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.