Micro-macro homogenization of gradient-enhanced Cosserat media

• Published in: European journal of mechanics, A, Solids Vol. 30; no. 3; pp. 362 - 372
• Main Authors: Li, Xikui, Zhang, Junbo, Zhang, Xue
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Masson SAS 01-05-2011; Elsevier
• Subjects: Average-field theory; Boundary conditions; Continuums; Exact sciences and technology; Frames; Fundamental areas of phenomenology (including applications); Gradient-enhanced Cosserat continuum; Hill–Mandel condition; Hill’s lemma; Homogenization; Homogenizing; Microstructure; Physics; RVE boundary conditions; Sampling; Solid mechanics; Static elasticity (thermoelasticity...); Strain; Stress tensors; Structural and continuum mechanics; Hill’s lemma; Hill–Mandel condition; Average-field theory; Gradient-enhanced Cosserat continuum; RVE boundary conditions; Hill's lemma; Representative volume element; Homogenization; Stress tensor; Modeling; Hill-Mandel condition; Global local method; Continuum; Microstructure; Cosserat material
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2010.10.008

Based on the Hill’s lemma for classical Cauchy continuum, a generalized Hill’s lemma for micro-macro homogenization modeling of heterogeneous gradient-enhanced Cosserat continuum is presented in the frame of the average-field theory. In this context not only the strain and stress tensors defined in classical Cosserat continuum but also their gradients at each macroscopic sampling point are attributed to associated microstructural representative volume element (RVE). The admissible boundary conditions required to prescribe on the RVE for the modeling are extracted as a corollary of the presented generalized Hill’s lemma and discussed to ensure the satisfaction of the enhanced Hill–Mandel energy condition and the average-field theory.