Codes

Set of COMSOL models that enable simulating a wide range of hydrogen transport and embrittlement phenomena straightforwardly.

Papers: A. Díaz, J.M. Alegre, I.I. Cuesta, E. Martínez-Pañeda. A COMSOL framework for predicting hydrogen embrittlement, Part II: phase field fracture. Engineering Fracture Mechanics 319, 111008 (2025)

A. Díaz, J.M. Alegre, I.I. Cuesta, E. Martínez-Pañeda. A COMSOL framework for predicting hydrogen embrittlement, Part I: coupled hydrogen transport. Engineering Fracture Mechanics 319, 111007 (2025)

Combination of user subroutines to enable thermo-metallurgical welding simulations in ABAQUS, enabling the prediction of phase fractions, residual stresses and hardness maps.

Paper: J. Wijnen, J. Parker, M. Gagliano, E. Martínez-Pañeda. A computational framework to predict weld integrity and microstructural heterogeneity: application to hydrogen transmission. Materials and Design 249, 113533 (2025)

MATLAB App to rigorously simulate hydrogen desorption with the main hydrogen transport and trapping models (Oriani, McNabb-Foster) and arbitrary trapping characteristics. See https://tdssimulator.web.ox.ac.uk/

Paper: E. García-Macías, Z.D. Harris, E. Martínez-Pañeda. TDS Simulator: A MATLAB App to model temperature-programmed hydrogen desorption. International Journal of Hydrogen Energy 94, 510-524 (2024)

UMAT Abaqus subroutine to implement the phase field fracture model over pre-defined interfaces (e.g., grain boundaries or fibre-matrix interfaces) such that the phase field only evolves over those.

Paper: K. Au-Yeung, A. Quintanas-Corominas, E. Martínez-Pañeda, W. Tan. Hygroscopic phase field modelling of composite materials. Engineering with Computers 39, 3847–3864 (2023)

Software (wrapper) that allows Abaqus user material subroutines (UMATs) to be used as an External Material library in the software COMSOL Multiphysics.

Paper: S. Lucarini, E. Martínez-Pañeda. UMAT4COMSOL: An Abaqus user material (UMAT) subroutine wrapper for COMSOL. Advances in Engineering Software 190, 103610 (2024)

MATLAB code to simulate hydrogen embrittlement using phase field fracture and electrolyte modelling.

Paper: T. Hageman, E. Martínez-Pañeda. A phase field-based framework for electro-chemo-mechanical fracture: crack-contained electrolytes, chemical reactions and stabilisation. Computer Methods in Applied Mechanics and Engineering 415, 116235 (2023)

COMSOL implementation of a phase field model for prediting biocorrosion.

Paper: S. Kovacevic, W. Ali, E. Martínez-Pañeda, J. LLorca. Phase-field modeling of pitting and mechanically-assisted corrosion of Mg alloys for biomedical applications. Acta Biomaterialia 164, 641-658 (2023)

COMSOL implementation of a phase field-based model for predicting corrosion-induced cracking in concrete.

Paper: E. Korec, M. Jirasek, H.S. Wong, E. Martínez-Pañeda. A phase-field chemo-mechanical model for corrosion-induced cracking in reinforced concrete. Construction and Building Materials 393, 131964 (2023)

MATLAB code to simulate natural corrosion rates in the absence of external current sources.

Paper: T. Hageman, C. Andrade, E. Martínez-Pañeda. Corrosion rates under charge-conservation conditions. Electrochimica Acta 461, 142624 (2023)

COMSOL implementation of phase field corrosion accounting for the role of mechanics and electrolyte electrochemistry.

Paper: C. Cui, R. Ma, E. Martínez-Pañeda. Electro-chemo-mechanical phase field modeling of localized corrosion: theory and COMSOL implementation. Engineering with Computers 39, 3877–3894 (2023)

Abaqus UEL subroutine to simulate coupled deformation-electrical-phase field fracture behaviour in CNT-based composites.

Paper: L. Quinteros, E. García-Macías, E. Martínez-Pañeda. Electromechanical phase-field fracture modelling of piezoresistive CNT-based composites. Computer Methods in Applied Mechanics and Engineering 407, 115941 (2023)

Julia code for efficient fracture and fatigue predictions using the phase field method.

Paper: P.K. Kristensen, A. Golahmar, E. Martínez-Pañeda, C.F. Niordson. Accelerated high-cycle phase field fatigue predictions. European Journal of Mechanics A/Solids 100, 104991 (2023)

Finite element MATLAB code for electrochemical reactions, using lumped integration for efficiency and robustness, and particularised to the case of hydrogen uptake.

Paper: T. Hageman, E. Martínez-Pañeda. Stabilising effects of lumped integration schemes for the simulation of metal-electrolyte reactions. Journal of The Electrochemical Society 170, 021511 (2023)

COMSOL-MATLAB files to fit the output of an isothermal TDS experiment so as to obtain the diffusivity of hydrogen in metals.

