PC-NCLaws: Physics-Embedded Conditional Neural Constitutive Laws for Elastoplastic Materials

While data-driven methods offer significant promise for modeling complex materials, they often face challenges in generalizing across diverse physical scenarios and maintaining physical consistency. To address these limitations, we propose a generalizable framework called Physics-Embedded Conditional Neural Constitutive Laws for Elastoplastic Materials, which combines the partial differential equations with neural networks. Specifically, the model employs two separate neural networks to model elastic and plastic constitutive laws. Simultaneously, the model incorporates physical parameters as conditional inputs and is trained on comprehensive datasets encompassing multiple scenarios with varying physical parameters, thereby enabling generalization across different properties without requiring retraining for each individual case. Furthermore, the differentiable architecture of our model, combined with its explicit parameter inputs, enables the inverse estimation of physical parameters from observed motion sequences. This capability extends our framework to objects with unknown or unmeasured properties. Experimental results demonstrate state-of-the-art performance in motion reconstruction, robust long-term prediction, geometry generalization, and precise parameters estimation for elastoplastic materials, highlighting its versatility as a unified simulator and inverse analysis tool.