Finite elasticity and evolving discontinuities in soft tissues using peridynamic states

Abstract A correspondence model for use with peridynamic states is presented, tailored to the description of finite elasticity in soft tissues within a plane-strain setting. A deviatoric–volumetric energy split leads to a stable one-field correspondence formulation, based on spherical and bond-associated non-local deformation measures, which is free from zero-energy modes and avoids artificial stiffening near the incompressible limit. The framework naturally accommodates both invariant-based polynomial and principal-stretch forms of strain-energy functions, and, in particular, the Ogden model, which is widely used in the mechanical characterization of soft biological tissues. The model is applied to human brain tissue mechanics, demonstrating its ability to capture key macroscopic elastic features including strain stiffening induced by the alignment of fibre-like networks and the tension–compression asymmetry arising from the distinct microstructural characteristics of grey and white matter. The proposed model is validated against semi-analytical and numerical hyperelastic benchmark solutions representative of the principal brain tissues. An illustrative example involving cortical indentation, representing a simplified surgical instrument interaction, is also presented. Finally, the proposed framework naturally captures the evolution of material discontinuities, enabling the simulation of complex deformation and failure processes in soft biological tissues.