  When sheared, most elastic solids such as metals, rubbers and polymer
hydrogels dilate in the direction perpendicular to the shear plane. This
well-known behaviour known as the Poynting effect is characterized by a
positive normal stress. Surprisingly, biopolymer gels made of fibrous proteins
such as fibrin and collagen, as well as many biological tissues exhibit the
opposite effect, contracting under shear and displaying a negative normal
stress. Here we show that this anomalous behaviour originates from the open
network structure of biopolymer gels, which facilitates interstitial fluid flow
during shear. Using fibrin networks with a controllable pore size as a model
system, we show that the normal stress response to an applied shear is positive
at short times, but decreases to negative values with a characteristic time
scale set by pore size. Using a two-fluid model, we develop a quantitative
theory that unifies the opposite behaviours encountered in synthetic and
biopolymer gels. Synthetic polymer gels are impermeable to solvent flow and
thus effectively incompressible at typical experimental time scales, whereas
biopolymer gels are effectively compressible. Our findings suggest a new route
to tailor elastic instabilities such as the die-swell effect that often hamper
processing of polymer materials and furthermore show that poroelastic effects
play a much more important role in the mechanical properties of cells and
tissues than previously anticipated.
