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

Seishiro Matsubara, Kenjiro Terada, Ryusei Maeda, Takaya Kobayashi, Masanobu Murata, Takuya Sumiyama, Kenji Furuichi, Chisato Nonomura

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1703-1735
Number of pages33
JournalEngineering Computations
Issue number5
Publication statusPublished - 2020 May 11


  • Glassy amorphous polymers
  • Multiplicative decomposition
  • Polycarbonate
  • Thermodynamics
  • Viscoelasto–viscoplasticity


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