  Under many physiological and pathological conditions such as division and
migration, cells undergo dramatic deformations, under which their mechanical
integrity is supported by cytoskeletal networks (i.e. intermediate filaments,
F-actin, and microtubules). Recent observations of cytoplasmic microstructure
indicate interpenetration among different cytoskeletal networks, and
micromechanical experiments have shown evidence of complex characteristics in
the mechanical response of the interpenetrating cytoplasmic networks of living
cells, including viscoelastic, nonlinear stiffening, microdamage, and healing
characteristics. However, a theoretical framework describing such a response is
missing, and thus it is not clear how different cytoskeletal networks with
distinct mechanical properties come together to build the overall complex
mechanical features of cytoplasm. In this work, we address this gap by
developing a finite-deformation continuum-mechanical theory with a multi-branch
visco-hyperelastic constitutive relation coupled with phase-field damage and
healing. The proposed interpenetrating-network model elucidates the coupling
among interpenetrating cytoskeletal components, and the roles of finite
elasticity, viscoelastic relaxation, damage, and healing in the
experimentally-observed mechanical response of interpenetrating-network
eukaryotic cytoplasm.
