Emerging anisotropy and tethering with memory effects in fibrous materials

Fibrous materials may undergo an internal reorganization, which turns out in the emergence of preferential directions. This is a peculiar behavior of many biological tissues, which drive reorientation by external stimuli at chemo-mechanical levels. In particular, it is detected that contractile cells can reorganize fibrous extracellular matrices and form dense tracts of aligned fibers (tethers), that guide the development of tubular tissue structures and may provide paths for the invasion of cancer cells. Tether formation is caused by buckling instability of network fibers under cell-induced compression. We present a simple mechanical model, within a variational framework, that captures the essential aspects of these phenomena. The model qualitatively describes: (i) the emergence, induced by local compressive strain, of anisotropy, where fibrous materials exhibit directional preferences; (ii) the occurrence of micro-buckling, which leaves a lasting plastic deformation in the material; and (iii) the formation of localized field patterns, which contribute to the overall behavior of the material. By considering these fundamental aspects, our model provides insights into the mechanical response of fibrous materials and sheds light on the underlying mechanisms driving their behavior.