A decoupling scheme for two-scale finite thermoviscoelasticity with thermal and cure-induced deformations

Risa Saito, Yosuke Yamanaka, Seishiro Matsubara, Tomonaga Okabe, Shuji Moriguchi, Kenjiro Terada

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1 Citation (Scopus)


This article proposes a decoupling scheme for two-scale analysis of fiber-reinforced plastics (FRP) exhibiting finite thermoviscoelasticity in consideration of the dependences of resin's mechanical and nonmechanical deformation characteristics on the degree of cure (DOC) and ambient temperature. To characterize the macroscopic material behavior, numerical material tests are carried out on a unit cell composed of a polymer resin matrix and carbon fibers. The generalized Maxwell model (GMM) is employed for resin' material behavior, while its orthotropic version is assumed for FRP. The evolution of DOC is reflected in the evaluation of the nonmechanical deformation by cure shrinkage in addition to thermal expansion/contraction. The key ingredient of this study is the novel strategy for identifying the macroscopic coefficients of these nonmechanical deformations, both of which must be separately defined in the equilibrium and nonequilibrium elements of the orthotropic GMM. In addition, a modification is originally made on the evolution equations of the nonequilibrium stresses in the GMM. The verification analyses are carried out to confirm the adequateness of the proposed identification methods and followed by numerical examples of two-scale analysis to demonstrate the capability of simulating the macro- and microscopic thermomechanical responses of FRP subjected to curing.

Original languageEnglish
Pages (from-to)1133-1166
Number of pages34
JournalInternational Journal for Numerical Methods in Engineering
Issue number4
Publication statusPublished - 2021 Feb 28


  • FRP
  • anisotropy
  • cure shrinkage
  • finite strain viscoelasticity
  • multiscale analysis
  • thermomechanical coupling

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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