Equivalent mechanical properties of textile monolayers from discrete asymptotic homogenization Ibrahim Goda a,b,n , Mohamed Assidi c , Jean-François Ganghoffer a a LEMTA, Université de Lorraine, 2, Avenue de la Forêt de Haye, TSA 60604, 54518 Vandœuvre-lès-Nancy Cedex, France b Department of Industrial Engineering, Faculty of Engineering, Fayoum University, Fayoum 63514, Egypt c Centre de Recherche Public Henri Tudor. 29, Avenue John Kennedy, L-1885, Luxemburg article info Article history: Received 8 February 2013 Received in revised form 26 July 2013 Accepted 30 July 2013 Available online 14 August 2013 Keywords: Textile monolayers Micromechanical model Discrete homogenization Micropolar constants Meso-scale unit-cell model abstract The determination of the effective mechanical moduli of textiles from mechanical measurements is usually difficult due to their discrete architecture, which makes micro- mechanical analyses a relevant alternative to access those properties. Micropolar continuum models describing the effective mechanical behavior of woven fabric monolayers are constructed from the homogenization of an identified repetitive pattern of the textile within a representative unit cell. The interwoven yarns within the textile are represented as a network of trusses connected by nodes at their crossover points. These trusses have extensional and bending rigidities to allow for yarn stretching and flexion, and a transverse shear deformation is additionally considered. Interactions between yarns at the crossover points are captured by beam segments connecting the nodes. The woven fabric is modeled after homogenization as an anisotropic planar continuum with two preferred material directions in the mean plane of the textile. Based on the developed methodology, the effective mechanical properties of plain weave and twill are evaluated, including their bending moduli and characteristic flexural lengths. A satisfactory agreement is obtained between the effective moduli obtained by homogenization and numerical values obtained by finite element simulations performed over periodic unit cells. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction Over the past decade, considerable attention from the composite manufacturing sector has been devoted to textile composites and especially woven fabrics. These materials have many advantages over unidirectional fibers reinforced composites, such as enhanced dimensional stability over a large range of temperatures (Tabiei and Yi, 2002), more balanced properties in the fabric plane, and better impact resistance. The mechanical behavior of woven fabrics is of interest in numerous applications, including apparel, fabric reinforced composites, and body armor for ballistic protection. The development of these technologies requires a thorough under- standing of the mechanical behavior of woven fabrics. Such fabrics are produced by the assembly of two or more fiber bundles (called yarns) in a specific architecture defining the armor (e.g. plain weave, twill, satin). Their fabrication involves Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jmps Journal of the Mechanics and Physics of Solids 0022-5096/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jmps.2013.07.014 n Corresponding author at: LEMTA, Université de Lorraine, 2, Avenue de la Forêt de Haye, TSA 60604, 54518 Vandœuvre-lès-Nancy Cedex, France. Tel.: þ33 605593435. E-mail addresses: ibrahim.goda9@etu.univ-lorraine.fr, igm00@fayoum.edu.eg (I. Goda). Journal of the Mechanics and Physics of Solids 61 (2013) 2537–2565