DOI: 10.1002/pc.28207 ISSN: 0272-8397

A 3D viscoelastic–viscoplastic behavior of carbon nanotube‐reinforced polymers: Constitutive model and experimental characterization

Reza Yazdanparast, Roham Rafiee
  • Materials Chemistry
  • Polymers and Plastics
  • General Chemistry
  • Ceramics and Composites


Due to the widespread use of carbon nanotube (CNT)‐reinforced polymers in various industries, investigating the dynamic mechanical response of these materials under impact loading is of significant importance. A three‐dimensional viscoelastic (VE)–viscoplastic (VP) constitutive model for CNT/epoxy nanocomposites is developed. A proper rheological model is established using the generalized Maxwell model to represent the VE behavior and propose an exponential function to express the elasto‐VP response. Employing an empirical logarithmic relationship to estimate material properties at different strain rates, the VP behavior is modeled based on the overstress concept. The 3D numerical discretization of the proposed rate‐dependent material model is also carried out to develop a user‐defined material model (UMAT) for the commercial finite element (FE) software of Abaqus. The performed FE simulations based on the proposed rate‐dependent constitutive material can properly capture stress relaxation and hysteresis behaviors of the nanocomposites. Comparing the estimated tensile and shear stress–strain curves through developed material models with experimental measurements, an excellent agreement is observed.


Tensile/shear properties of CNT/epoxy are measured at three strain rates.

An empirical constitutive model is proposed for any arbitrary strain rates

Viscoplastic behavior is captured based on over‐stress concept

A 3D incremental form of a viscoelastic–viscoplastic material model is developed.

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