Simulation of Damage Hysteresis in Soft Biological Tissues

Arterial lumen reductions result in hypertension and possibly rupture of plaque deposits as a consequence of atherosclerotic degeneration which can finally cause a heart attack or a stroke. Hence, therapeutical treatments such as balloon angioplasty and stenting are required. The aim of this work is to propose a new model for the softening hysteresis observed in overstretched arterial tissues and related computer simulations. The physiological loading domain is described by a purely elastic polyconvex anisotropic strain‐energy function, which is decoupled into an isotropic part related to the non‐collagenous matrix material, and into a transversely isotropic part related to the embedded (collagen) fibers. A scalar‐valued damage variable is taken into account for the fibers to cover a saturation function converging to a maximal damage value at a fixed maximum load level. In addition, the model captures remnant strains in the fiber direction after unloading. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)