Abstract In this study, a computational framework is proposed for thermomechanical contact and debonding problems with proper thermal resistance at the interface. Using the Variational Multiscale (VMS) framework, we present a fully coupled thermomechanical formulation with an explicit expression of the pressure at the contact interface. The formulation considers the quasi-static balance of the momentum and the transient heat transfer problem in a fully coupled fashion. At the interface, two different contact constitutive models are utilized for tension and compression. For tensile problems, in the mechanical phase, a tensile debonding model is employed, whereas in the thermal phase, the displacement-dependent model is employed. For compressive problems, in the mechanical phase, a Coulomb frictional model is employed while in the thermal phase, a pressure-dependent model is embedded. Because of the naturally derived interface stability terms that possess area- and stress-weighting, the proposed VMS formulation accommodates contact/debonding and contact/frictional sliding at the interface due to both thermal and mechanical loading without losing numerical stability. The proposed method is applied to a class of numerical test problems with discontinuity at the interfaces, and good agreement with analytical and numerical data is achieved.

中文翻译：

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全耦合热机械界面接触和脱粘问题的变分多尺度方法

摘要 在这项研究中，提出了一种计算框架，用于在界面处具有适当热阻的热机械接触和脱粘问题。使用变分多尺度 (VMS) 框架，我们提出了一个完全耦合的热机械公式，其中明确表达了接触界面处的压力。该公式以完全耦合的方式考虑了动量的准静态平衡和瞬态传热问题。在界面处，两种不同的接触本构模型用于拉伸和压缩。对于拉伸问题，在机械阶段，采用拉伸脱粘模型，而在热阶段，采用位移相关模型。对于压缩问题，在机械阶段，使用库仑摩擦模型，而在热阶段，嵌入了一个与压力相关的模型。由于具有面积权重和应力权重的自然衍生的界面稳定性项，所提出的 VMS 公​​式可以在不损失数值稳定性的情况下适应由于热和机械载荷而导致的界面处的接触/脱粘和接触/摩擦滑动。将该方法应用于一类界面不连续的数值试验问题，与解析数据和数值数据吻合良好。