Steady-State Creep of a Long Membrane in a Rigid Matrix with a Piecewise Constant Dependence of the Rate of Change in Transverse Pressure on Time

Abstract

The problem of steady-state creep of a rectangular membrane in a rigid matrix with a height-to-width ratio of not less than 0.5 is studied in the case of a piecewise constant dependence of the rate of change in transverse pressure on time. The creep of the membrane with a single change in transverse pressure over time is investigated. Two types of contact conditions between the membrane and matrix are considered: perfect slip and no-slip. Three stages of creep of the membrane are investigated. The analysis is carried out to 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 valid.