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

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:216

Article

Yamanaka, Yosuke¹  Matsubara, Seishiro²  Saito, Risa¹  Moriguchi, Shuji³  Terada, Kenjiro³ 

[1] Tohoku Univ, Dept Civil & Environm Engn, Aoba Ku, Aza Aoba 6-6-06, Sendai, Miyagi 9808579, Japan

[2] Nagoya Univ, Dept Mech & Syst Engn, Chikusa Ku, Furo Cho, Nagoya, Aichi 4648603, Japan

[3] Tohoku Univ, Int Res Inst Disaster Sci, Aoba Ku, Aza Aoba 468-1, Sendai, Miyagi 9808572, Japan

关键词: Incremental variational formulation;    Variational constitutive update;    Degree of cure;    Viscoelasticity;    Heat conduction;    Cure shrinkage;    Thermodynamics;    Finite element method;   

DOI  :  10.1016/j.ijsolstr.2021.01.014

来源: Elsevier

【 摘 要 】

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 tasted 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. (C) 2021 Elsevier Ltd. All rights reserved.

【 授权许可】

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