Modeling elasto-viscoplastic free-surface flows with different yield surfaces

Elasto-viscoplasticity provides a unified way of describing yield-stress fluids which may exhibit both solid-like and fluid-like behavior. In this work, we present a finite strain overstress-type elasto-viscoplastic framework designed to facilitate the incorporation of different yield surfaces. Within this framework, we compare several yield-surface choices and assess the associated challenges. We consider three representative yield surfaces: (i) pressure-independent, (ii) pressure-sensitive frictional and (iii) capped surfaces, corresponding to von Mises, Drucker–Prager, and modified Cam–clay models, respectively. In the case of von Mises, the proposed formulation naturally recovers the well-known Bingham and Herschel–Bulkley rheologies which are characterized by a single critical yield stress. We discuss in detail the singularity of the Drucker–Prager yield surface which requires a special treatment. In particular, we show that the modified Cam–clay model can be used to conveniently circumvent this singularity under the right conditions, retrieving the expected solution of Drucker–Prager. Implemented within a hybrid Eulerian–Lagrangian scheme, the general framework presented here enables efficient simulations of elasto-viscoplastic flows in two or three spatial dimensions, not requiring regularizing the solid-fluid transition nor a separate free-surface treatment. Numerical benchmark simulations illustrate how yield surface geometry affects velocity profiles, plug formation and compressibility.