Chiral Cosserat homogenized constitutive models of architected media based on micromorphic homogenization. (October 2022)

• Record Type: Journal Article
• Authors: Alavi, S Ehsan; Ganghoffer, Jean-François; Sadighi, Mojtaba
• Other Names: Bersani Alberto Maria guest-editor.; Cazzani Antonio M guest-editor.; Eremeyev Victor guest-editor.; Giorgio Ivan guest-editor.; Spagnuolo Mario guest-editor.
• Is Part Of: Mathematics and mechanics of solids. Volume 27:Number 10(2022)
• Page Start: 2287
• Page End: 2313
• Publication Date: 2022-10
• Subjects: Chiral Cosserat mechanics -- architected media -- higher order homogenization -- variational principles -- micromorphic homogenization -- degeneration conditions; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/10812865221106941
• Languages: English
• ISSNs: 1081-2865

Abstract

The present contribution aims to build chiral Cosserat effective models of architectured media prone to such effects, recoursing to dedicated homogenization methods. In order to develop a method in full generality, the effective Cosserat model is obtained from the degeneration of the micromorphic effective continuum, by projecting the micromorphic kinematic degrees of freedom onto the Cosserat variables. The proposed homogenization method relies on variational principles and a decomposition of the microscopic displacement into a so-called homogeneous part and a periodic fluctuation. The homogeneous contribution to the total microscopic displacement accounts for the postulated effective generalized continuum, and it is corrected by a displacement fluctuation. The energy of the fluctuating displacement is shown to define a measure of the accuracy of the homogenized chiral Cosserat model. Applications of the proposed homogenization framework are done for centrosymmetric and non-centrosymmetric chiral architected media.