An isogeometric analysis Bézier interface element for mechanical and poromechanical fracture problems

Interface elements are a powerful tool for modelling discontinuities. Herein, we develop an interface element that is based on the isogeometric analysis concept. Through Bezier extraction, the novel interface element can be casted in the same format as conventional interface elements. Consequently, the isogeometric interface element can be implemented in a straightforward manner in an existing finite element software by a mere redefinition of the shape functions. The interface elements share the advantages of isogeometric continuum elements in that they can exactly model the geometry. On the other hand, they inherit the simplicity of conventional interface elements, but also some deficiencies, such as the occurrence of traction oscillations when a high interface stiffness is used. The extension towards poroelasticity is rather straightforward, and in this situation, the smoother flow profiles and the ensuing preservation of local mass balance are additional advantages. These are demonstrated at the hand of some example problems.

[1]  M. Ortiz,et al.  Computational modelling of impact damage in brittle materials , 1996 .

[2]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[3]  J. Rots.  Smeared and discrete representations of localized fracture , 1991 .

[4]  Julien Réthoré,et al.  A Numerical Approach for Arbitrary Cracks in a Fluid-Saturated Medium , 2006 .

[5]  de R René Borst,et al.  Free edge delamination in carbon-epoxy laminates: a novel numerical/experimental approach , 1994 .

[6]  Julien Réthoré,et al.  A two-scale model for fluid flow in an unsaturated porous medium with cohesive cracks , 2008 .

[7]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[8]  A. Ingraffea,et al.  Numerical modeling of discrete crack propagation in reinforced and plain concrete , 1985 .

[9]  A. Needleman,et al.  A cohesive segments method for the simulation of crack growth , 2003 .

[10]  J. Rots.  Smeared and discrete representations of localized fracture , 1991 .

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

[12]  Julien Réthoré,et al.  A two‐scale approach for fluid flow in fractured porous media , 2006 .

[13]  Ignacio Carol,et al.  Coupled HM analysis using zero‐thickness interface elements with double nodes. Part I: Theoretical model , 2008 .

[14]  D. Borst,et al.  A NON-LINEAR FINITE ELEMENT APPROACH FOR THE ANALYSIS OF MODE-I FREE EDGE DELAMINATION IN COMPOSITES , 1993 .

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

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

[17]  de R René Borst,et al.  On the numerical integration of interface elements , 1993 .

[18]  René de Borst,et al.  A discrete model for the dynamic propagation of shear bands in a fluid‐saturated medium , 2007 .

[19]  John A. Evans,et al.  Isogeometric finite element data structures based on Bézier extraction of NURBS , 2011 .

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

[21]  Cv Clemens Verhoosel,et al.  Isogeometric finite element analysis of poroelasticity , 2013 .

[22]  K. Seffen,et al.  International Journal of Solids and Structures , 2015 .

[23]  Cv Clemens Verhoosel,et al.  The cohesive band model: a cohesive surface formulation with stress triaxiality , 2013, International Journal of Fracture.

[24]  Thomas J. R. Hughes,et al.  An isogeometric approach to cohesive zone modeling , 2011 .

[25]  K. Bathe.  Finite Element Procedures , 1995 .

[26]  René de Borst,et al.  A large deformation formulation for fluid flow in a progressively fracturing porous material , 2013 .

[27]  Cv Clemens Verhoosel,et al.  A phase-field description of dynamic brittle fracture , 2012 .

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

[29]  R. de Borst,et al.  A consistent geometrically non‐linear approach for delamination , 2002 .

[30]  M. Cox.  The Numerical Evaluation of B-Splines , 1972 .

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

[32]  Thomas J. Boone,et al.  A numerical procedure for simulation of hydraulically-driven fracture propagation in poroelastic media , 1990 .

[33]  O. Allix,et al.  Interlaminar interface modelling for the prediction of delamination , 1992 .

[34]  Bernhard A. Schrefler,et al.  Mesh adaptation and transfer schemes for discrete fracture propagation in porous materials , 2007 .

[35]  C. D. Boor,et al.  On Calculating B-splines , 1972 .