Constitutive learning of feature-dependent texture in hydrated materials
Please login to view abstract download link
Recent advances in constitutive modeling integrated with machine learning are transforming how material behavior is characterized across engineering, biological, and soft-matter systems. These approaches enable data-driven identification of constitutive relations while preserving physical consistency and offer a powerful alternative to classical phenomenological models. In food science, such methods create new opportunities to quantitatively link ingredients, processing variables, and resulting texture. In this study, we focus on tofu as a benchmark material [1]. Composed solely of soy protein and water, tofu provides a unique platform to investigate how small variations in intrinsic features, such as hydration and processing conditions, translate into pronounced changes in mechanical response. We conduct systematic uniaxial compression experiments across multiple tofu types and loading conditions to probe nonlinear, rate-dependent, and inelastic behavior. To extract governing constitutive equations from the experimental data, we employ automated model discovery using inelastic constitutive artificial neural networks [2]. This framework autonomously identifies the dominant elastic and inelastic mechanisms without prescribing one single material law a priori. Importantly, feature dependencies such as the water content are embedded directly into the constitutive representation and allow the model to learn how these variables modulate texture and mechanical performance. The resulting models establish quantitative relationships between material composition and macroscopic texture. By tracing back these relations from the learned constitutive equations, we provide a pathway toward rational product design, where desired mechanical or sensory attributes can be achieved by adjusting ingredient-level features rather than relying on empirical trial-and-error. Beyond tofu, the proposed framework is broadly applicable to other food systems and hydrated soft materials and demonstrates how physics-informed machine learning can support inverse design and targeted texture optimization across multiple sectors. 1] Boes B, Simon JW, Holthusen H, Kuhl E., The mechanics and physics of tofu: Understanding hydrated soft solids through feature networks, bioRxiv. doi:10.64898/2025.12.10.693552, 2025. [2] Holthusen H, Kuhl E., A complement to neural networks for anisotropic inelasticity at finite strains, Comp Meth Appl Mech Eng, 450, 118612, 2026
