Finite viscoelastic modeling of yeast cells with an axisymmetrical shell approach

Based on the use of shell kinematics, a theoretical model is developed to predict time-dependent responses of Saccharomyces cerevisiae yeasts. These cells are herein described as thin-walled shells with axisymmetrical shapes and, due to their soft nature, the finite strain range is a priori adopted. Accordingly, a finite viscoelastic modeling is assumed for the cell-wall. An Ogden-type energy function is used together with a creep-like potential, this latter to describe the way overstresses vanish at thermodynamic equilibrium. The cell-volume conservation due to the inner incompressible fuid is accounted for via an update procedure of the Uzawa type. Numerical simulations highlight the efficiency of the proposed framework. As a further outcome, the emergence of a necessary cell-wall representation by at least two sets of layers with sensitively different mechanical properties is established.