface crack between two different viscoelastic media , 2001 .

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

[8]  Ean Tat Ooi,et al.  A mesh distortion tolerant 8-node solid element based on the partition of unity method with inter-element compatibility and completeness properties , 2007 .

[9]  Zvi Hashin,et al.  Complex moduli of viscoelastic composites—I. General theory and application to particulate composites , 1970 .

[10]  T. Belytschko,et al.  Finite element derivative recovery by moving least square interpolants , 1994 .

[11]  C. V. Ramakrishnan,et al.  Fracture behaviour of creeping materials under biaxial loading by finite element method , 1995 .

[12]  Jean-François Remacle,et al.  A computational approach to handle complex microstructure geometries , 2003 .

[13]  Christophe Petit,et al.  A Finite Element Analysis of Creep-Crack Growth in Viscoelastic Media , 1998 .

[14]  A. V. Pyatigorets,et al.  Linear viscoelastic analysis of a semi-infinite porous medium , 2008 .

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

[17]  R. Christensen.  Theory of viscoelasticity : an introduction , 1971 .

[18]  T. Strouboulis,et al.  The generalized finite element method: an example of its implementation and illustration of its performance , 2000 .

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

[20]  Genki Yagawa,et al.  Linear dependence problems of partition of unity-based generalized FEMs , 2006 .

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

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

[23]  R. Talreja,et al.  Linear viscoelastic behavior of matrix cracked cross-ply laminates , 2001 .

[24]  Richard Schapery,et al.  A theory of crack initiation and growth in viscoelastic media , 1975 .

[25]  Baili Zhang,et al.  A “FE-meshfree” QUAD4 element based on partition of unity , 2007 .

[26]  David L. Chopp,et al.  A hybrid extended finite element/level set method for modeling phase transformations , 2002 .

[27]  G. J. Creus,et al.  Finite elements analysis of viscoelastic fracture , 1993 .

[28]  C. Petit,et al.  An incremental formulation for the linear analysis of thin viscoelastic structures using generalized variables , 1995 .

[29]  T. Belytschko,et al.  The extended finite element method (XFEM) for solidification problems , 2002 .