Polynomial-based damage model with EAS approach to model isotropic continuum damage in hyperelastic materials

Abstract

The models used for damage evolution in hyperelastic regime typically depend on material parameters like dissipation and the damage threshold. The rupture of cross-linked chains is a fundamental aspect of damage in rubbery polymers. To address this, a new reduction factor has been introduced, which extends the existing damage evolution law by incorporating a polynomial order $n$. This formulation is designed to precisely represent the isotropic continuum damage that occurs in nearly incompressible hyperelastic materials. The incompressibility constraint is handled by using an enhanced assumed strain (EAS) approach by enhancing the Green Lagrangian strain. Hence the total strain at a point is additively decomposed into compatible and enhanced strains. The proposed model is validated through the analysis of four standard problems — uni and biaxial tension, plate with hole and double edge notch involving a nearly incompressible Neo-Hookean material model. This validation includes varying the polynomial order to assess its impact on the results. All problems are resolved using generalized displacement control technique which is essential for handling displacement loading and observing the force–displacement response beyond the peak load.