Relaxation in Polymer Networks under Uniaxial Extension and Biaxial Compression

TL;DR

This paper develops a unified theoretical framework to predict the time and temperature-dependent mechanical response of polymer networks under uniaxial and biaxial deformations, validated by experiments on PMMA and PVAc.

Contribution

It introduces a consistent model based on van der Waals network theory that describes both deformation modes using the same formalism and relaxation spectrum.

Findings

The model accurately predicts relaxation behavior across deformation modes.

Temperature dependence follows the WLF equation.

Experimental validation confirms the model's applicability to different polymers.

Abstract

Predicting the time and temperature dependent behavior of polymer networks under complex loading is essential for the design of advanced elastomeric materials. Many practical applications involve combinations of deformation modes, such as uniaxial extension and biaxial compression, yet a unified description of their mechanical response remains challenging. In this study, we apply a consistent theoretical framework to describe both uniaxial and biaxial deformation modes, using the same constitutive formalism based on van der Waals network theory. The time dependence of the material response in both cases is governed by a substance specific relaxation spectrum, introduced through irreversible thermodynamics as a linear coupling to the quasi static reference state of the permanent network. The temperature dependence of the relaxation times is well described by the Williams Landel Ferry (WLF) equation in the high temperature or low strain rate regime, demonstrating that the same physical mechanisms underlie time dependent behavior across different loading geometries. Experimental results are presented for cross linked poly(methyl methacrylate) (PMMA) and polyvinyl acetate (PVAc), validating the theoretical model across both materials and deformation modes.