Coupled Solid-Fluid Problems

Abstract

We considered a variety of problems in Chapters 2–10 that fall within the domain of either biosolid mechanics or biofluid mechanics, each of which is very important in its own right. Whether in the body (in vivo) or in the laboratory (in vitro), however, many “real-life” problems simultaneously involve solid-fluid interactions. For example, although we may seek to determine the stresses in the limbs of a pilot who has ejected from an aircraft, for purposes of identifying safety measures, it is the wind that induces the applied loads of importance; aneurysms may be considered as thin-walled, nearly spherical membranes that exhibit a solidlike character, but the applied loads are due to the internal flowing blood and the surrounding cerebrospinal fluid; mechanotransduction in bone, which exhibits a strong solidlike behavior, appears to be influenced directly by both loads due to weight bearing and those due to the flow of blood and bone fluid within the many different canals within the bone; and an atomic force microscopic examination of the mechanics of a cell may primarily reveal the properties of the cortical membrane and underlying solidlike cytoskeleton, but flow of the cytosol likely plays a key role as well. Hence, from these simple examples and many more like them, we see that solid-fluid interactions are important at the organism, organ, tissue, cellular, and molecular levels. Indeed, although it tends to be convenient to introduce students to a subject by focusing only on that subject, most research and clinical problems require interdisciplinary and multidisciplinary approaches (i.e., analysis and design of coupled problems). Such problems are typically complex and require advanced approaches, but here we consider a few introductory examples.