A Micromechanical Model for Fibrous Biological Membranes at Finite Strain

The mechanical model of a number of biological tissues is a membrane, i.e., a sheetlike structure with small thickness, where deformation and stress can be described locally in two dimensions. Many bio-membranes, particularly if subjected to large mechanical loads, present a fibrous structure, with stiff fibers, sometimes with preferential orientations, embedded in a more compliant matrix. Among this tissues are, e.g., the arterial walls, the amniotic membrane, and the skin. The stiff fibers, typically made of collagen, are initially wrinkled and they follow the deformation of the embedding matrix without contributing to the mechanical response until they are fully distended. In this paper, the response of a fibrous membrane is described in the framework of hyperelasticity, with aim to the implementation in an existing finite element code. A micro-mechanical recruitment model, based on the statistical distribution of the activation stretch of the collagen fibers is introduced, leading to the definition of a simple form of the strain-energy function, depending on physically well-defined parameters. After some validation tests performed in homogeneous strain conditions, an application to the study of the stress field around circular holes in large deformation is presented, showing the capabilities of the proposed model.