AutoMat -- Automatic Differentiation for Generalized Standard Materials on GPUs

TL;DR

AutoMat introduces a GPU-accelerated, automatic differentiation-based method for efficiently evaluating generalized standard materials, simplifying implementation and improving performance in computational mechanics applications.

Contribution

It presents a universal, automatic differentiation-based approach for material law evaluation that is efficiently implemented on GPUs, reducing complexity and enhancing performance.

Findings

AutoMat achieves GPU acceleration with minimal implementation effort.

The method improves runtime performance compared to traditional routines.

AutoMat enhances solution accuracy in homogenization and elasto-viscoplastic simulations.

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.