Self-heating phenomenonrepresents thermal evolution in materials resulting from mechanical loading. It is presentlyinvestigated during fatigue tests at 20 kHz. The aim of this article is to compare the variation of temperature, in the range 20 to 80 ^∘C, of a material body due to self-heating computed from an innovative point of view: requiring a covariant formulation of the thermomechanical behavior, we propose a spacetime approach for heat conduction and heat equation based on spacetime thermodynamics. In this article, we prove the feasibility to use such a spacetime framework to solve thermal problems. Thus computational methods performed with FEniCS platform, using finite element method, lead to a numerical approach for investigating self-heating. The integral form of the spacetime problem with the adapted boundary conditions directly usable are provided for heat conduction problem. The identification process of the parameters obtained from the experimental data of fatigue tests is also particularly studied to obtain the best accuracy and reliability of the numerical simulations, presently applied to metallic material (C65 steel) and 1D beam (60 mm length). Moreover, by use of optimization techniques, some numerical values for these input parameters are obtained, especially the characteristic time (in the range 40 to 130 s) and the heat source related to thermomechanical phenomena (intrinsic dissipation in the range 0.3 to 12 ^∘C ⋅ s^− 1). They have been successfully used to obtain spacetime temperature distributions in comparison to experimental measurements.

自热现象代表材料因机械载荷而产生的热演化。目前正在 20 kHz 的疲劳测试中对其进行研究。本文的目的是比较温度在 20 到 80 ^∘范围内的变化C，从创新的角度计算由于自热而产生的物质体：需要热机械行为的协变公式，我们提出了一种基于时空热力学的热传导和热方程的时空方法。在本文中，我们证明了使用这种时空框架解决热问题的可行性。因此，在 FEniCS 平台上执行的计算方法，使用有限元方法，导致研究自热的数值方法。为热传导问题提供了具有可直接使用的自适应边界条件的时空问题的积分形式。还特别研究了从疲劳试验的实验数据中获得的参数的识别过程，以获得最佳的数值模拟精度和可靠性，目前应用于金属材料（C65 钢）和一维梁（60 毫米长）。此外，通过使用优化技术，获得了这些输入参数的一些数值，特别是特征时间（在 40 到 130 s 范围内）和与热机械现象相关的热源（在 0.3 到 12 范围内的固有耗散）^∘ C ⋅ s ^{− 1} )。与实验测量相比，它们已成功用于获得时空温度分布。