TY - JOUR

T1 - An optimization strategy for customizable global elastic deformation of unit cell-based metamaterials with variable material section discretization

AU - Thalhamer, Andreas

AU - Fleisch, Mathias

AU - Schuecker, Clara

AU - Fuchs, Peter Filipp

AU - Schlögl, Sandra

AU - Berer, Michael

N1 - Publisher Copyright: © 2024 The Author(s)

PY - 2024/11/12

Y1 - 2024/11/12

N2 - Metamaterials with their distinctive unit cell-based periodic architecture feature a wide range of possible properties with unusual characteristics and a high potential for optimization. Due to their complex interaction between unit cell geometry and material properties, as well as their inherent multi-scale nature, suitable optimization strategies need to be developed for metamaterials. One potential approach is to optimize the distribution of unit cells within a part to achieve a predefined deformation response. However, a significant challenge lies in determining the appropriate number and distribution of areas with varying properties (material sections) to facilitate an efficient optimization. In this study, a variable material section discretization scheme is presented, which is aimed at automatically updating the discretization to enhance the efficiency of metamaterial optimizations. This scheme is implemented as an extension to a previously proposed Finite Element simulation-based optimization framework for unit cell-based metamaterials. The framework includes a numerical homogenization method and interpolation scheme for efficiently correlating unit cell parameters with homogenized material properties, coupled with a black-box optimization method. In the present study, the previously proposed framework was extended to incorporate a scheme for monitoring and adjusting the material section discretization during the optimization process. To assess the effectiveness of the implemented routine, it was tested in conjunction with a genetic algorithm for optimizing the parameter distribution of a 2D tri-anti-chiral metamaterial to match a predefined lateral deformation under load.

AB - Metamaterials with their distinctive unit cell-based periodic architecture feature a wide range of possible properties with unusual characteristics and a high potential for optimization. Due to their complex interaction between unit cell geometry and material properties, as well as their inherent multi-scale nature, suitable optimization strategies need to be developed for metamaterials. One potential approach is to optimize the distribution of unit cells within a part to achieve a predefined deformation response. However, a significant challenge lies in determining the appropriate number and distribution of areas with varying properties (material sections) to facilitate an efficient optimization. In this study, a variable material section discretization scheme is presented, which is aimed at automatically updating the discretization to enhance the efficiency of metamaterial optimizations. This scheme is implemented as an extension to a previously proposed Finite Element simulation-based optimization framework for unit cell-based metamaterials. The framework includes a numerical homogenization method and interpolation scheme for efficiently correlating unit cell parameters with homogenized material properties, coupled with a black-box optimization method. In the present study, the previously proposed framework was extended to incorporate a scheme for monitoring and adjusting the material section discretization during the optimization process. To assess the effectiveness of the implemented routine, it was tested in conjunction with a genetic algorithm for optimizing the parameter distribution of a 2D tri-anti-chiral metamaterial to match a predefined lateral deformation under load.

KW - Finite Element Method

KW - Genetic Algorithm

KW - Homogenization

KW - Optimization

KW - Simulation

UR - http://www.scopus.com/inward/record.url?scp=85208674219&partnerID=8YFLogxK

U2 - 10.1016/j.advengsoft.2024.103817

DO - 10.1016/j.advengsoft.2024.103817

M3 - Article

AN - SCOPUS:85208674219

VL - 199.2025

JO - Advances in Engineering Software

JF - Advances in Engineering Software

SN - 0965-9978

IS - January

M1 - 103817

ER -