Constitutive Law

Constitutive laws mathematically describe the relationship between stress and strain in materials, aiming to predict material behavior under various loading conditions. Current research heavily emphasizes data-driven approaches, employing neural networks (including physics-informed and symmetry-enforcing architectures) and peridynamics to learn constitutive laws directly from experimental data, often bypassing the need for explicit analytical formulations. This focus on data-driven methods is driven by the need to model complex, heterogeneous, and nonlinear material responses, particularly in biological tissues and advanced materials, leading to improved accuracy and efficiency in simulations and design.