A data-driven approach to characterizing nonlinear elastic behavior of soft materials.

The Autoprogressive (AutoP) method is a data-driven inverse method that leverages finite element analysis (FEA) and machine learning (ML) techniques to build constitutive relationships from measured force and displacement data. Previous applications of AutoP in tissue-like media have focused on linear elastic mechanical behavior as the target object is infinitesimally compressed. In this study, we extended the application of AutoP in characterizing nonlinear elastic mechanical behavior as the target object undergoes finite compressive deformation. Guided by the prior of nonlinear media, we modified the training data generated by AutoP to speed its ability to learn to model deformations. AutoP training was validated using both synthetic and experimental data recorded from 3D objects. Force-displacement measurements were obtained using ultrasonic imaging from heterogeneous agar-gelatin phantoms. Measurement on samples of phantom components were analyzed to obtain independent measurements of material properties. Comparisons validated the material properties found from neural network constitutive models (NNCMs) trained using AutoP. Results were found to be robust to measurement errors and spatial variations in material properties.