An engineer concerned with cumulative damage due to fatigue anticipates monitoring the deformation (actually the strain) versus time of a main structural member in a room at a newspaper press where the rolls of blank paper are stored prior to being placed on the presses. The (discretized) states are strains; the time (observation) points are each day just after the delivery of the rolls. Therefore the strains are assumed to represent peaks in the strain-time process. The loads are random in time, but the load-strain diagram of the member has been obtained exactly by accurate, in-place measurements.
(a) What conditions must the load-strain diagram of the member satisfy in order that the engineer can consider using a Markov-chain model of this process? In particular, does the diagram have to be linear and elastic, or nonlinear and elastic, or can it be generally nonlinear and nonelastic?
(b) Assume that the material is linearly elastic. What conditions must the load process satisfy in order that the deformation process can be assumed to be a Markov process?