Possible Approaches in Modelling Rearrangement in a Microstructured Material

Biological materials can be regarded as composites with spheroidal and fibre-like inclusions, representing cells and collagen fibres, respectively. The orientation and arrangement of the inclusions in a biological tissue is crucial to the determination of the mechanical properties of the material. Furthermore, the reorientation and rearrangement of the inclusions due to the deformation and external forces is of primary interest when dealing with growth and remodelling. We propose to look at the presence of inclusions as a source of internal hyperstaticity: when the material undergoes deformation, a generic inclusion is drifted by the deformation, but at the same time it “feels” the stress field and tends to carry a portion of stress proportional to its stiffness relative to that of the surrounding matrix. With this assumption, we can extend the classical “drift” evolution law for the unit vector field, in order to take the hyperstaticity into account. This method might be used in the description of remodelling in disordered media, such as biological tissues, and may be extended to investigate the reorientation of preferred directions of micro-structural elements in media described with a continuum approach.