A second‐order reduced asymptotic homogenization approach for nonlinear periodic heterogeneous materials. (1st April 2019)

• Record Type: Journal Article
• Authors: Fish, Jacob; Yang, Zhiqiang; Yuan, Zifeng
• Is Part Of: International journal for numerical methods in engineering. Volume 119:Number 6(2019)
• Page Start: 469
• Page End: 489
• Publication Date: 2019-04-01
• Subjects: periodic microstructure -- reduced order homogenization -- second‐order asymptotic homogenization; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6058
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: An efficient second‐order reduced asymptotic homogenization approach is developed for nonlinear heterogeneous media with large periodic microstructure. The two salient features of the proposed approach are (i) an asymptotic higher‐order nonlinear homogenization that does not require higher‐order continuity of the coarse‐scale solution and (ii) an efficient model reduction scheme for solving higher‐order nonlinear unit cell problems at a fraction of computational cost in comparison to the direct computational homogenization. The former is a consequence of a sequential solution of increasing order solutions, which permits evaluation of higher‐order coarse‐scale derivatives by postprocessing from the zeroth‐order solution. The efficiency and accuracy of the formulation in comparison to the classical zeroth‐order homogenization and direct numerical simulations are assessed on hyperelastic and elastoplastic periodic structures.