  Through modelling and simulations we show that material instabilities play a
dominant role in the mechanical behavior of the fibrous collagen Extracellular
Matrix (ECM), as observed when the ECM is deformed by contractile biological
cells. We compare two families of fiber network models, Family 1 with stable
and Family 2 with unstable force-stretch response of individual fibers in
compression. The latter is a characteristic of post-buckling of beams with
hierarchical structure. Our simulations reveal different compression
instabilities at play in each family, namely, fiber collapse (buckling) in
Family 2 and fiber element collapse (snap-through) in Family 1. These result in
highly localized densification zones consisting of strongly aligned fibers
emanating from individual contractile cells or joining neighbouring cells, as
observed in experiments. Despite substantial differences in the response of the
two families, our work underscores the importance of buckling/compression
instabilities in the behavior of fibrous biological tissues, with implications
in cancer invasion and metastasis.
