On behavior of perfect elastoplasticity under rectilinear paths (Q1286193)

We investigate a perfect elastoplastic model for the relation of generalized stresses and their conjugate generalized strain rates. The exact solutions are obtained for the model subjected to rectilinear generalized strain paths, and the concepts of response subspace and visualization are introduced such that the \(n\)-dimensional problem is reduced to a two-dimensional problem in the response subspace. The generalized stress-strain curves are classified by geometrical shapes into ten types, in contrast to the superficial impression of only one type of shape, an inclined straight line followed by a horizontal line. The existence of a limit strength vector and a limit power of dissipation is demonstrated by the long-term behavior based on the exact solutions, and the existence together with the response's stability is further verified by Lyapunov's direct method.