Information transfer between incompatible finite element meshes: Application to coupled thermo-viscoelasticity

This article is concerned with information transfer between non-matching finite element meshes. Such a feature is not new in the literature, but we focus herein on a geometric approach to transfer solution fields in order to be as application independent as possible. Moreover, the dedicated case concerns the transfer of finite element fields defined at integration points of the meshes, and allows iterative exchange of fields in both directions. To do so, we propose an extension to the mortar technique that fulfills these goals and that does not suffer from a high computational cost. The application is the simulation of a strongly coupled thermo-viscoelastic problem with phase transition, solved with a partitioning technique.

[1]  Jean E. Roberts,et al.  Mixed and hybrid finite element methods , 1987 .

[2]  O. Zienkiewicz,et al.  The finite element patch test revisited a computer test for convergence, validation and error estimates , 1997 .

[3]  Hachmi Ben Dhia,et al.  Multiscale mechanical problems: the Arlequin method , 1998 .

[4]  C. Bernardi,et al.  A New Nonconforming Approach to Domain Decomposition : The Mortar Element Method , 1994 .

[5]  Zdeněk P. Bažant,et al.  Mechanics of solid materials , 1992 .

[6]  John D. Whitcomb,et al.  Iterative Global/Local Finite Element Analysis , 1990 .

[7]  Jeffrey Grandy,et al.  Conservative Remapping and Region Overlays by Intersecting Arbitrary Polyhedra , 1999 .

[8]  J. L. Steger,et al.  A chimera grid scheme , 2011 .

[9]  José M. Goicolea,et al.  Linear and non‐linear finite element error estimation based on assumed strain fields , 2002 .

[10]  Pierre Villon,et al.  Transfert de champs plastiquement admissibles , 2002 .

[11]  Yvon Maday,et al.  The mortar element method for three dimensional finite elements , 1997 .

[12]  Roger Ohayon,et al.  Fluid-Structure Interaction: Applied Numerical Methods , 1995 .

[13]  Anthony T. Patera,et al.  Domain Decomposition by the Mortar Element Method , 1993 .

[14]  Marc Garbey,et al.  Asymptotic and numerical methods for partial differential equations with critical parameters , 1993 .

[15]  Singiresu S Rao,et al.  Encyclopedia of vibration , 2002 .

[16]  D. A. Dunavant High degree efficient symmetrical Gaussian quadrature rules for the triangle , 1985 .

[17]  Philip Rabinowitz,et al.  Methods of Numerical Integration , 1985 .

[18]  C. Sun,et al.  A refined global‐local finite element analysis method , 1991 .

[19]  P. Tallec,et al.  Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity , 1998 .

[20]  Nicholas Zabaras,et al.  An updated Lagrangian finite element sensitivity analysis of large deformations using quadrilateral elements , 2001 .

[21]  David Dureisseix,et al.  A LATIN computational strategy for multiphysics problems: application to poroelasticity , 2003 .

[22]  Michael Ortiz,et al.  Adaptive mesh refinement in strain localization problems , 1991 .

[23]  Graham Williams,et al.  Anelastic and Dielectric Effects in Polymeric Solids , 1991 .

[24]  David Dureisseix,et al.  A micro / macro approach for parallel computing of heterogeneous structures , 2000 .

[25]  Ahmed K. Noor,et al.  Global-local methodologies and their application to nonlinear analysis , 1986 .

[26]  Charbel Farhat,et al.  Matching fluid and structure meshes for aeroelastic computations : a parallel approach , 1995 .

[27]  Barbara I. Wohlmuth,et al.  A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier , 2000, SIAM J. Numer. Anal..

[28]  M. Ortiz,et al.  The variational formulation of viscoplastic constitutive updates , 1999 .

[29]  C. Farhat,et al.  Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems , 2000 .

[30]  J. L. Steger,et al.  On the use of composite grid schemes in computational aerodynamics , 1987 .

[31]  Jean-François Richard,et al.  Methods of Numerical Integration , 2000 .

[32]  M. M. Rashid,et al.  Material state remapping in computational solid mechanics , 2002 .

[33]  Martin W. Heinstein,et al.  A three dimensional surface‐to‐surface projection algorithm for non‐coincident domains , 2003 .

[34]  Charbel Farhat,et al.  Partitioned analysis of coupled mechanical systems , 2001 .

[35]  Faker Ben Belgacem,et al.  The Mortar finite element method with Lagrange multipliers , 1999, Numerische Mathematik.

[36]  Panayot S. Vassilevski,et al.  Multiplier Spaces for the Mortar Finite Element Method in Three Dimensions , 2001, SIAM J. Numer. Anal..

[37]  Antonio Orlando,et al.  Analysis of transfer procedures in elastoplasticity based on the error in the constitutive equations: Theory and numerical illustration , 2004 .

[38]  David R. Owen,et al.  Transfer operators for evolving meshes in small strain elasto-placticity , 1996 .

[39]  Barry Hilary Valentine Topping,et al.  Advances in computational structures technology , 1996 .

[40]  David R. Owen,et al.  On adaptive strategies for large deformations of elasto-plastic solids at finite strains : computational issues and industrial applications , 1999 .

[41]  Xiao-Chuan Cai,et al.  Overlapping Nonmatching Grid Mortar Element Methods for Elliptic Problems , 1999 .