LLMs as designers of physics-constrained neural networks for constitutive modeling: a demonstration on hyperelastic solids

Abstract Large language model (LLM)-based frameworks extend beyond agents; they also enable the on-demand creation of specialized scientific and engineering tools. We demonstrate this concept in the field of solid mechanics. There, so-called constitutive models describe the relationship between body deformation and mechanical stress. They are essential for both the scientific understanding and industrial application of materials. However, even recent data-driven methods of constitutive modeling, such as constitutive artificial neural networks (CANNs), still require substantial expert knowledge and human labor. We present a framework in which an LLM generates a CANN on demand, tailored to a given material class and dataset provided by the user. The framework covers LLM-based architecture selection, integration of physical constraints, and complete implementation. Evaluation on three benchmark problems demonstrates that LLM-generated CANNs achieve accuracy and generalization comparable to or greater than manually engineered counterparts, while substantially reducing the expertise required for constitutive modeling.