  In this paper, we introduce a novel convex formulation that seamlessly
integrates the Material Point Method (MPM) with articulated rigid body dynamics
in frictional contact scenarios. We extend the linear corotational hyperelastic
model into the realm of elastoplasticity and include an efficient return
mapping algorithm. This approach is particularly effective for MPM simulations
involving significant deformation and topology changes, while preserving the
convexity of the optimization problem. Our method ensures global convergence,
enabling the use of large simulation time steps without compromising
robustness. We have validated our approach through rigorous testing and
performance evaluations, highlighting its superior capabilities in managing
complex simulations relevant to robotics. Compared to previous MPM based
robotic simulators, our method significantly improves the stability of contact
resolution -- a critical factor in robot manipulation tasks. We make our method
available in the open-source robotics toolkit, Drake.
