Comparaison of two homogenization methods using a damage model for a fibrous membrane, based on the fibers’ fracture process at the microscale

The objective of this paper is to evaluate two existing homogenization methods using a simple damage model for fibrous membrane and compare them. A macroscopic damage model of a fibrous membrane tissue based on the knowledge of the behavior and fracture process of a single fiber is constructed. Under some simplifying assumptions (linear behavior of the fibers, brittle fibers, constant angular distribution of the fibers), the evolution of fiber fracture is described by two macroscopic scalar variables; this enables the tissue’s damage to be modeled without requiring a second discretization at the microscale. For the homogenization of the fibers contribution, an energetic method and a kinematic method are adapted and compared. Both lead to similar macroscopic behavior in the elastic phase, but the behavior differs in the fracture ∗Corresponding author. Laboratoire de Mécanique des Contacts et des Structures Institut National des Sciences Appliquées de Lyon (INSA), Bâtiment Jean d’Alembert, 18-20 rue des Sciences, F69621 Villeurbanne Cedex, France. Tel:+33472436426; Fax:+33478890980. Email address: [email protected] (A. Combescure) Preprint submitted to European Journal of Mechanics A/Solids October 18, 2012 ha l-0 07 89 31 6, v er si on 1 19 F eb 2 01 3 Author manuscript, published in "European Journal of Mechanics A/Solids 39 (2013) 1-10" DOI : 10.1016/j.euromechsol.2012.10.006