  Biological processes, from morphogenesis to tumor invasion, spontaneously
generate shear stresses inside living tissue. The mechanisms that govern the
transmission of mechanical forces in epithelia and the collective response of
the tissue to bulk shear deformations remain, however, poorly understood. Using
a minimal cell-based computational model, we investigate the constitutive
relation of confluent tissues under simple shear deformation. We show that an
initially undeformed fluidlike tissue acquires finite rigidity above a critical
applied strain. This is akin to the shear-driven rigidity observed in other
soft matter systems. Interestingly, shear-driven rigidity can be understood by
a critical scaling analysis in the vicinity of the second order critical point
that governs the liquid-solid transition of the undeformed system. We further
show that a solidlike tissue responds linearly only to small strains and but
then switches to a nonlinear response at larger stains, with substantial
stiffening. Finally, we propose a mean-field formulation for cells under shear
that offers a simple physical explanation of shear-driven rigidity and
nonlinear response in a tissue.
