Fibre Reinforcement in Living Cells: A Preliminary Study of the F-actin Filaments

Cells are continuously exposed to physical stresses and strains from the Extracellular Matrix (ECM), thus, refining through numer- ical simulations the in vitro conditions during the cultures, may likely promote adequate tissue growth and remodelling [1].This paper describes a simplified three-dimensional constitutive model of the mechanical behaviour of the living cells. The necessary continuum mechanics background is skipped, along with derivations of the stress and spatial elasticity tensors for a transversely isotropic and hyperelastic material. The particular form of the strain energy proposed by Weiss [2] is used to describe the family of fibers. Also, the implementation of hyperelastic materials resorting the commercial finite-element-software Abaqus is discussed.Numerical examples are presented that demonstrate the utility and effectiveness of this approach. More specifically, homoge- neous deformations are imposed and the results compared with the analytical solution. Also, the convergence rate is checked for each case. Following, the use of UMAT routines using jacobian material matrices based on the Jaumann rate of Kirchhoff stress tensor ensured quadratic convergence rates.