Endochronic Simulation on the Effect of Curvature Rate at the Preloading Stage on the Subsequent Creep or Relaxation of Thin-Walled Tubes Under Pure Bending

Abstract

ABSTRACTIn this paper, the first-order ordinary differential constitutive equations of endochronic theory were combined with the principle of virtual work for simulating the response of creep (moment is kept constant for a period of time) or relaxation (curvature is kept constant for a period of time) of thin-walled tubes subjected to pure bending with different curvature-rates at the preloading stage. A group of Fourier series was used to describe the circumferential displacements of the tube. Thus, a system of nonlinear algebraic equations was determined. This system of equations can be solved by numerical method. Experimental data tested by Pan and Fan [1] were compared with the theoretical simulations in this study. It is shown that the theoretical formulations effectively simulate the experimental data.