论文标题
热电弹性的非线性和线性化模型
Nonlinear and Linearized Models in Thermoviscoelasticity
论文作者
论文摘要
我们考虑了在开尔文 - 维格特流变学中有限型固定环境下的热弹性非线性模型，其中弹性和粘性应力张量均符合旋转下框架无关的原理。力平衡是通过诉诸非简单材料概念在参考配置中提出的，而传热方程在变形构型中受傅里叶法律的约束。弱解决方案是通过交替更新的变形和温度更新的交流时交流的交流后的弱解决方案获得的。我们的结果完善了Mielke＆Roub \'ıček[Arxiv：1903.11094]的最新作品，因为我们的近似不需要任何粘度项的正规化。之后，我们专注于身份和较小温度附近的变形案例，我们通过严格的线性化过程表明，弱的非线性系统解决方案在适当的意义上与线性热弹性弹性的系统溶液相聚。相同的属性适用于时间散落的近似值，我们提供相应的通勤结果。
We consider a quasistatic nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin-Voigt rheology where both the elastic and viscous stress tensors comply with the principle of frame indifference under rotations. The force balance is formulated in the reference configuration by resorting to the concept of nonsimple materials whereas the heat transfer equation is governed by the Fourier law in the deformed configurations. Weak solutions are obtained by means of a staggered in-time discretization where the deformation and the temperature are updated alternatingly. Our result refines a recent work by Mielke & Roub\'ıček [arXiv:1903.11094] since our approximation does not require any regularization of the viscosity term. Afterwards, we focus on the case of deformations near the identity and small temperatures, and we show by a rigorous linearization procedure that weak solutions of the nonlinear system converge in a suitable sense to solutions of a system in linearized thermoviscoelasticity. The same property holds for time-discrete approximations and we provide a corresponding commutativity result.
