---
title: Physics-Informed Electrochemical Corrosion Model
url: https://www.emergentmind.com/topics/physics-informed-electrochemical-corrosion-model
type: topic
---

# Physics-Informed Electrochemical Corrosion Model

Physics-informed electrochemical corrosion models are computational formulations in which corrosion is determined from electrochemical kinetics, mass and charge transport, interfacial thermodynamics, and, in more general settings, mechanics, microstructure, passivation, hydrogen uptake, or physics-constrained operator learning. In recent arXiv work, this designation covers models that treat the metal potential as an unknown under charge-conservation conditions, diffuse-interface phase-field formulations for pitting and stress corrosion cracking, electro-chemo-mechanical theories for dissolution-driven cracking, and neural surrogates that embed the residuals of governing PDEs into the training objective [2305.12204; 2408.14905; 2011.12068; 2603.09693].

## 1. Foundational concept and scope

A central distinction in this literature is between laboratory conditions with imposed potential or current and corrosion in the absence of external current sources. One representative framework states that the metal potential $E_m$ is a free variable determined at each timestep by enforcing charge balance, so that anodic electron production and cathodic electron consumption balance over the full metal-electrolyte interface. In that setting, the total current from all reactions must sum to zero,
$$
I_\mathrm{c} + I_\mathrm{o} + I_\mathrm{h}
= \int_\Gamma [i_\mathrm{c} + i_\mathrm{o} + i_\mathrm{h}]\, d\Gamma = 0,
$$
and corrosion rates become outputs of the model rather than prescribed inputs [2305.12204].

The electrochemical core is typically expressed through Butler-Volmer-type kinetics. A general formulation used for cathodic corrosion in alkaline media writes
$$
J = J_0 \left[\exp\left(\frac{E-E_0}{b_a}\right) - \exp\left(-\frac{E-E_0}{b_c}\right)\right],
$$
with separate parameters for metal dissolution and the hydrogen evolution reaction. In that model, the corrosion potential $E_{\rm corr}$ follows from the steady-state condition $J_{\rm M} + J'_{\rm H} \approx 0$, after which the corrosion current density $J_{\rm corr}$ and corrosion rate $C_R$ are computed. The same framework explicitly accounts for exchange current density $J_0$, redox potential $E_0$, Gibbs free energy of hydrogen adsorption $\Delta G_{\rm H}$, electrolyte concentration $C$, system pressure $P$, and temperature $T$ [2508.12431].

In phase-field variants, the model is recast as a diffuse-interface problem. The phase-field variable $\phi(\mathbf{x},t)$ distinguishes metal from electrolyte, the interface evolves without explicit tracking, and electrochemistry enters through the interfacial mobility or through free-energy derivatives. This places electrochemical corrosion in the broader class of moving-boundary problems that can be solved on fixed meshes while retaining electrochemical driving forces and transport constraints [2408.14905; 1804.08517].

## 2. Governing transport, reaction, and electrostatic laws

The electrolyte subproblem is commonly built from Nernst-Planck transport. A representative charge-conserving formulation writes, for each ionic species $\pi$,
$$
\dot{C}_\pi + \nabla\cdot\left(-D_\pi \nabla C_\pi\right)
+ \frac{z_\pi F}{RT} \nabla\cdot\left(-D_\pi C_\pi \nabla\varphi\right) + R_\pi = 0,
$$
subject to electroneutrality,
$$
\sum_\pi z_\pi C_\pi = 0.
$$
This enables corrosion rates, pit acidification, and the coupling between corrosion and hydrogen or oxygen evolution reactions to be predicted under realistic charge-conservation conditions [2305.12204].

Reactive-transport models for localized corrosion use the same structure, augmented by homogeneous chemistry. In the multi-species model for artificial pit experiments, species concentrations evolve according to
$$
\frac{\partial C_i}{\partial t} = -\nabla \cdot \mathbf{J}_i + R_i,
$$
with flux
$$
\mathbf{J}_i = - D_i \nabla C_i - \frac{z_i F}{R^* T} D_i C_i \nabla \psi,
$$
and homogeneous reactions are enforced through local equilibrium assumptions for water dissociation, metal ion hydrolysis, and chloride complexation. That model was used to study “Stable pitting under a salt film” and “Film-free dissolution that transitions to repassivation,” and it identified a pit stability product $X_{ps} = i_L \cdot d$, surface metal cation concentrations at repassivation of $60$–$75\%$ of saturation, and a critical pH at repassivation of approximately $2.2$ [2008.04280].

