1560 Research Article Received: 16 January 2013 Revised: 15 June 2013 Accepted article published: 23 July 2013 Published online in Wiley Online Library: 18 September 2013 (wileyonlinelibrary.com) DOI 10.1002/pi.4591 Cooperative viscoplasticity theory based on the overstress approach for modeling large deformation behavior of amorphous polymers Ozgen U C ¸ olak, a Sa¨ ıd Ahzi b,c* and Yves Remond b Abstract A micromechanically based formulation of the cooperative model is incorporated into the viscoplasticity theory based on overstress (VBO) model. The plastic shear strain rate given by the cooperative model is used as a flow function which is responsible for rate and temperature dependence in the VBO model. In this way, thermomechanical analysis can be performed under different loading rates and temperatures of amorphous polymers. Introducing strain softening, the temperature- and strain-rate-dependent elasticity moduli are two other modifications of the VBO formulation. The validity of the newly proposed cooperative VBO model is demonstrated by modeling the uniaxial compression behavior of poly(methyl methacrylate) under different temperatures and strain rates. c  2013 Society of Chemical Industry Keywords: viscoplasticity; amorphous polymers; large deformation INTRODUCTION Polymeric materials undergo a large variety of mechanical loading conditions wherein the influences of temperature and strain rate are of prime importance. Therefore, the advanced applications of polymers require the development of physically based models with a detailed quantitative knowledge of the effects of temperature and strain rate on the mechanical response of the material. The kinetics of the macromolecular chains constitute the basic deformation mechanism of polymers. Among the theories developed for the local deformation behavior response of amorphous polymers are the Eyring 1 and the Argon 2 models. Modeling of the macroscopic responses of the polymer under various deformation conditions such as temperature and strain rate has been extensively addressed by several authors. Among the pioneering work in this area is the elastic-viscoplastic approach for the deformation behavior of glassy polymers proposed by Boyce et al. 3 This approach was based on the introduction of an analogue model where the inelastic part of deformation was represented by two parallel resistances, intermolecular and network resistances. In the model, the flow behavior of the intermolecular part was modeled using Argon’s model and the network resistance was modeled using the three-chain or eight-chain network Arruda and Boyce 4 theory. 4 – 6 Richeton et al. 7,8 have shown that the Eyring and Argon models do not correctly account for the strain rate and temperature effects over a large range of loading rate and temperature conditions. For a better account of strain rate and temperature effects, Richeton et al. 9 – 11 developed the cooperative model for amorphous polymers and incorporated it into the Boyce approach. 3,12 In this new approach, the mechanical response of amorphous polymers over a wide range of temperatures and strain rates is described, including the rubbery region and impact loading rates. To macroscopically model the behavior of polymers, a different approach based on state variable theory was also developed and used for the simulation of the deformation response of amorphous and semicrystalline polymers. This theory is known as the viscoplasticity theory based on overstress (VBO) model. 13 – 19 Note that the VBO model is a macroscopic approach based on the unified state variable theories. One of the advantages of this approach is that the strain rate dependence, creep, relaxation, recovery and cyclic behavior of polymeric materials can be correctly and easily simulated as shown in the work of D ¨ us ¸¨ unceli and C ¸ olak. 17 In this paper, we propose to develop a micromechanically based VBO approach where the cooperative model of Richeton et al. 9 is coupled with the VBO theory. The proposed formulation leads to the development of a new approach for cooperative viscoplasticity theory based on overstress for the deformation behavior of amorphous polymers. The plastic shear strain rate given by the cooperative model is used as a flow function such that thermomechanical analysis can be performed. The uniaxial compression behavior of poly(methyl methacrylate) (PMMA) is simulated and predicted results are compared with experimental results from the literature. ∗ Correspondence to: Sa¨ ıd Ahzi, University of Strasbourg, ICube /CNRS, 2 Rue Boussingault, 67000, Strasbourg, France. E-mail: ahzi@unistra.fr a Yı ldı z Technical University, Department of Mechanical Engineering, Istanbul, Turkey b University of Strasbourg, ICube / CNRS, 2 Rue Boussingault, 67000 Strasbourg, France c Georgia Institute of Technology, School of Materials Science and Engineering, Atlanta, GA 30332, USA Polym Int 2013; 62: 1560–1565 www.soci.org c  2013 Society of Chemical Industry