AutoMat -- Automatic Differentiation for Generalized Standard Materials on GPUs

Abstract

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.

28 pages, 15 figures, 7 tables; new layout, more detailed proof of Theorem 1

References in corpus (4)

• A numerical method for computing the overall response of nonlinear composites with complex microstructure
• Fourier-based schemes for computing the mechanical response of composites with accurate local fields
• Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients
• On the accuracy of spectral solvers for micromechanics based fatigue modeling

Cited by in corpus (2)

• Automated discovery of generalized standard material models with EUCLID
• Batched Second-Order Adjoint Sensitivity for Reduced Space Methods