LARGE-STRAIN ANALYSIS OF SOFT BIOLOGICAL-MEMBRANES - FORMULATION AND FINITE-ELEMENT ANALYSIS

This paper presents a general formulation of thin incompressible membr anes and investigates the behavior of soft biotissues using the finite element method. In particular the underlying hyperelastic model is ch osen to examine the highly non-linear constitutive relation of blood v essels 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-L agrangian strains. Based on the principle of virtual work the finite e lement equations are provided and briefly discussed. Consistent linear ization of the weak form of equilibrium and the external pressure term ensures a quadratic convergence rate of the iterative solution proced ure. On the computational side of this work an effort was undertaken t o show a novel approach on the investigation of soft tissue biomechani cs. Representative numerical analyses of problems in vascular mechanic s are discussed that show isochoric finite deformations (large rotatio ns and large strains). In particular, a numerical simulation of the in teraction between an inflated balloon catheter and a plaque deposit on the wall of a blood vessel is presented.