STEADY-STATE CREEP OF A LONG NARROW RECTANGULAR MEMBRANE INSIDE A LOW RIGID MATRIX WITH A PROPORTIONAL DEPENDENCE OF THE MAGNITUDE OF THE TRANSVERSE PRESSURE ON TIME

The problem of steady-state creep of a long narrow rectangular membrane under constrained conditions inside a rigid matrix with a proportional increase in the transverse pressure with time (at different velocities) is studied. The problem is solved taking into account the geometric and physical nonlinearity. The problem considers a long rigid matrix of rectangular cross section, in which the height is not more than half the width. Two variants of the contact conditions between the membrane and the matrix are considered: ideal slip and sticking. In this work, three stages of membrane creep are studied. At the first stage, the membrane is deformed under steady-state creep conditions up to the moment it touches the transverse wall of the matrix. The second stage ends at the moment the membrane touches the longitudinal walls of the matrix. At the third stage, the membrane is in contact with the matrix along the transverse and longitudinal sides. The calculation is carried out until the time of almost complete adherence of the membrane to the matrix. It is of interest to compare these times under different contact conditions. In the general case, the ratio of these times depends on two parameters: the exponent in the constitutive equation of the steady-state creep of the membrane material and the value of the dimensionless height of the matrix. In this problem, at different rates of increase in the transverse pressure and at different degrees of proximity of the membrane to the matrix, the times of completion of loading stages in ideal slip are shorter than in adhesion. The research results can be used in calculations of membrane formation in a rigid matrix.