A variational method for the simulation of hydrogen diffusion in metals

TL;DR

This paper introduces a fully variational computational method for simulating hydrogen diffusion in metals, efficiently handling nonlinear stress-diffusion coupling and inelastic mechanical behavior.

Contribution

It develops a novel variational approach that ensures symmetric tangent operators, improving computational efficiency in modeling hydrogen transport in metals.

Findings

The method accurately captures hydrogen diffusion behavior in metals.

It demonstrates superior computational efficiency over existing methods.

The approach effectively handles nonlinear and inelastic effects.

Abstract

We present a new method for the approximate solution of the strongly coupled, nonlinear stress-diffusion problem that appears when modeling hydrogen transport in metals. The most salient feature of the proposed approximation is that it is fully variational, meaning that all the discrete equations are obtained from the optimality conditions of an incremental potential, even for inelastic mechanical behavior. Like other variational methods, the proposed algorithm has remarkable properties, including the symmetry of the tangent operator, making its solution extremely efficient compared to other similar methods available in the literature.