Comparison 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 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.

► A damage model for a fibrous membrane describes the evolution of anisotropy.
► The anisotropic macroscopic damage results from the failure of the brittle fibers.
► Two homogenization methods are adapted to the damage model and compared.
► The main difference between the two methods is observed on the less loaded direction.
► Fiber crimp and fiber damage can be included in the model.