The aim of this work is to introduce a thermo-electromagnetic model for calculating the temperature and the power dissipated in cylindrical pieces whose geometry var\'ies with time and undergoes large deformations; the motion will be a known data. The work will be a first step towards building a complete thermoelectromagnetic-mechanical model suitable for simulating electrically assisted forming processes, which is the main motivation of the work. The electromagnetic model will be obtained from the time-harmonic eddy current problem with an inplane current; the source will be given in terms of currents or voltages defined at sorne parts of the boundary. Finite element methods based on a Lagrangian weak formulation will be used for the numerical solution. This approach will avoid the need to compute and remesh the thermo-electromagnetic domain along the time. The numerical tools will be implemented in FEniCS and validated by using a suitable test also solved in Eulerian coordinates.

翻译：本文旨在提出一种热电磁模型，用于计算几何形状随时间变化并经历大变形圆柱形工件内的温度及耗散功率，其中运动轨迹为已知数据。该工作是为构建适用于模拟电辅助成形过程的完整热-电磁-力学耦合模型奠定基础，这也是本研究的主要动机。电磁模型基于时谐涡流问题建立，考虑面内电流激励，激励源由边界特定区域的电流或电压定义。数值求解采用基于拉格朗日弱形式的有限元方法，该方法可避免随时间对热电磁域进行网格重构。数值工具基于FEniCS实现，并通过欧拉坐标系下的标准算例进行验证。