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Homogenization applied in modelling of arteries

Lukes V., Rohan E.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

2003

nr 21

165-170

The paper deals with homogenization method applied in modelling mechanics of arterial wall. The influence of microstructure on the wave propagation is pursued. The multi-layered structure of arterial wali is considered, each layer is modelled using fibre reinforced materiał consisting of hyperelastic materiał with periodic distribution of fluid filled incompressible inclusions. The effective parameters are derived by the method of homogenization. The fluid-structure interaction problem is assumed to be axisymmetric, one dimensional flow is considered through symmetric shelł which oscillates in both radial and longitudinal directions. Various arrangements of the microstructure are examined.

Sensitivity analysis and material identification for activated smooth muscle

Rohan E., Cimrman R.

Computer Assisted Mechanics and Engineering Sciences

2002

Vol. 9, No. 4

519-541

The paper deals with the problem of material identification for smooth muscle tissue in activated, or passive states. In [1] a composite type mathematical model has been proposed describing the complexity of the tissue reduced to the networks of muscle and collagen fibres. The computational model is based on the total Lagrangian formulation with incompressibility of the bulk material. The problem of inflating vessels is considered in order to allow simulation of real experimental conditions and, thus, to determine constitutive parameters of muscle in active state. These parameters are identified also from hysteresis, or relaxation curves. The direct differentiation, or the adjoint systems techniques are applied to the sensitivity analysis. Results of numerical tests are given.