A related treatment of local chemistry is the stiff solution dynamics model, which computes the space-time dynamics of metal ions, hydroxy complexes, $\mathrm{H}^+$, and $\mathrm{OH}^-$ near a corroding metal by combining diffusion with rapid hydrolysis and water self-hydrolysis. Its key simplification is to solve diffusion equations for atom balances and then reconstruct local speciation from equilibrium constraints. Passivation onset is identified when the concentration product $[\mathrm{M}^{2+}][\mathrm{OH}^-]^2$ reaches the solubility product of the relevant hydroxide [1304.7903].

Electrostatics can be formulated either through electroneutrality or through a solution-potential equation. Outside the electric double layer, one phase-field model solves
$$
\nabla \cdot (\lambda \nabla \psi_l) = 0,
$$
and imposes a time-dependent boundary value for the solution potential at the electrode-electrolyte interface. This replacement of explicit EDL resolution by an equivalent resistor-capacitor boundary condition is one of the characteristic physics-informed devices in recent mesoscale corrosion models [2408.14905].

## 3. Phase-field formulations of evolving corrosion fronts

Phase-field corrosion models express interfacial motion through a free-energy functional and evolution equations for diffuse order parameters. In a microstructure-sensitive electro-chemo-mechanical formulation, the total free energy is
$$
\mathscr{F} = \int_\Omega \left[
f^{\text{chem}}(\vec{c},\phi) +
f^{\text{grad}}(\nabla\phi) +
f^{\text{elec}}(\vec{c},\psi_l) +
f^{\text{mech}}(\nabla \mathbf{u},\phi)
\right] d\Omega,
$$
and the interface evolves by an Allen-Cahn equation,
$$
\frac{\partial \phi}{\partial t}
= -L \frac{\delta \mathscr{F}}{\delta \phi}.
$$
This class of models is designed to simulate pitting and stress corrosion in polycrystalline materials and to account explicitly for dependencies of mechanical properties and corrosion potential on crystallographic orientation [2403.20301].

A nonlinear phase-field model of corrosion with charging kinetics of the electric double layer uses the same diffuse-interface variable $\phi$, couples it to ionic concentrations and solution potential, and makes the interfacial mobility proportional to the Butler-Volmer current density:
$$
L = L_0 \left[
\exp\left(\frac{\alpha z_1 F \eta}{RT}\right) -
\exp\left(-\frac{(1-\alpha) z_1 F \eta}{RT}\right)
\right].
$$
The model was validated against the classic benchmark pencil electrode test and was reported to reproduce experimental measurements of both pit kinetics and transient current density response [2408.14905].

Earlier phase-field work on galvanic corrosion established the diffuse-interface formulation on fixed meshes and showed, by asymptotic analysis, the sharp-interface limit of the phase-field model. In that formulation, the phase field is coupled to the electrolyte potential through
$$
\nabla \cdot (\sigma(\phi)\nabla \eta) = 0,
$$
and surface recession emerges naturally from the phase-field evolution rather than explicit boundary tracking. Benchmark problems included a magnesium alloy-mild steel couple in 5\% NaCl solution and crevice corrosion for nickel in 1N sulfuric acid, with good agreement against available experimental data and ALE or finite-volume results [1804.08517].

For dissolution-driven stress corrosion cracking, the phase-field formulation also accommodates the transition from activation-controlled corrosion to diffusion-controlled corrosion. In that setting, increasing the interface kinetics coefficient $L$ moves the response from linear pit-depth growth in time to the $\sqrt{t}$ kinetics characteristic of diffusion control, while the same framework captures pitting, stress corrosion cracking, and pit-to-crack transition in 2D and 3D geometries [2011.12068].

