By using of combining theoretical model with empirical model, the nonlinear viscoelastic-plastic constitutive equations of soybean and cottonseed were developed on the basis of the creep test. The parameter inverse problem of constitutive model was proposed using improved particles swarm optimization. Numerical simulations of creep of soybean and cottonseed were carried out. The definition of critical pressing time for oil extraction and the method for determining the critical pressing time using creep rate were proposed. The values of critical pressing time for extruded soybean and cottonseed under six applied pressures were evaluated. Results indicated that the nonlinear viscoelastic-plastic constitutive model could simulate rheological behaviors of soybean and cottonseed very well. Mean relative deviations between the experimental and predicted values of soybean and cottonseed were 1.55% and 1.93%, respectively. There were significant decreases in the values for the creep rates in the early stage of pressing, and decreases to an insignificant and stabilize value in the later stage.
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