The “flow of stresses” concept: The analogy between mechanical strength and heat convection

Here we show that there is a complete analogy between the configuring of heat and fluid flow and the configuring of the “flow of stresses”. The common principle is the avoidance of flow strangulations. This endows the flow systems (fluid, heat, stresses) with high density: for example, strongest for a fixed volume, or lightest for a fixed load. Examples treated in detail are “ducts” for the flow of stresses (slender bars in tension of compression), bifurcated bars shaped as Y and V, and slender and tapered plates (adhesive joints, tendons, ligaments), which are shown to be analogous to convection boundary layers. The design value of the “flow of stresses” concept is emphasized: to facilitate the flow of stresses (and the flow of fluid and heat) is to generate the configuration of the flow system, in accord with the constructal law.