A new elastoviscoplastic model based on the Herschel–Bulkley viscoplastic model

The aim of this paper is to introduce a new three-dimensional elastoviscoplastic model that combines both the Oldroyd viscoelastic model and the Herschel–Bulkley viscoplastic model with a power-law index n>0n>0. The present model is derived to satisfy the second law of thermodynamics. Various fluids of practical interest, such as liquid foams, droplet emulsions or blood, present such elastoviscoplastic behavior: at low stress, the material behaves as a viscoelastic solid, whereas at stresses above a yield stress, the material behaves as a fluid. When n=1n=1, a recently introduced elastoviscoplastic model proposed by the author is obtained. When 01n>1, the material exhibits the unusual shear thickening behavior.