Numerical modeling of functionally graded materials using a variational formulation

An approach of numerical modeling of heterogeneous, functionally graded materials, by using the finite element method, is proposed. The variational formulation is derived from the generic case so that the implementation of material coefficients, which are functions in space, is realized without any further assumptions. An analytical solution for a simple case is presented and used for validation of the numerical model.

[1]  Peter Greil,et al.  Functionally graded materials for biomedical applications , 2003 .

[2]  S. Suresh,et al.  Fundamentals of functionally graded materials , 1998 .

[3]  J. McWhirter.  Variational Methods in Mathematics, Science and Engineering , 1978 .

[4]  C. Truesdell,et al.  The Classical Field Theories , 1960 .

[5]  M. Peters,et al.  Graded coatings for thermal, wear and corrosion barriers , 2003 .

[6]  Anders Logg,et al.  Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book , 2012 .

[7]  V. P. Plevako,et al.  On the theory of elasticity of inhomogeneous media: PMM, vol. 35, n≗ 5, 1971, pp. 853–860 , 1971 .

[8]  G. Paulino,et al.  ISOPARAMETRIC GRADED FINITE ELEMENTS FOR NONHOMOGENEOUS ISOTROPIC AND ORTHOTROPIC MATERIALS , 2002 .

[9]  Glaucio H. Paulino,et al.  Application of Graded Finite Elements for Asphalt Pavements , 2006 .

[10]  Martin H. Sadd,et al.  Elasticity: Theory, Applications, and Numerics , 2004 .

[11]  Toshio Nakamura,et al.  Simulations of crack propagation in elastic-plastic graded materials , 2004 .

[12]  Mark Hoffman,et al.  Finite element simulations of crack propagation in functionally graded materials under flexural loading , 2005 .

[13]  Anders Logg,et al.  DOLFIN: Automated finite element computing , 2010, TOMS.

[14]  Maria Kashtalyan,et al.  Three-dimensional elasticity solution for bending of functionally graded rectangular plates , 2004 .

[15]  Santosh Kapuria,et al.  Synthesis and characterization of Al/SiC and Ni/Al2O3 functionally graded materials , 2008 .

[16]  A. Kawasaki,et al.  Functionally graded materials : design, processing and applications , 1999 .

[17]  Yujuan Wu,et al.  Hertzian contact response of single-layer, functionally graded and sandwich coatings , 2007 .

[18]  A. González,et al.  GNU General Public License v3: A Legal Analysis , 2006 .

[19]  Michael H. Santare,et al.  USE OF GRADED FINITE ELEMENTS TO MODEL THE BEHAVIOR OF NONHOMOGENEOUS MATERIALS , 2000 .

[20]  David Hilbert,et al.  The Foundations of Geometry , 1903, The Mathematical Gazette.

[21]  Victor Birman,et al.  Modeling and Analysis of Functionally Graded Materials and Structures , 2007 .

[22]  W. Müller.  Streifzüge durch die Kontinuumstheorie , 2011 .

[23]  S. Suresh,et al.  Fundamentals of functionally graded materials: processing and thermomechanical behaviour of graded metals and metal-ceramic composites , 1998 .

[24]  Christof Vömel,et al.  ScaLAPACK's MRRR algorithm , 2010, TOMS.

[25]  M. Kashtalyan,et al.  Revisiting displacement functions in three-dimensional elasticity of inhomogeneous media , 2009 .

[26]  A. Khatibi,et al.  3D finite element simulation of sandwich panels with a functionally graded core subjected to low velocity impact , 2009 .

[27]  Wolfgang A. Kaysser,et al.  Functionally graded materials for sensor and energy applications , 2003 .