TY - JOUR
T1 - Two-scale kinematics and linearization for simultaneous two-scale analysis of periodic heterogeneous solids at finite strain
AU - Terada, K.
AU - Saiki, I.
AU - Matsui, K.
AU - Yamakawa, Y.
N1 - Funding Information:
This work is partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Encouragement of Young Scientists, 11750054 (1999–2000) and 13750436 (2001–2002).
PY - 2003/8/1
Y1 - 2003/8/1
N2 - We introduce the notion of two-scale kinematics and the procedure of two-scale linearization, which are indispensable to the simultaneous two-scale analysis method for the mechanical behavior of periodic heterogeneous solids at finite strain. These are accomplished by formulating the two-scale boundary value problem in both material and spatial descriptions with reference to the two-scale modeling strategy developed in [Comput. Methods Appl. Mech. Engrg. 190 (40-41) (2001) 5427] that utilized the convergence results of mathematical homogenization. The formulation brings the intimate relationship between micro- and macro-scale kinematics in describing the micro-macro coupling behavior inherent in heterogeneous media. It is also shown that the two-scale linearization necessitates the strict consistency with the micro-scale equilibrated state and naturally invites the tangential homogenization process for both material and spatial descriptions. Several numerical examples of simultaneous two-scale computations are presented to illustrate the two-scale nature of the deformation of a heterogeneous solid at finite strain.
AB - We introduce the notion of two-scale kinematics and the procedure of two-scale linearization, which are indispensable to the simultaneous two-scale analysis method for the mechanical behavior of periodic heterogeneous solids at finite strain. These are accomplished by formulating the two-scale boundary value problem in both material and spatial descriptions with reference to the two-scale modeling strategy developed in [Comput. Methods Appl. Mech. Engrg. 190 (40-41) (2001) 5427] that utilized the convergence results of mathematical homogenization. The formulation brings the intimate relationship between micro- and macro-scale kinematics in describing the micro-macro coupling behavior inherent in heterogeneous media. It is also shown that the two-scale linearization necessitates the strict consistency with the micro-scale equilibrated state and naturally invites the tangential homogenization process for both material and spatial descriptions. Several numerical examples of simultaneous two-scale computations are presented to illustrate the two-scale nature of the deformation of a heterogeneous solid at finite strain.
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U2 - 10.1016/S0045-7825(03)00365-7
DO - 10.1016/S0045-7825(03)00365-7
M3 - Article
AN - SCOPUS:0042125263
VL - 192
SP - 3531
EP - 3563
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0374-2830
IS - 31-32
ER -