Nonlinear homogenization for topology optimization

Wallin, Mathias; Tortorelli, Daniel A.

doi:10.1016/j.mechmat.2020.103324

Title: Nonlinear homogenization for topology optimization

Journal Article · Mon Jun 01 00:00:00 EDT 2020 · Mechanics of Materials

DOI:https://doi.org/10.1016/j.mechmat.2020.103324· OSTI ID:1608742

Wallin, Mathias; Tortorelli, Daniel A.

Non-linear homogenization of hyperelastic materials is reviewed and adapted to topology optimization. The homogenization is based on the method of multiscale virtual power in which the unit cell is subjected to either macroscopic deformation gradients or equivalently to Bloch type displacement boundary conditions. A detailed discussion regarding domain symmetry of the unit cell and its effect on uniaxial loading conditions is provided. The density approach is used to formulate the topology optimization problem which is solved via the method of moving asymptotes. The adjoint sensitivity analysis considers response functions that quantify both the displacement and incremental displacement. Notably, the transfer of the sensitivities from the microscale to the macroscale is presented in detail. A periodic filter and thresholding are used to regularize the topology optimization problem and to generate crisp boundaries. The proposed methodology is used to design hyperelastic microstructures comprised of Neo-Hookean constituents for maximum load carrying capacity subject to negative Poisson’s ratio constraints.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); Swedish Research Council (SRC)

Grant/Contract Number:: AC52-07NA27344; 2015–05134

OSTI ID:: 1608742

Alternate ID(s):: OSTI ID: 1660521

Report Number(s):: LLNL-JRNL-770805; S0167663619302418; 103324; PII: S0167663619302418

Journal Information:: Mechanics of Materials, Journal Name: Mechanics of Materials Vol. 145 Journal Issue: C; ISSN 0167-6636

Publisher:: ElsevierCopyright Statement

Country of Publication:: Netherlands

Language:: English

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Cited by: 15 works

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