## 4. Electro-chemo-mechanical coupling, passivation, and microstructure sensitivity

Mechanics enters modern corrosion models through stress equilibrium, elastic-plastic constitutive laws, and mechanochemical acceleration factors. In dissolution-driven stress corrosion cracking, the local corrosion current density is amplified by plastic strain and hydrostatic stress according to
$$
i_a(t) = \left( \frac{\varepsilon^p}{\varepsilon_y} + 1 \right)
\exp\left(\frac{\sigma_h V_m}{RT}\right) i(t_i),
$$
and passive-film rupture is tied to a critical accumulated plastic strain. The interface kinetics coefficient $L$ is then modulated by both mechanochemical acceleration and film rupture-dissolution-repassivation kinetics [2011.12068].

The multi-phase-field generalization extends this picture to simultaneous anodic dissolution and hydrogen embrittlement. It introduces displacement $\mathbf{u}$, corrosion phase field $\phi_d$, metal ion concentration $c_\mathrm{M}$, fracture phase field $\phi_f$, and hydrogen concentration $c_\mathrm{H}$ as primary fields, with governing equations for mechanical equilibrium, dissolution, metal ion transport, fracture, and hydrogen diffusion. In that framework, the interplay between anodic dissolution- and hydrogen-driven failure mechanisms, including their transition, synergistic action, and individual occurrence, emerges from the coupled equations rather than from ad hoc switching rules [2205.12096].

Hydrogen ingress models resolve the electrolyte, the hydrogen and corrosion reactions, surface adsorption, absorption, diffusion, trapping, and mechanical deformation in a single electro-chemo-mechanical framework. The hydrogen absorption flux is written as
$$
\overline{J} = \nu_A - \nu_A' = k_A (N_L - C_L) \theta_{ads} - k_A' C_L (1-\theta_{ads}),
$$
and the lattice hydrogen balance includes a stress-assisted diffusion term proportional to $\nabla \sigma_H$. This allows hydrogen uptake to be mapped as a function of applied potential, specimen geometry, and fluid velocity, and shows that simplified fixed-concentration or fixed-flux boundary conditions can substantially under- or overestimate actual hydrogen uptake [2209.08635].

Microstructure-sensitive corrosion models go further by making both the elastic stiffness tensor and the local equilibrium corrosion potential orientation-dependent. In the polycrystalline phase-field model, the stiffness tensor is rotated with the Euler angles of each grain, and the local corrosion potential is given by
$$
E_{eq}^\theta = E_{eq} + \Delta E^\theta.
$$
The model also uses an orientation-dependent Butler-Volmer law and a mobility that depends on overpotential, plastic strain, and hydrostatic stress. Simulations with various grain morphology distributions showed more extensive defects, faster defect kinetics, and irregular pit and crack shapes relative to a homogeneous material scenario; the homogeneous model consistently underestimated defect sizes, growth rates, and material loss [2403.20301].

A separate SCC framework for steel structures uses a single phase-field parameter to aggregate damage due to mechanical loading and electro-chemical corrosion. It modifies the Allen-Cahn equation to include elastic-damage strain energy, interfacial reaction energy, and energy resulting from changes in corrosion ion concentration, and introduces interfacial kinetic coefficients that link corrosion current effects to mechanical degradation. By tuning these coefficients, the model recovers pure mechanical fracture, pure corrosion, or coupled SCC [2307.16739].

## 5. Calibration, validation, and materials-specific implementations

Physics-informed electrochemical corrosion models are frequently calibrated against polarization curves, pit-growth data, current transients, or local chemistry measurements. In the multi-species reactive-transport model for stainless steel, data of current density and electrical potential obtained from rapid polarization scans of pits with different depths were used to calibrate the elapsed time and the electrode kinetics of each stage. The model reproduced resistance, concentration, and pH profiles and linked repassivation to dilution of the pit chemistry and renewed local cathodic reaction [2008.04280].

First-principles and transition-state theory have also been embedded directly into corrosion models. In the multiscale treatment of ZrO$_2$-coated aluminum alloys, DFT and transition state theory supply rate constants for bulk and interfacial reactions, while a continuum transport-kinetics FEM model evolves species concentrations, potential, and the moving pit boundary. The model quantitatively links corrosion rate and pit stability to environmental parameters and applied potential, and attributes the enhanced corrosion performance of Zr-based conversion coatings to zirconium involvement in interfacial kinetics [2202.12990].

