Steady-state creep of a long narrow membrane inside a high rigid matrix at variable lateral pressure

This paper describes a problem of steady-state creep of a long narrow rectangular membrane in the case of a linear dependence between the transverse pressure and time. The membrane is located inside a tall long rigid matrix with a rectangular cross section, the ratio of the height to half the width is greater than unity. A power-series relationship between the stress intensities and creep strain rates of the membrane is used. Two variants of contact conditions for the membrane and the matrix are considered: ideal sliding and adhesion. The analysis of the problem is carried out until the time at which the membrane is almost completely adjacent to the matrix walls. It is shown that, if the relative height of the membrane is smaller than a certain value, then the creep duration of the membrane until the moment at which it almost completely adjoins the matrix walls is shorter in the case of ideal sliding than in the case of adhesion, and vice versa. An explanation of this effect is provided.