Physics-informed recovery of nonlinear residual stress fields in an inverse continuum framework

Residual stresses play a critical mechanical role in both industrial and biomechanical applications. In biological tissues, residual stresses arise from growth and remodeling processes under physiological or pathological conditions and have been extensively modeled within the framework of nonlinear elasticity. These modeling efforts have enabled direct computation of residual stress patterns based on phenomenological growth laws. However, experimental validation and feedback for these models remain limited due to the inherent challenges in measuring complex stress distributions. To address this limitation, we propose and develop an inverse approach for estimating nonlinear residual stresses using information from an externally loaded configuration. Specifically, the algorithm employs domain displacement fields and externally applied loads as input data, which can be experimentally obtained through biaxial testing and digital image correlation (DIC) techniques. This novel formulation and numerical scheme are rooted in a physics-informed continuum framework that enforces universal principles of mechanics. To evaluate the framework, a synthetically generated ground-truth solution serves as a reference, allowing assessment of the accuracy of residual stress field reconstruction across varying levels of noise in the input data. Performance metrics indicate a significant improvement in reconstruction accuracy when multiple load cases and combined datasets are used. This approach paves the way for the formulation of growth laws and residual patterns based on experimental data.