TY - JOUR

T1 - A data-driven micro-macro coupled multiscale analysis for hyperelastic composite materials

AU - Hatano, Ryo

AU - Matsubara, Seishiro

AU - Moriguchi, Shuji

AU - Terada, Kenjiro

N1 - Publisher Copyright:
© 2019 by the Japan Society for Computational Engineering and Science.

PY - 2019

Y1 - 2019

N2 - A data-driven approach is developed for micro-macro coupled multiscale analysis of hypere-lastic composite materials. The offline process in this approach is to make a database that stores the microscopic stress distributions in response to various patterns of macroscopic deformation gradients. This can be done by carrying out an adequate number of numerical material tests on a periodic microstructures, or equivalently, a unit cell and followed by the proper orthogonal decomposition (POD) to extract the principal components of the data along with the corre-sponding basis vectors. In order to realize FE2-type two-scale analysis in the online process, we interpolate each of the coefficients with the radial basis functions as a function of a macroscopic deformation gradient and make the resulting continuous function gently varying by means of the L2-regularization followed by the cross-validation and Bayesian optimization techniques. Each of the functions thus obtained is referred to as “data-driven function” of the microscopic stress distribution and can be used to obtain the macroscopic stress by the averaging process in the homogenization method. A representative numerical example is presented to validate the proposed data-driven FE2 analyses in comparison with high-fidelity direct FE2 .

AB - A data-driven approach is developed for micro-macro coupled multiscale analysis of hypere-lastic composite materials. The offline process in this approach is to make a database that stores the microscopic stress distributions in response to various patterns of macroscopic deformation gradients. This can be done by carrying out an adequate number of numerical material tests on a periodic microstructures, or equivalently, a unit cell and followed by the proper orthogonal decomposition (POD) to extract the principal components of the data along with the corre-sponding basis vectors. In order to realize FE2-type two-scale analysis in the online process, we interpolate each of the coefficients with the radial basis functions as a function of a macroscopic deformation gradient and make the resulting continuous function gently varying by means of the L2-regularization followed by the cross-validation and Bayesian optimization techniques. Each of the functions thus obtained is referred to as “data-driven function” of the microscopic stress distribution and can be used to obtain the macroscopic stress by the averaging process in the homogenization method. A representative numerical example is presented to validate the proposed data-driven FE2 analyses in comparison with high-fidelity direct FE2 .

KW - Data-driven Analysis

KW - Multi-scale Analysis

KW - Proper Orthogonal Decomposition

UR - http://www.scopus.com/inward/record.url?scp=85091095616&partnerID=8YFLogxK

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U2 - 10.11421/jsces.2019.20190015

DO - 10.11421/jsces.2019.20190015

M3 - Article

AN - SCOPUS:85091095616

VL - 2019

SP - 1

EP - 16

JO - Transactions of the Japan Society for Computational Engineering and Science

JF - Transactions of the Japan Society for Computational Engineering and Science

SN - 1344-9443

M1 - 20190015

ER -