Time‐Dependent Response of Three‐Filament Cord

Abstract

A method is presented in which the time‐dependent creep response of a three‐filament cord, constrained by a no‐end rotation boundary condition, may be predicted. This method is an initial attempt to describe the viscoelastic response of the cord by incorporating the stress‐relaxation data for a linearly viscoelastic construction material. The particular material used in this paper is polymethyl methacrylate (PMMA). The stress relaxation for PMMA is modeled analytically by utilizing the Schapery collocation method that determines the constant coefficient values for the elements of a Wiechert response model. The geometric effects of the cord are then combined with the time‐dependent analytical solution for the Wiechert model to develop a system of convolution integrals that satisfy the equilibrium and imposed boundary conditions for the cord construction. The solutions for these integrals are approximated numerically using a modified Newton's iterative method combined with a linear time‐step approximation technique.