DNLR Approach of the Behavior and Damage of Thermoplastic Polymers (HDPE)

Abstract

  This study proposes a novel formulation of the Distribution of Non-Linear Relaxation (DNLR) model to accurately capture the mechanical behavior and damage evolution of semi-crystalline thermoplastic polymers, specifically high-density polyethylene (HDPE), under large uniaxial deformations. Building upon the generalized Gibbs relationship for out-of-equilibrium systems, the proposed approach integrates an effective elastic modulus to account for damage-induced stiffness degradation. The model uses an empirical constitutive law to describe the evolution of the Young’s modulus as a function of axial strain, coupled with a statistical hyperelastic framework to define the equilibrium stress response. Numerical simulations reveal that the apparent elastic modulus initially decreases significantly due to micro-cavitation damage, followed by a continuous recovery phase driven by macromolecular chain reorientation until ultimate failure. The predicted stress-strain curves and modulus evolution demonstrate strong agreement with experimental tensile data across the entire deformation range. These findings confirm that the enhanced DNLR formulation effectively bridges dissipative thermodynamics with microscopic deformation mechanisms, providing a robust predictive tool for modeling damage progression and non-linear viscoelastic behavior in thermoplastic and biopolymer systems. The model’s capacity to quantitatively reproduce high-deformation experimental responses highlights its potential for advanced material characterization and structural integrity assessment.