Humans have a remarkable capacity to understand the physical dynamics of objects in their environment, flexibly capturing complex structures and interactions at multiple levels of detail. Inspired by this ability, we propose a hierarchical particle-based object representation that covers a wide variety of types of three-dimensional objects, including both arbitrary rigid geometrical shapes and deformable materials. We then describe the Hierarchical Relation Network (HRN), an end-to-end differentiable neural network based on hierarchical graph convolution, that learns to predict physical dynamics in this representation. Compared to other neural network baselines, the HRN accurately handles complex collisions and nonrigid deformations, generating plausible dynamics predictions at long time scales in novel settings, and scaling to large scene configurations. These results demonstrate an architecture with the potential to form the basis of next-generation physics predictors for use in computer vision, robotics, and quantitative cognitive science.