Thermo-mechanical coupled incremental variational formulation for thermosetting resins subjected to curing process

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

Research output: Contribution to journalArticlepeer-review


This study presents an incremental variational formulation (IVF) for the thermo-mechanical problem of resin products subjected to curing, for which a dual dissipation potential (DDP) for the cure state is originally derived in conjunction with that for viscoelasticity. Following the thermodynamically consistent formulation for the time evolution equation of the degree of cure (DOC) of a thermosetting resin and the linear viscoelastic law, we derive these DDPs by way of Legendre-Fenchel transformations with respect to characteristic dissipations. The evolution of DOC is then casted into the flow rule in mathematical theory of plasticity with the introduction of the curing multiplier as a new internal state variable in an analogous fashion to Perzyna's viscoplastic regularization theory. Then, the pseudo stress is introduced as a new internal state variable to parameterize the derived flow rule of DOC. By virtue of this pseudo stress, we naturally define an incremental variational problem constrained by the parameterized flow rule in order to construct a semi-implicit scheme for the variational constitutive update. The finite element discretization is applied to the governing equations that satisfy the stationary conditions so that we could perform thermo-mechanical analyses of a thermosetting resin subjected to curing with the strong coupling procedure. The verification analysis is conducted to confirm the validity of the numerical result obtained by the proposed method in comparison with that of the conventional framework and followed by a demonstrative numerical example to simulate the stress development and relaxation in a virtual device subjected to different thermal histories.

Original languageEnglish
Pages (from-to)30-42
Number of pages13
JournalInternational Journal of Solids and Structures
Publication statusPublished - 2021 May 1
Externally publishedYes


  • Cure shrinkage
  • Degree of cure
  • Finite element method
  • Heat conduction
  • Incremental variational formulation
  • Thermodynamics
  • Variational constitutive update
  • Viscoelasticity

ASJC Scopus subject areas

  • Modelling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


Dive into the research topics of 'Thermo-mechanical coupled incremental variational formulation for thermosetting resins subjected to curing process'. Together they form a unique fingerprint.

Cite this