Topology optimization of micro-structure for composites applying a decoupling multi-scale analysis

The present study proposes topology optimization of a micro-structure for composites considering the ma-cro-scopic structural response, applying a decoupling multi-scale analysis based on a homogenization approach. In this study, it is assumed that topology of macro-structure is unchanged and that topology of micro-structure is unique over the macro-structure. The stiffness of the macro-structure is maximized with a prescribed material volume of constituents under linear elastic regime. A gradient-based optimization strategy is applied and an analytical sensitivity approach based on numerical material tests is introduced. It was verified from a series of numerical examples that the proposed method has great potential for advanced material design.

[1]  M. Denda,et al.  A dual homogenization and finite-element study on the in-plane local and global behavior of a nonlinear coated fiber composite , 2000 .

[2]  C. S. Jog,et al.  Stability of finite element models for distributed-parameter optimization and topology design , 1996 .

[3]  Surya N. Patnaik,et al.  Merits and limitations of optimality criteria method for structural optimization , 1995 .

[4]  O. Sigmund,et al.  Design and fabrication of compliant micromechanisms and structures with negative Poisson's ratio , 1996, Proceedings of Ninth International Workshop on Micro Electromechanical Systems.

[5]  W. Brekelmans,et al.  Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling , 1998 .

[6]  H. Rodrigues,et al.  Hierarchical optimization of material and structure , 2002 .

[7]  Kenjiro Terada,et al.  A method of two-scale analysis with micro-macro decoupling scheme: application to hyperelastic composite materials , 2013 .

[8]  O. Sigmund.  Morphology-based black and white filters for topology optimization , 2007 .

[9]  Ole Sigmund,et al.  Design of materials with extreme thermal expansion using a three-phase topology optimization method , 1997, Smart Structures.

[10]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[11]  Shutian Liu,et al.  Size-dependent optimal microstructure design based on couple-stress theory , 2010 .

[12]  E. A. de Souza Neto,et al.  Topological derivative for multi‐scale linear elasticity models applied to the synthesis of microstructures , 2010 .

[13]  O. Sigmund,et al.  Checkerboard patterns in layout optimization , 1995 .

[14]  Z. Więckowski.  Dual finite element methods in homogenization for elastic–plastic fibrous composite material , 2000 .

[15]  O. Sigmund.  Materials with prescribed constitutive parameters: An inverse homogenization problem , 1994 .

[16]  Jun Yan,et al.  Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency , 2009 .

[17]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[18]  Ekkehard Ramm,et al.  Multiphase material optimization for fiber reinforced composites with strain softening , 2009 .

[19]  J. Chaboche,et al.  FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials , 2000 .

[20]  M. Zhou,et al.  The COC algorithm, Part II: Topological, geometrical and generalized shape optimization , 1991 .

[21]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[22]  K. Terada,et al.  A method of predicting macroscopic yield strength of polycrystalline metals subjected to plastic forming by micro–macro de-coupling scheme , 2010 .

[23]  N. Kikuchi,et al.  A class of general algorithms for multi-scale analyses of heterogeneous media , 2001 .