Steady-state creep of a long membrane in a rigid matrix with a piece-constant dependence of the rate of change in transverse pressure versus time

This paper deals with the problem of steady-state creep of a rectangular membrane in a rigid matrix with a ratio of the height to width of not less than 0.5 in the case of piecewise constant dependence lateral velocity over time. The creep of the membrane with a single change in the rate of transverse pressure over time is investigated. Two variants of the contact conditions of the membrane and matrix: perfect slip and no-slip are considered. Three stages of creep of the membrane are investigated. The analysis is carried out until the time at which the membrane is in almost complete contact with the walls of the matrix. Time dependences of the variable thickness of the membrane and the stress intensity in the membrane are obtained. It is shown that in this problem, the rule of summation of partial times is not performed.