Finite Deformations under Pressurisation in an Infinitely Lon Thick-Waled, Nonlinearly Viscoelastic Cylinder Ideally Bonded to a Thin Elastic Case

摘要

A constitutive equation for a nonlinearly viscoelastic, incompressible, Mooney-Voigt material is developed. Use is made of the equation to arrive at a nonlinear differential equation for the quasistatic finite-deformational response under internal pressurization of an infinitely long, thick cylinder of a nonlinearly viscoelastic material bonded to a linearly elastic thin case. Careful mathematical analysis of the differential equation is carried out. The equation is solved numerically for step and ramp pressure programs for a realistic set of data and the results are compared with those of the corresponding linearized program.nSeveral peculiarities of the results of the nonlinear theory are discussed at length.