Hyperelastic modeling based on generalized Landau invariants and multi-stage calibration

Abstract

Hyperelastic modeling has long faced two challenges, that is, the non-uniqueness of fitted parameters and limited predictive capability. In this work, we propose a new modeling framework in conjunction with a multi-stage fitting method. In the model construction, we generalize Landau invariants by introducing the generalized strains and use them as the building blocks for the model family. The models are mathematically concise yet sufficiently general, encompassing the Ogden model and the hyperelasticity of Hill’s class as special cases. A new micro-to-macro transition is proposed using the generalized strain, and the generalized Landau invariants emerge naturally from the homogenization procedure, providing a clear micromechanical interpretation. This enables the construction of a suite of models with micromechanical foundation. A key feature is the emergence of a pseudo-universal relation derived from the generalized invariants, which forms the basis of the multi-stage fitting method. It enables the separated calibration of the invariant parameters and material modulus in the fitting. The proposed strategy demonstrates strong predictive performance in that it accurately predicts biaxial mechanical responses using parameters identified from a single pure shear test. This robustness is further confirmed through a three-dimensional benchmark involving non-homogeneous strain. In addition, the multi-stage method yields mathematically sound models that maintain convex energy contours, a property correlated with predictive reliability. Several models within the proposed framework also demonstrate competitive fitting and prediction accuracy compared to state-of-the-art models using the same number of parameters. This work establishes a new paradigm for constitutive modeling by unifying theoretical development with a robust calibration methodology. The proposed approach promotes the practical applicability of hyperelastic models and offers a promising foundation for modeling more complex material behaviors.