A Finite Deformation Theory for Nonlinearly Permeable Soft Hydrated Biological Tissues

Abstract

Our work on the biomechanics of diarthrodial joints began in 1969 with the publication of the paper “The Role of Lubrication in Biomechanical Joints” (Mow, 1969), in which we followed Fung’s (1968) urging that, in order “to put biomechanics on a firm foundation, the first important task for the future is to obtain the stress-strain-history relations for biological tissues.” At that time, there was almost no real appreciation of the constitutive laws governing the deformational behaviors of nature’s bearing materials—cartilage, synovial fluid, or, for that matter, any of the ligaments and tendons surrounding a joint—so that many contradictory lubrication theories (MacConaill, 1932, 1951; Charnley, 1959; McCutchen and Lewis, 1959; Linn, 1968; Walker et al, 1968) and, in retrospect, erroneous models were proposed to describe the mechanism involved in diarthrodial joint lubrication. Thus, we began our attempt to provide the required “firm foundation” by developing valid constitutive equations to describe these bearing materials prior to any further nonproductive speculations on diarthrodial joint lubrication. In order to gain some insight into the motivations for our approach to constitutive modeling of articular cartilage, a brief historical account of this effort is required. (In this chapter, we treat only the subject of modeling the deformational behavior of cartilage and other hydrated soft connective tissues.) The reader is referred to a review chapter by Armstrong and Mow (1980) and review papers by Mow and Lai (1979,1980) for discussions on diarthrodial joint lubrication mechanisms.