TY - JOUR
T1 - A class of general algorithms for multi-scale analyses of heterogeneous media
AU - Terada, K.
AU - Kikuchi, N.
N1 - Funding Information:
This work is partially supported by Ministry of Education, Science, Sports and Culture under grant number 11750054. Thanks are offered to Mr. Kazumi Matsui and Mr. Atsushi Mano for help with some numerical analyses as well as their visualizations. I am also indebted to a father of computational mechanics, Professor J.T. Oden (TICAM, The University of Texas at Austin), for his valuable suggestions and corrections on our manuscript.
PY - 2001/7/20
Y1 - 2001/7/20
N2 - A class of computational algorithms for multi-scale analyses is developed in this paper. The two-scale modeling scheme for the analysis of heterogeneous media with fine periodic microstructures is generalized by using relevant variational statements. Instead of the method of two-scale asymptotic expansion, the mathematical results on the generalized convergence are utilized in the two-scale variational descriptions. Accordingly, the global-local type computational schemes can be unified in association with the homogenization procedure for general nonlinear problems. After formulating the problem in linear elastostatics, that with local contact condition and the elastoplastic problem, we present representative numerical examples along with the computational algorithm consistent with our two-scale modeling strategy as well as some direct approaches.
AB - A class of computational algorithms for multi-scale analyses is developed in this paper. The two-scale modeling scheme for the analysis of heterogeneous media with fine periodic microstructures is generalized by using relevant variational statements. Instead of the method of two-scale asymptotic expansion, the mathematical results on the generalized convergence are utilized in the two-scale variational descriptions. Accordingly, the global-local type computational schemes can be unified in association with the homogenization procedure for general nonlinear problems. After formulating the problem in linear elastostatics, that with local contact condition and the elastoplastic problem, we present representative numerical examples along with the computational algorithm consistent with our two-scale modeling strategy as well as some direct approaches.
KW - Heterogeneous media
KW - Homogenization theory
KW - Multi-scale analysis
KW - Nonlinear behavior
KW - Variational methods
UR - http://www.scopus.com/inward/record.url?scp=0035919604&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035919604&partnerID=8YFLogxK
U2 - 10.1016/S0045-7825(01)00179-7
DO - 10.1016/S0045-7825(01)00179-7
M3 - Article
AN - SCOPUS:0035919604
SN - 0374-2830
VL - 190
SP - 5427
EP - 5464
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 40-41
ER -