A consistent finite-strain thermomechanical quasi-nonlinear-viscoelastic viscoplastic constitutive model for thermoplastic polymers

Abstract

Thermomechanical models for thermoplastics address the highly nonlinear constitutive behaviour of semicrystalline polymers using a combination of viscoelastic and viscoplastic theories. This paper introduces a novel thermodynamically consistent quasi-non-linear thermoviscoelastic formulation in finite strain using Maxwell elements with strain-dependent moduli. The novelty encompasses the solution to the convolution integrals arising from quasi-non-linearity and the corresponding internal dissipation. This formulation is intended to produce large non-linearities in the elastic regime, including tension–compression asymmetry, which is apparent in semi-crystalline polymers subjected to thermomechanical cyclic loading. To model thermoviscoplasticity, a Drucker–Prager yield function and a Perzyna-type flow rule are considered. Additionally, reversible Mullins’-type damage as a function of the quasi-non-linear thermoviscoelastic model’s deformation energy to describe the unloading response is considered. The model is formulated in a thermodynamically consistent manner by considering appropriate strain and stress measures in an intermediate configuration. For validation, this model is applied to conventional thermoplastic semicrystalline polymers, polypropylene and thermoplastic polyurethane (TPU). The experimental campaign for calibration and validation consists of Dynamic Mechanical Analyses (DMA) and uniaxial monotonic and cyclic tests in tension and compression. To further elucidate the applicability of this model, validation is performed by comparing numerical results to experimental performance under torsion of 3D-printed TPU specimens at varying strain rates.