The frame-indifferent thermodynamically-consistent model of thermoviscoelasticity at large strain is formulated in the reference configuration by using the concept of the second-grade nonsimple materials. We focus on physically correct viscous stresses that are frame indifferent under time-dependent rotations. Also elastic stresses are frame indifferent under rotations and respect positivity of the determinant of the deformation gradient. The heat transfer is governed by the Fourier law in the actual deformed configuration, which leads to a nontrivial description when pulled back to the reference configuration. The existence of weak solutions in the quasistatic setting, that is inertial forces are ignored, is shown by time discretization.

中文翻译：

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大应变下 Kelvin-Voigt 流变学中的热粘弹性

通过使用二级非简单材料的概念，在参考配置中制定了大应变下热粘弹性的框架无关热力学一致模型。我们专注于物理上正确的粘性应力，这些应力在时间相关的旋转下与框架无关。此外，弹性应力在旋转下与框架无关，并尊重变形梯度的决定因素的正性。在实际变形配置中，热传递受傅立叶定律支配，当拉回参考配置时，这会导致不平凡的描述。准静态设置中弱解的存在，即忽略惯性力，通过时间离散化显示。