  The material point method (MPM) is frequently used to simulate large
deformations of nearly incompressible materials such as water, rubber, and
undrained porous media. However, MPM solutions to nearly incompressible
materials are susceptible to volumetric locking, that is, overly stiff behavior
with erroneous strain and stress fields. While several approaches have been
devised to mitigate volumetric locking in the MPM, they require significant
modifications of the existing MPM machinery, often tailored to certain basis
functions or material types. In this work, we propose a locking-mitigation
approach featuring an unprecedented combination of simplicity, efficacy, and
generality for a family of explicit MPM formulations. The approach combines the
assumed deformation gradient ($\bar{\boldsymbol{F}}$) method with a
volume-averaging operation built on the standard particle-grid transfer scheme
in the MPM. Upon explicit time integration, this combination yields a new and
simple algorithm for updating the deformation gradient, preserving all other
MPM procedures. The proposed approach is thus easy to implement, low-cost, and
compatible with the existing machinery in the MPM. Through various types of
nearly incompressible problems in solid and fluid mechanics, we verify that the
proposed approach efficiently circumvents volumetric locking in the explicit
MPM, regardless of the basis functions and material types.
