Nonlinear homogenization for topology optimization

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Nonlinear homogenization for topology optimization. / Wallin, Mathias; Tortorelli, Daniel A.

In: Mechanics of Materials, Vol. 145, 103324, 06.2020.

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TY - JOUR

T1 - Nonlinear homogenization for topology optimization

AU - Wallin, Mathias

AU - Tortorelli, Daniel A.

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.

UR - http://www.scopus.com/inward/record.url?scp=85082832228&partnerID=8YFLogxK

U2 - 10.1016/j.mechmat.2020.103324

DO - 10.1016/j.mechmat.2020.103324

M3 - Article

VL - 145

JO - Mechanics of Materials

JF - Mechanics of Materials

SN - 0167-6636

M1 - 103324

ER -