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<p>By implementing an asymptotic homogenization method modified for finite deformations, this work presents a topology optimization(TO) formulation for the design of meta-materials with prescribed, non-linear elastic behaviors. The meta-material analysis and the TO problem are formulated such that meta-materials can be designed for any general deformation mode. Additional constraints for the TO formulations are proposed to address numerical issues. The TO formulation is used to design meta-materials for various target stress–strain curves under various uniform deformation load cases. The formulation is also used to design meta-material&#xa0;based structures under non-uniform deformation fields using a multi-scale FE<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(^2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>2</mn> </mmultiscripts> </math></EquationSource> </InlineEquation> approach.</p>

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A generalized topology optimization formulation for design of meta-materials and structures for prescribed non-linear elastic behavior

  • 期刊论文

  • 发表日期：

    2025年12月9日

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  • Rushabh Rajesh Sadiwala,
  • Georges Fadel,
  • Nicole Coutris,
  • Gang Li

摘要

By implementing an asymptotic homogenization method modified for finite deformations, this work presents a topology optimization(TO) formulation for the design of meta-materials with prescribed, non-linear elastic behaviors. The meta-material analysis and the TO problem are formulated such that meta-materials can be designed for any general deformation mode. Additional constraints for the TO formulations are proposed to address numerical issues. The TO formulation is used to design meta-materials for various target stress–strain curves under various uniform deformation load cases. The formulation is also used to design meta-material based structures under non-uniform deformation fields using a multi-scale FE \(^2\) 2 approach.