Numerical simulation of the transient hydrogen trapping process using an analytical approximation of the McNabb and Foster equation. Part 2: Domain of validity

In a previous study [1], a resolution scheme called Generalized Oriani's Approximation (GOA) was proposed to solve a transient transport and trapping problem in the Abaqus Finite Element software. This proposition was motivated by the convergence of the Finite Element problem linked to the estimation of several functions during the computation (and especially the dudt one). In this study, the GOA is shown to be able to provide an accurate estimation of the trapped concentration in transient trapping processes as soon as the time increment is small enough for two configurations: hydrogen in metals and water in polymers. An estimation of the induced error is given. The GOA approach is illustrated on a simple configuration with various trapping parameters. Last, the ability of Abaqus to converge while modeling a transient trapping and transport problem is analyzed considering several dudt: it is shown especially that its estimation based on the GOA allows the solver to efficiently converge toward the solution. •The Generalized Oriani's Approximation is used to solve kinetic trapping problem.•It's implementation in Abaqus software is described using UMATHT subroutine.•GOA domain of validity is studied and the error induced by its use estimated.•An illustration is made based using a simple known function.•A focus is paid on the Abaqus needed function influence on global convergence.