Viscoelastic-viscoplastic combined constitutive model for glassy amorphous polymers under loading/unloading/no-load states

Abstract

Purpose This study aims to propose a novel viscoelastic–viscoplastic combined constitutive model for glassy amorphous polymers within the framework of thermodynamics at finite strain that is capable of capturing their rate-dependent inelastic mechanical behavior in wide ranges of deformation rate and amount. Design/methodology/approach The rheology model whose viscoelastic and viscoplastic elements are connected in series is set in accordance with the multi-mechanism theory. Then, the constitutive functions are formulated on the basis of the multiplicative decomposition of the deformation gradient implicated by the rheology model within the framework of thermodynamics. Dynamic mechanical analysis (DMA) and loading/unloading/no-load tests for polycarbonate (PC) are conducted to identify the material parameters and demonstrate the capability of the proposed model. Findings The performance was validated in comparison with the series of the test results with different rates and amounts of deformation before unloading together. It has been confirmed that the proposed model can accommodate various material behaviors empirically observed, such as rate-dependent elasticity, elastic hysteresis, strain softening, orientation hardening and strain recovery. Originality/value This paper presents a novel rheological constitutive model in which the viscoelastic element connected in series with the viscoplastic one exclusively represents the elastic behavior, and each material response is formulated according to the multiplicatively decomposed deformation gradients. In particular, the yield strength followed by the isotropic hardening reflects the relaxation characteristics in the viscoelastic constitutive functions so that the glass transition temperature could be variant within the wide range of deformation rate. Consequently, the model enables us to properly represent the loading process up to large deformation regime followed by unloading and no-load processes.

Fractional description for the rate‐dependent viscoelastic response of tough hydrogels

“…As a novel modeling approach, the fractional order derivative model has attracted great interest due to its simple form and more flexible description of various physical phenomena 29 including anomalous diffusion, 30 biomedical engineering, 10 and control system, 31 especially in the field of viscoelastic mechanics 32 where the mechanical property of described materials can be revealed by the index of fractional order 33 . Recently, the variable‐order fractional operator has been established, enables the fractional order to be functions of independent state variables, such as time 34 and temperature, 35 existing excellent applications in rheology, 36,37 mechanics 38,39 and chaotic systems 40 . However, a difficulty of the above method lies in how to appropriately define the suitable variable‐order function which is not only able to meet the requirement of fractional modeling but also the subsequent mathematical analysis.…”

Experimental investigation of yield and hysteresis behaviour of an epoxy resin under cyclic compression in the large deformation regime

“…The inconsistency between the observation of Colak et al [21] on the one hand and Nikoukalam and Sideri [20], on the other hand can be related to the influence of the applied cyclic deformation magnitude and number of loading cycles. Recent research regarding the modelling of the cyclic response of polymers can be found in several references [22][23][24][25][26][27][28][29]. A coupled hyperelastic-viscoplastic model in Shojaei and Volgers [23] and a parallel elastic-viscoplastic network model in Qi et al [27] shows capability for the investigation of a highly-crystalline and semi-crystalline polymers, respectively.…”