In this work, an efficient thermo-mechanically coupled two-scale finite element (FE)-fast Fourier transform (FFT)-based simulation approach for elasto-viscoplastic polycrystalline materials is proposed. Assuming a separation of scales, the macroscopic and microscopic boundary value problems are solved individually and linked by a scale transition. While the macroscopic boundary value problems are solved by means of the finite element method, the microscopic boundary value problems are computed using an FFT-based simulation technique. In order to solve the two-scale boundary value problem, the deformation and temperature gradients as well as the temperature values are first applied from the macroscopic integration points to the corresponding microscopic unit cells. After local convergence, the macroscopic quantities such as the stress, the internal heat generation, and the heat flux are defined as averages over the corresponding micromechanical or microthermal fields, and the macroscopic balance equations can be solved. The thermo-mechanically coupled microscopic material model is derived in a thermodynamically consistent manner based on the Clausius–Duhem inequality and, in order to maintain the generality of the proposed model, the geometrically nonlinear case is considered. To increase the efficiency of the two-scale simulation, a CPU- and memory-efficient solution strategy based on a coarse microstructure discretization is employed. Different numerical examples, in which the macroscopic and microscopic material behavior of a polycrystal is predicted, are used to demonstrate the applicability of the proposed model.

中文翻译：

---

基于弹性-粘塑性多晶材料的高效热机械耦合和几何非线性双尺度 FE-FFT 建模


在这项工作中，提出了一种高效的基于热机械耦合的双尺度有限元 （FE） 快速傅里叶变换 （FFT） 的弹性-粘塑性多晶材料仿真方法。假设尺度分离，宏观和微观边界值问题将单独求解，并通过尺度过渡进行链接。宏观边界值问题是通过有限元方法解决的，而微观边界值问题是使用基于 FFT 的仿真技术计算的。为了解决双尺度边界值问题，首先将变形和温度梯度以及温度值从宏观积分点应用于相应的微观晶胞。局部收敛后，应力、内部热量产生和热通量等宏观物理量定义为相应微机械场或微热场的平均值，并且可以求解宏观平衡方程。热机械耦合微观材料模型是基于 Clausius-Duhem 不等式以热力学一致的方式推导的，为了保持所提模型的通用性，考虑了几何非线性情况。为了提高双尺度仿真的效率，采用了基于粗略微结构离散化的 CPU 和内存高效求解策略。使用不同的数值示例来证明所提模型的适用性，其中预测了多晶的宏观和微观材料行为。