Axisymmetric shell modelling of viscoelastic yeast cells in the finite strain range

Abstract

A novel theoretical model is developed to describe the whole response of Saccharomyces cerevisiae yeasts. In this contribution, a yeast is represented as a thin-walled, liquid-filled, impermeable, spherical shell structure. Herein, we adopt the quasi-Kirchhoff shell theory that we extend to the range of finite viscoelasticity. The used kinematics is the multiplicative decomposition of the deformation gradient into an elastically relaxing part and a viscous part. Motivated by a generalized Maxwell model, we assume an incompressible hyper-viscoelastic model of N=1-Ogden-Ogden type. In addition, the cell-wall is regarded as homogeneous and isotropic in a first approach. On another hand, the internal cell-liquid resists to external loads by a normal pressure on the cell-wall. This pressure is represented by using follower loads, the magnitude of which is accounted for via an updated procedure of the Uzawa-type to insure the incompressibility of this inner fluid. Furthermore, adopting a frictionless contact, on one hand, and using intrinsic parameters from the literature, on the other hand, we predict within the finite element method the responses of various compressed cells between flat parallel surfaces and probes of different geometries.