TY - JOUR
T1 - Nonlinear homogenization for topology optimization
AU - Wallin, Mathias
AU - Tortorelli, Daniel A.
N1 - Funding Information:
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA33344 . MW is also grateful for the financial support provided by the Swedish research council, grant ngb. 2015–05134.
PY - 2020/6
Y1 - 2020/6
N2 - 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.
AB - 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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U2 - 10.1016/j.mechmat.2020.103324
DO - 10.1016/j.mechmat.2020.103324
M3 - Article
AN - SCOPUS:85082832228
VL - 145
JO - Mechanics of Materials
JF - Mechanics of Materials
SN - 0167-6636
M1 - 103324
ER -