We propose a universal method for the evaluation of generalized standard materials that greatly simplifies the material law implementation process. By means of automatic differentiation and a numerical integration scheme, AutoMat reduces the implementation effort to two potential functions. By moving AutoMat to the GPU, we close the performance gap to conventional evaluation routines and demonstrate in detail that the expression level reverse mode of automatic differentiation as well as its extension to second order derivatives can be applied inside CUDA kernels. We underline the effectiveness and the applicability of AutoMat by integrating it into the FFT-based homogenization scheme of Moulinec and Suquet and discuss the benefits of using AutoMat with respect to runtime and solution accuracy for an elasto-viscoplastic example.

中文翻译：

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AutoMat -- GPU 上通用标准材料的自动微分

我们提出了一种通用的评估通用标准材料的方法，极大地简化了材料法的实施过程。通过自动微分和数值积分方案，AutoMat 将实现工作减少到两个潜在函数。通过将 AutoMat 移至 GPU，我们缩小了与传统评估例程的性能差距，并详细证明了自动微分的表达水平反向模式及其对二阶导数的扩展可以应用于 CUDA 内核中。我们通过将 AutoMat 集成到 Moulinec 和 Suquet 的基于 FFT 的均质化方案中来强调 AutoMat 的有效性和适用性，并讨论使用 AutoMat 在运行时间和弹性粘塑性示例的求解精度方面的好处。