©Freund Publishing House Ltd., International Journal of Nonlinear Sciences & Numerical Simulation 11(10): 817-830, 2010 Effects of Solid Compressibility on Responses of Hydrated Soft Biological Tissues Zhaochun Yang a '*, Jeen-Shang Lin b , Patrick Smolinski 3 a Department ofMechanical Engineering, University of Pittsburgh, Pittsburgh, PA, 15261 b Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, PA, 15261 Abstract The Biot theory and Mixture theory are the two main approaches for the mechanical analysis of hydrated soft biological tissues. Aside from the fact that the Mixture theory employs an entropy measure, one main difference between these theories stems from the consideration of the compressibility of the solid phase. The Biot theory often considers the solid phase to be nearly incompressible, whereas the Mixture theory considers it to be fully incompressible. The objective of this study is to investigate the significance of solid compressibility through analytical and numerical analysis. Both quasi-static and dynamic analyses were carried out on one-dimensional problems for which the analytical solutions can be derived. The results of the study clearly indicate that the compressibility of the solid phase can have a significant impact and is an important factor that may have to be included for soft tissues. Keywords: Mixture Porous theory; Poroelastic theory; analytic solution; hydrated soft tissue 1. Introduction Different varieties of soft connective tissues, such as articular cartilage and intervertebral disc, exist in the human body. Significant amounts of mobile fluid, relative to the solid material, move, impacting the convection path for transport, heating or cooling, and the mechanical function of the structure. Because the electric-chemical interaction of the mobile fluids with the porous solid matrix is a complex process, a number of theoretical models have been developed to describe this process [1-19]. Theoretically, hydrated soft biological tissues are considered as a multi-phasic poroelastic continuum. As Cowin [20] points * Corresponding Author: zcyang2010@gmail.com out, Biot theory and Mixture theory are the dominant approaches for the mechanical analysis of biological tissues. Biot theory has its origin in geomechanics, starting with Biot work on the consolidation of soils following Terzaghi's ground breaking work on the concept of effective stress [21]. Biot theory builds a model in an average sense by establishing governing equations over an infinitesimal volume, whereas the Mixture theory considers entities surrounding a point. Mow et al [8] were the first to consider hydrated soft tissues as a biphasic medium by using the mixture theory. Their models become more sophisticated over time with the addition of the electric-chemical effects [9, 19]. Biot theory, as exemplified by Simon [2-4], Laible [5], and Iatridis [6], was later adopted. The scope of this study encompasses the biphasic model, the simplest form of the poroelastic model of tissues. Soft tissues were