turkmath.org

Biomechanics is mainly concerned with the better understanding of the physiology and the patho-physiology of living systems by applying the principles of mechanics. In fact, practical and ethical limitations generally impede the purely experimental characterization of the relations between the mechanical loads acting on cells, tissues, organs, thereby favoring the use of numerical modeling and simulations. In the first part of the talk, some historical remarks will be made which will be followed by the description of the essential terms biomechanics and mechanobiology in relation to continuum mechanics. Afterwards, the histological and mechanical aspects of elastic arterial walls with their three distinct layers, namely intima, media, and adventitia will be discussed. In particular, two mechanically relevant proteins, i.e. elastin and collagen, included in the structure of these layers will be introduced. In the sequel, some information regarding residual stresses in the wall, aortic dissection, atherosclerosis, wall thickening and aging will be provided. In the second part of the talk, the emphasis will be placed on the continuum and computational modeling of inelasticity, particularly the rupture of the aortic wall suffering from aortic dissection. To this end, the the kinematics of the deformation and phase fields will be given in relation to anisotropic mechanical (both elatic and fracture) response of the tissue. Subsequently, a power balance including the energy storage (due to strain), the external power (due to the loading) and the dissipation (due to fracture) functionals will be proposed that yield the governing balance equations, namely the balance of linear momentum and the crack evolution equation upon considering the variation, see variational calculus, thereof. A novel energetic criterion determining the macroscopic crack initiation and crack propagation will also be the subject matter of the theory. Finally, the model proposed will be substantiated by representative numerical examples fitting the respective experimental data in terms of uniaxial extension and simple shear tests. Besides, an in silico propagation of the aortic dissection will be shown in a movie clip.