Recent Advances in the Virtual Fields Method for Evaluating and Identifying Tissue Biomechanical Properties and Constitutive Parameters

The derivation of material parameters for soft tissues has recently been transformed by advances in full-field measurement techniques providing high-resolution, volume-wide displacement data in soft tissues, either in vivo or in vitro during experimental tests. In this context, the virtual fields method (VFM), which is an inverse mechanics technique leveraging full-field deformation data and equilibrium principles, is flourishing. This review first provides the background on which the VFM is founded for the identification of constitutive parameters of soft tissue mechanics, focusing first on hyperelastic constitutive models. Then we review recent advances of the VFM in biomechanical contexts along the following trends: (1) formulation of a more accessible and modern VFM where virtual fields are automatically generated, (2) enhancement of robustness for the identification of regionally variable constitutive parameters, (3) extension to inelastic constitutive behavior, (4) novel in vivo applications, and (5) novel machine-learning integration. These recent advances pave the way to real-time clinical applications of the VFM for complex soft tissue modeling.