The rheological (deformation and flow) properties of biological tissues
are important in processes such as embryo development, wound healing and
tumour invasion. Indeed, processes such as these spontaneously generate
stresses within living tissue via active process at the single cell level.
Tissues are also continually subject to external stresses and deformations
from surrounding tissues and organs. The success of numerous physiological
functions relies on the ability of cells to withstand stress under some
conditions, yet to flow collectively under others. Biological tissue is
furthermore inherently viscoelastic, with a slow time-dependent mechanics.
Despite this rich phenomenology, the mechanisms that govern the
transmission of stress within biological tissue, and its response to bulk
deformation, remain poorly understood to date.

This talk will describe three recent research projects in modelling the
rheology of biological tissue. The first predicts a strain-induced
stiffening transition in a sheared tissue [1]. The second elucidates the
interplay of external deformations applied to a tissue as a whole with
internal active stresses that arise locally at the cellular level, and
shows how this interplay leads to a host of fascinating rheological
phenomena such as yielding, shear thinning, and continuous or
discontinuous shear thickening [2]. The third concerns the formulation of
a continuum constitutive model that captures several of these linear and
nonlinear rheological phenomena [3].

[1] J. Huang, J. O. Cochran, S. M. Fielding, M. C. Marchetti and D. Bi,
Physical Review Letters 128 (2022) 178001

[2] M. J. Hertaeg, S. M. Fielding and D. Bi, Physical Review X 14 (2024)
011017.

[3] S. M. Fielding, J. O. Cochran, J. Huang, D. Bi, M. C. Marchetti,
Physical Review E (Letter) 108 (2023) L042602.