For compositionally complex alloys, the physics-informed element is sometimes shifted from PDE structure to physically motivated screening metrics. A machine-learning framework for corrosion-resistant high-entropy alloys used three metrics—single-phase formability, surface energy, and Pilling-Bedworth ratios—and combined random forest classifiers with machine-learned interatomic potentials trained on first-principles data. The framework was demonstrated on AlCrFeCoNi high-entropy alloys, and the predicted single-phase formability and corrosion-resistant compositions agreed well with experiments; the authors also note that the method does not explicitly model chloride effects [2307.06384].

In alkaline water electrolyzers, a dedicated physics-informed electrochemical corrosion model evaluates cathodic corrosion through exchange current density, redox potential, hydrogen adsorption energetics, concentration, pressure, and temperature. Potentiodynamic polarization and cyclic voltammetry in KOH concentrations from $0.25$ to $2.0$ M were used for validation, and the reported mean absolute percentage error was below $10\%$ for the main metrics. The findings from potentiodynamic polarization indicate that gold shows the highest durability, while copper and nickel are promising cost-effective alternatives [2508.12431].

## 6. Physics-informed machine learning and accelerated corrosion simulation

In this literature, “physics-informed” does not refer only to continuum constitutive structure; it also denotes neural architectures that enforce governing corrosion PDEs during training. PF-PINO is a physics-informed neural operator built on the Fourier Neural Operator and trained with a loss
$$
\mathcal{L} = w_\mathrm{d} \mathcal{L}_\mathrm{d}
+ \sum_{k=1}^{N_\text{eq}} w_{\mathrm{p},k} \mathcal{L}_{\mathrm{p},k},
$$
where the physics terms are PDE residuals for the Allen-Cahn and Cahn-Hilliard equations. For a one-dimensional pencil-electrode corrosion problem, PF-PINO reported a relative $L^2$ error of $0.53\%$ and a relative Hausdorff distance of $0.33$, compared with $1.58\%$ and $0.83$ for a conventional FNO [2603.09693].

Sharp-PINNs address the strong coupling of corrosion phase-field systems by alternately minimizing the residuals of the Allen-Cahn and Cahn-Hilliard equations instead of minimizing all PDE residuals simultaneously. The method combines staggered training, random Fourier feature embeddings, a modified multilayer perceptron backbone, and hard constraints in the output layer. In three-dimensional cases, it was reported to be $5$–$10$ times faster than traditional finite element methods while maintaining competitive accuracy [2502.11942].

FM-tfPINN extends physics-informed learning to tempered time-fractional coupled phase-field systems with memory-dependent transport and relaxation mechanisms. Its neural trial solution embeds tempered fractional memory through latent memory-source functions and a tempered fractional integral operator, while sum-of-exponentials history compression reduces storage to $\mathcal{O}(N_q)$. On tempered fractional corrosion phase-field benchmarks, it produced relative $L^2$ errors for the fields on the order of $10^{-3}$ in one-dimensional corrosion-front propagation, relative $L^2$ errors below $10^{-3}$ in two-dimensional semi-circular pitting corrosion, and inverse mobility relative errors of $2.6 \times 10^{-5}$ for phase-field mobility and $1.5 \times 10^{-2}$ for concentration mobility from sparse observations [2606.22191].

A plausible implication is that the contemporary meaning of a physics-informed electrochemical corrosion model now spans two closely connected layers. The first is the mechanistic layer, in which Butler-Volmer kinetics, Nernst-Planck transport, charge conservation, electric-double-layer charging, passivation, hydrogen uptake, and mechanics are imposed explicitly. The second is the solver or surrogate layer, in which neural operators, PINNs, or fractional-memory networks preserve those governing structures while reducing the cost of high-throughput parametric studies, long autoregressive rollouts, or inverse identification [2408.14905; 2305.12204; 2603.09693; 2502.11942].

Source: https://www.emergentmind.com/topics/physics-informed-electrochemical-corrosion-model