A linearly elastic homogeneous and isotropic circular rod of radius a+δ (where δ is positive and small) and elastic constants Ei and v, is forcefully inserted into a linearly elastic isotropic homogeneous thick-walled cylinder with inner radius a and outer radius b and elastic constants E2 and v2. Assuming plane strain conditions (a) Find the stress state in both bodies. (b) How much pressure is generated at the interface between the two bodies? (Find this in terms of δ and the two sets of elastic constants). (c) Assuming that both materials have the same yield stress and they both fail according to a Tresca condition, which will fail first: the rod or the cylinder? (Procedure: Consider a Free Body Diagram of each body separately and solve each problem separately. Then apply a contact condition at the interface, i.e. answer in your mind the question: the amount of displacement that the rod gets squeezed in plus the amount the cylinder gets squeezed out have to add up to how much?).
