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An Inverse Problem Approach Based on a Novell Mixing Model for the Mechanical Characterization of Arterial Tissues
Castro Urdiales, España
Conferencia; International Conference: Continuum Biomechanics of Biological Tissues; 2009
Institución organizadora:
Centro Internacional de Encuentros Matemáticos, Grupo de Mecánica Computacional de la Universidad Politécnica de Madrid
Mechanical factors such as stresses and strains play a major role in the growth and remodeling of soft tissues. Each of the main constituents of tissues also undergoes different processes reacting to mechanical stimulus. So, in order to characterize the growth and remodeling of tissues it is necessary to have an accurate estimation of the stress and strain in their main components. The aim of this work is to characterize the mechanical behavior of the arterial tissue constituents. To this end a novel mechanical approach based on a modified rule of mixtures, in a finite deformation framework is proposed. The arterial tissue is mechanically modeled as an isotropic soft matrix reinforced with preferentially oriented collagen fibers. The soft matrix contains, predominantly, highly distensible elastin and a small amount of randomly oriented collagen fibers both embedded in a ground substance.  The wavy nature of the collagen fibers is treated phenomenologicaly, so the mechanical properties of a single material that account for the average behavior of the preferentially aligned fiber bundles in the sample is obtained. This model is suitable to represent the behavior of the arterial media layer because, in general, the fibers are arranged with a preferential orientation. A general scheme based on a general mixture rule is proposed and it is used in conjunction with constraints provided by thermodynamic principles to obtain the stress-strain behavior of the components fitting experimental data. These data are the uniaxial tensile stress-stretch responses for media samples in circumferential and longitudinal directions published by Holzapfel (2005). As a result of the inverse problem solution the mechanical properties of matrix and reinforce are obtained, which are within the range of the published values. In order to get a useful numerical model for FEM the stress-strain curves for the matrix and reinforce can be characterized by an adequate model, for instance, in the present work the Yeoh (1993) model is employed. It is important to point out that the rule of mixtures proposed in the present work, incorporates structural considerations from histological evidence, such as, the volume participation ratios of matrix and reinforce, and the main fiber preferential orientation.