Large strain analysis of soft biological membranes: Formulation and finite element analysis
This paper presents a general formulation of thin incompressible membranes and investigates the behavior of soft biotissues using the finite element method. In particular, a hyperelastic model is chosen to examine the highly nonlinear constitutive relation of blood vessels which are considered to be perfectly elastic, homogeneous and (nearly) incompressible. First, the stress-deformation relation and the elastic tangent moduli are derived in a very general material setting which is subsequently specified for blood vessels in terms of Green-Lagrangian strains. Based on the principle of virtual work, the finite element equations are provided and briefly discussed. Consistent linearization of the weak form of equilibrium and the external pressure term ensures a quadratic convergence rate of the iterative solution procedure. Finally, we present a numerical simulation of the interaction between an inflated balloon catheter and a plaque deposit on the wall of a blood vessel.
scientific article; zbMATH DE number 1081947
scientific article