AutoMat: automatic differentiation for generalized standard materials on GPUs

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