Phase transitions in one-dimensional nonlinear viscoelasticity: admissibility and stability

摘要: For the motion of a one-dimensional viscoelastic material rate type with non-monotonic stress-strain relation, mixed initial boundary value problem is considered. A simple existence theory outlined, based on novel transformation equation into form degenerate reaction-diffusion system. This leads to new results characterizing regularity weak solutions. It shown that each solution tends strongly stationary state asymptotically in time. Stable states are characterized. may contain coexistent phases, i.e. they have discontinuous strain. They need not be minimizers energy strong sense calculus variations; “metastable” and “absolutely stable” phases coexist stable state. Furthermore, such do arise as long-time limits smooth Beyond above, “hysteresis” “creep” phenomena exhibited model loaded bar. Also, viscosity criterion proposed for admissibility propagating waves associated purely elastic model. then applied describe formation some phase boundaries