Beyond Elasticity: Plasticity and Viscosity

*Author of this lecture: Chang Yu, University of California, Los Angeles

In physics-based simulation, the continuum assumption enables us to model a wide range of materials with rich and diverse behaviors. While hyperelasticity provides a convenient and elegant model for materials that return to their rest shape after deformation, such as rubber or soft tissue, it represents only a small portion of the physical phenomena observed in the real world.

Many natural and everyday materials, including sand, snow, mud, metal, foam, and fracturing solids, exhibit irreversible deformation, dissipation, or flow-like behavior that cannot be captured by purely elastic models. These materials require constitutive models that incorporate plasticity (permanent deformation) and viscosity (rate-dependent stress response).

The core difference between elasticity and plasticity lies in how materials store and dissipate energy. Elastic deformation is reversible and energy-conservative; plastic deformation is irreversible, governed by yield criteria, and involves energy dissipation through internal reconfiguration of the material structure.

MPM is particularly well suited for simulating plastic and viscous materials, as it naturally supports large deformations, history-dependent state updates, and localized inelastic flow, without suffering from mesh entanglement, element inversion, or remeshing-related artifacts common in traditional mesh-based methods.

In the remainder of this lecture, we will introduce how plasticity and viscosity are incorporated into MPM simulations. We begin with the discretization of plastic flow and the representation of irreversible deformation. We then describe how to enforce material-specific yield conditions and perform return mapping to constrain deformation within admissible limits.