Constitutive modeling of initially stressed solids from stress data using mechanics-informed neural networks

Predicting how initial stress alters the mechanical behavior of soft materials is essential for applications ranging from personalized surgical planning to soft robotics. In biomedical contexts, residual stresses and prestresses–such as those found in the cornea, skin, or arterial walls–significantly influence how tissues deform, heal, and respond to intervention. Accurate predictions, for example after LASIK surgery or vascular stenting, require constitutive models that account for initial stress. An additional challenge is that each tissue exhibits a unique mechanical response that should be characterized prior to intervention. Here, we introduce a mechanics-informed neural network (MINN) framework for constitutive modeling of initially stressed elastic solids from stress and deformation data. Our approach embeds the physical constraints associated with initially stressed elasticity–including initial stress compatibility and initial stress reference independence–into the network architecture. This enables standard strain-energy functions, such as the widely used Holzapfel–Gasser–Ogden model, to be extended to account for initial stress. As a proof-of-concept, we design an experiment to mimic the corneal deformation under varying intraocular pressure. Using non-invasive guided wave measurements, we identify constitutive parameters directly in the loaded configuration and validate the resulting model by predicting corneal deformations under altered loading conditions. These results demonstrate the feasibility of constitutive modeling directly from stress data and establish a framework for patient-specific biomechanical modeling and preoperative planning.