Two-scale kinematics and linearization for simultaneous two-scale analysis of periodic heterogeneous solids at finite strain

✍ Scribed by K. Terada; I. Saiki; K. Matsui; Y. Yamakawa

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 753 KB
• Volume: 192
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(03)00365-7

✦ Synopsis

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.