Visco-hyperelastic Model for Soft Elastomers Based on Power-Law Micro–Macro Transition

This work introduces a visco-hyperelastic constitutive model for soft materials based on a nonaffine micro–macro transition, integrating a nonaffine hyperelastic strain energy function with a nonlinear viscoelastic formulation. Time-dependent behavior is addressed through a deformation-dependent relaxation kernel rooted in physical entanglement dynamics, incorporated via a finite-strain convolution integral. The model is validated against experimental data across a diverse range of soft matter, including vulcanized rubbers, hydrogels, silicone, block copolymer, and biological tissue. Furthermore, predictive analysis involving a smooth synthetic data confirms that uniaxial calibration is structurally insufficient to constrain the nonaffine parameter space, necessitating high-stretch equibiaxial or pure shear data for robust generalization; conversely, for real noisy data sets, a reduced-order affine formulation offers superior predictability. Combining micromechanical fidelity with an invariant-based structure amenable to Finite Element implementation, the proposed framework provides a versatile tool for analyzing the nonlinear mechanics and stability of soft matter.