Decoupled two-scale viscoelastic analysis of FRP in consideration of dependence of resin properties on degree of cure

Risa Saito, Yuya Yamaguchi, Seishiro Matsubara, Shuji Moriguchi, Yasuko Mihara, Takaya Kobayashi, Kenjiro Terada

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13 Citations (Scopus)


In consideration of the dependence of resin properties on the degree of cure (DOC), a method of decoupled two-scale analysis of unidirectional fiber reinforced plastics (FRP) is proposed to simulate the curing process subjected to the temperature history that may cause residual stress and deformation at the macro-scale. Within the framework of computational homogenization, a series of numerical material tests (NMTs) are conducted on the periodic microstructure (unit cell), which is composed of fibers and resin, for various cure states to characterize the macroscopic material behavior and its dependency on DOC. The resin's material behavior at the micro-scale is assumed to be viscoelastic based on the generalized Maxwell model whose properties depend on DOC, and be accompanied with thermal expansion/contraction and cure shrinkage. On the assumption that the macroscopic mechanical behavior of FRP can be represented by the orthotropic version of the model employed for the resin, its DOC-dependent macroscopic viscoelastic properties as well as the macroscopic coefficient of thermal expansions (CTEs) and coefficient of cure shrinkages (CCSs) are identified from the relaxation curves obtained by the NMT results. In addition to this key ingredient, the noteworthy contribution in this study is the introduction of a new configuration of the rheology elements to formulate the macroscopic CTEs and CCSs in both the equilibrium and non-equilibrium parts of the generalized Maxwell model. After some verification analyses for these DOC-dependent material properties, we present a macroscopic analysis followed by a localization analysis for estimating the macro- and microscopic residual deformations and stresses of a laminate subject to curing to exemplify the successful decoupling for two-scale computational homogenization.

Original languageEnglish
Pages (from-to)199-215
Number of pages17
JournalInternational Journal of Solids and Structures
Publication statusPublished - 2020 May 1


  • Cure shrinkage
  • Finite element
  • FRP
  • Homogenization
  • Multiscale analysis
  • Viscoelastic


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