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

TL;DR

A generalizable framework called Physics-Embedded Conditional Neural Constitutive Laws for Elastoplastic Materials, which combines the partial differential equations with neural networks to model elastic and plastic constitutive laws.

Abstract

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.

Figures (6)

• Figure 1: The Pipeline of our PC-NCLaws. We embedded two neural networks in the dynamical system to express the elastic and plastic constitutive law, respectively. At the top row (a), we introduced physical parameters as inputs to guide the progress of motion. The bottom row shows the applicable materials of our model, the training process, and the testing process. In the training process (b), we use multiple objects with the same material type but different physical parameters to train PC-NCLaws, and optimize the weights of the neural networks throughout the training. In the testing process (c), the trained PC-NCLaws model acts as a high-fidelity simulator capable of performing various tasks.
• Figure 2: Parameters Estimation. After PC-NCLaws is trained, we can use it to reversely estimate the physical parameters from the object's motion sequence. By initializing a set of physical parameters and other physical information, we use PC-NCLaws for simulation, compute the loss with the ground truth, and backward the gradient to optimize the physical parameters. During this process, the weights of the neural networks in PC-NCLaws remain unchanged. When the loss converges, we consider the physical parameters at this time to be the properties of this object.
• Figure 3: Qualitative Results (via PC-NCLaws-M training strategy). We present visual results for the complex geometric generalization.
• Figure 4: The optimization process for Elasticity parameters estimation (the third experiment set, groundtruth: $E = 2.00 \times 10^5$, $\nu = 0.15$). Young's modulus and Poisson's ratio evolution are shown with uniform scaling. The red curve tracks the error.
• Figure 5: Real-World Experiments. Two dough samples with distinct initial shapes (cube: simple; star: complex) were released from rest at a height. Physical parameters were inversely estimated from captured motion trajectories and used for forward simulation from identical initial conditions. Top: ground truth; bottom: corresponding simulation results.