hi

Yes because of their hydrated states, soft tissues exhibit time-dependent mechanical behavior sometimes described as "viscoelastic" but in many cases a "poroelastic" framework is actually more appropriate.  In general, composite mechanics is a good background for studying tissues since they are inhomogeneous in general.  Continuum approaches have seen varying degrees of success in describing soft tissues, and recent attention has been on non-continuum aspects of soft tissue response including molecular and hierarchical modeling.

Part of the reason that the field is somewhat fragmented into groups by tissue type is that the microstructures of different soft tissues are quite different and therefore structure-properties interactions vary widely.  There are also some interesting questions regarding the reasons for studying biomechanics outside of general interest.  Articular cartilage is interesting for its role in arthritis.  Ligaments and tendons are often studied relating to sports injuries.  Bone is considered within the context of osteoporosis.  It's useful to keep in the back of your mind when considering your project that there probably should be some sort of concrete motivation for the problem you select and it can equally be some clinical/medical problem or some unanswered fundamental question about the class of collagenous materials.  Historically biomechanics research was driven on the clinical side, but more recently its rapid growth has been in more fundamental aspects.  

My best advice to you right now is to try to read a lot before you narrow down your focus.  There is a lot of structural biology to learn as well as a very large literature to consider.  It might be worth attending a meeting with symposia on biomechanics to see what others are doing in this subject and get a picture of the breadth of the topic in current research.