GaussianFlesh: A Total Lagrangian APIC Substrate for Unified Geometry, Material State, and Continuum Simulation
We present a unified particle substrate in which 3D Gaussian primitives simultaneously encode geometric shape, material anisotropy, and simulation state — removing the representational boundary between scene geometry and physical dynamics. Two architectural commitments distinguish our approach: a Total Lagrangian formulation with a fixed reference-configuration grid, and the Affine Particle-in-Cell (APIC) transfer scheme with additive deformation gradient updates. Together these choices eliminate the numerical drift that accumulates in Updated Lagrangian formulations under sustained elastic deformation. Constitutive behaviour is fully swappable at the material level. The system runs stably at real-time rates across three material regimes spanning three orders of stiffness magnitude.
Contemporary physically-grounded scene representations maintain a division of labour: geometry systems encode shape and appearance while physics systems simulate dynamics on separate proxy representations. The coupling between them — skinning, cage embedding, mesh-to-particle transfer — is an engineering afterthought. For applications demanding real-time, physically plausible dynamics in robotics, interactive simulation, and embodied world models, this separation is architecturally limiting.
GaussianFlesh proposes a substrate-first architecture in which the Gaussian particle is the primary design primitive, simultaneously encoding geometric shape (covariance matrix), material anisotropy (covariance orientation), and simulation state. When a particle deforms under simulation, its visual shape deforms automatically. There is no translation step. The geometry is the simulation state.
The core commitments
Two choices distinguish GaussianFlesh from prior work. The first is a Total Lagrangian MPM formulation: shape functions and gradients are computed once from the rest configuration and never rebuilt. This prevents the numerical drift that accumulates in Updated Lagrangian formulations under sustained elastic deformation, where the deformation gradient updates multiplicatively and small errors compound over hundreds of frames.
The second is corotated linear elasticity as the default constitutive model. The (F - R) stress term generates restoring stress proportional to the shear modulus, providing implicit shape restoration. For stiff materials, no explicit correction is needed at all. For high-restitution rubber, a small residual correction suffices. This eliminates a class of ad hoc shape-preservation hacks common in prior work.
Results
The system is evaluated on a unit sphere (120 particles) and a deformed sphere (120 particles), each dropped from 4.0 m, across three material regimes: rubber, metal, and jelly. All parameters other than the material preset are identical. The physics hot path runs via Taichi CUDA kernels on an RTX 4070 at real-time rates (42-72 ms/frame across all materials).
The same 120-particle substrate produces qualitatively distinct behaviours through constitutive law swap alone. Rubber compresses and rebounds elastically. Metal barely deforms visibly. Jelly spreads laterally and oscillates before recovering. Constitutive law is the only difference between them.
Why it matters
World models, AI systems that simulate physical behaviour, currently lack a grounded physics primitive. Video-based approaches learn correlations from pixels. They do not represent that a rubber ball and a metal ball dropped from the same height behave differently for reasons that can be computed, not just observed.
A substrate where objects are Gaussian particles with material identity, running forward simulation in real time, in the same representational space used for scene reconstruction, closes that loop. Future work will couple a vision-language model to existing 3D Gaussian scenes so that material properties can be inferred from appearance and simulation can begin immediately, without a separate physics representation, without a translation layer.