Comparison of two homogenization methods using a damage model for a fibrous membrane, based on the fibersʹ 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 tissueʹs 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 phase of the homogenized material. In the case of biological materials, the proposed law enables taking into account the often observed phenomena of crimping and damage of the fibers.