Metamorphic petrology — mineralogical, field, and tectonic aspects

Abstract

Poisson's ratio in viscoelastic materials is a function of time. However, recently developed waterhammer models of viscoelastic pipes consider it constant. This simplifying assumption avoids cumbersome calculations of double convolution integrals which appear if Poisson's ratio is time-dependent. The present research develops a mathematical model taking the time dependency of Poisson's ratio into account for linear viscoelastic pipes. Poisson's ratio is written in terms of relaxation function and bulk modulus which is assumed to be constant. The relaxation function is obtained from creep function given as the viscoelastic property data of pipe material. The results obtained from the present waterhammer model are compared with the experimental data for two different flow rates. The comparison reveals that with the application of the time-dependent Poisson's ratio and unsteady friction, the viscoelastic data of mechanical tests can directly be used for waterhammer analysis with less need for the calibration of the flow configuration. It was also shown that the creep curve calibrated based on the present model is closer to the actual creep curve than that calibrated based on previous models.