A VFM approach for identifying material parameters and data-driven constitutive models for biphasic hyperelasticity of soft biological tissues.

In a soft biological tissue with a fibrous network and interstitial fluid, osmotic pressure arises primarily from Donnan ion effects and macromolecular confinement, typically ranging from kPa to hundreds of kPa, and is mechanically balanced by stresses in the solid matrix. This study introduces a new data-driven framework based on the Virtual Fields Method (VFM) for identifying full-field material parameters and discovering constitutive models of osmotic pressure in biphasic hyperelasticity. In this framework, a two-step VFM strategy is proposed: (1) the virtual fields with zero-trace strains are applied to eliminate the osmotic pressure contribution and identify the parameters of the solid component, and (2) when the law for osmotic pressure is known a priori, the material parameters of the fluid component are further identified. When the law for osmotic pressure is unknown a priori, the osmotic pressure is identified as an independent field variable and the constitutive law for osmotic pressure is established using a machine learning method. The effectiveness of the proposed model is verified through examples including identifications with experimentally measured data.