Steady-State Creep of a Narrow Membrane Inside a Rigid Low Matrix

The problem of the steady-state creep of a long narrow rectangular membrane under constrained conditions inside a rigid matrix with a piecewise constant dependence of the transverse pressure on time is investigated. The problem considers a long rigid low matrix of rectangular cross section, in which the height is less than half the width. As an example, the creep of a membrane is studied with a single change in the transverse pressure with time. Two variants of membrane-matrix contact conditions are considered: perfect sliding and sticking. In this work, four stages of membrane creep are investigated. At the first stage (elastic deformation), the membrane, which is flat in the initial state, is instantly elastically deformed under the action of pressure, acquiring the shape of an open circular cylindrical shell. At the second stage, the membrane is deformed under conditions of steady creep up to the moment it touches the upper wall of the matrix. The third stage ends when the membrane touches the longitudinal walls of the matrix. At the fourth stage, the membrane contacts the matrix along the transverse and longitudinal sides. Calculation is carried out up to the time of almost complete contact of the membrane with the matrix. The rule of summation of the partial times of sticking of the membrane to the matrix is considered for this problem statement.