Paper: A. Zafra, Z. Harris, E. Korec, E. Martínez-Pañeda. On the relative efficacy of electropermeation and isothermal desorption approaches for measuring hydrogen diffusivity. International Journal of Hydrogen Energy 48, 1218-1233 (2023)

ABAQUS UMAT user subroutine for implementing a generalised version of phase field fracture allowing for any fracture driving force split (including Drucker-Prager) and any choice of crack density function.

Paper: Y. Navidtehrani, C. Betegón, E. Martínez-Pañeda. A general framework for decomposing the phase field fracture driving force, particularised to a Drucker-Prager failure surface. Theoretical and Applied Fracture Mechanics 121, 103555 (2022)

COMSOL Physics builder to predict hydrogen uptake through an electro-chemo-mechanics framework that resolves the HER.

Paper: T. Hageman, E. Martínez-Pañeda. An electro-chemo-mechanical framework for predicting hydrogen uptake in metals due to aqueous electrolytes. Corrosion Science 208, 110681 (2022)

MATLAB App that enables assessing the validity of the Brazilian test and provides the material strength from test data.

Paper: Y. Navidtehrani, C. Betegón, R.W. Zimmerman, E. Martínez-Pañeda. Griffith-based analysis of crack initiation location in a Brazilian test. International Journal of Rock Mechanics and Mining Sciences 159, 105227 (2022)

COMSOL implementation of a coupled deformation-diffusion-fracture/fatigue model with application to cracking in Li-Ion battery electrode particles.

Paper: W. Ai, B. Wu, E. Martínez-Pañeda. A generalised phase field model for fatigue crack growth in elastic-plastic solids with an efficient monolithic solver. Journal of Power Sources 544, 231805 (2022)

ABAQUS UELMAT subroutine to implement the phase field fracture method in combination with any material model available in ABAQUS.

Papers: Z. Khalil, A.Y. Elghazouli, E. Martínez-Pañeda. A generalised phase field model for fatigue crack growth in elastic-plastic solids with an efficient monolithic solver. Computer Methods in Applied Mechanics and Engineering 388, 114286 (2022)

M. Simoes, C. Braithwaite, A. Makaya, E. Martínez-Pañeda. Modelling fatigue crack growth in Shape Memory Alloys. Fatigue & Fracture of Engineering Materials & Structures 45, 1243-1257 (2022)

ABAQUS user-element subroutine (UEL) to use the phase field method to predict corrosion, pitting corrosion, the pit-to-crack transition and stress corrosion cracking.

Paper: C. Cui, R. Ma, E. Martínez-Pañeda. A phase field formulation for dissolution-driven stress corrosion cracking. Journal of the Mechanics and Physics of Solids 147: 104254 (2021)

ABAQUS UMAT user subroutine for implementing phase field fracture without the need for user elements by taking advantage of the heat transfer equation.

Papers: Y. Navidtehrani, C. Betegón, E. Martínez-Pañeda. A unified Abaqus implementation of the phase field fracture method using only a user material subroutine. Materials 14(8): 1913 (2021).

Y. Navidtehrani, C. Betegón, E. Martínez-Pañeda. A simple and robust Abaqus implementation of the phase field fracture method. Applications in Engineering Science 6: 100050 (2021).

ABAQUS user material (mechanical UMAT and thermal UMATHT) subroutines for implementing hydrogen diffusion coupled with mechanical deformation, suitable for multiple traps.

Paper: R. Fernández-Sousa, C. Betegón, E. Martínez-Pañeda. Analysis of the influence of microstructural traps on hydrogen assisted fatigue. Acta Materialia 199: 253-263 (2020)

ABAQUS user-element subroutine (UEL) for Gurtin (2004) distortion gradient plasticity formulation, incorporating the role of the plastic spin as well as dissipative and energetic higher order contributions.

Paper: S. Fuentes-Alonso, E. Martínez-Pañeda. Fracture in distortion gradient plasticity. International Journal of Engineering Science 156: 103369 (2020)

ABAQUS user-material subroutine (UMAT) with a plane strain/3D implementation of von Mises plasticity with isotropic power law hardening. Includes documentation.

Paper: E. Martínez-Pañeda, S. Fuentes-Alonso, C. Betegón. Gradient-enhanced statistical analysis of cleavage fracture. European Journal of Mechanics – A/Solids 77: 103785 (2019)

ABAQUS user-element subroutine (UEL) with phase field fatigue (and fracture). Includes an input file for using Quasi-Newton to run in a robust monolithic manner and a document with detailed instructions.

Paper: P.K. Kristensen, E. Martínez-Pañeda. Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme. Theoretical and Applied Fracture Mechanics 107: 102446 (2020)

FEniCS Python script with a staggered implementation of the phase field fracture method, suitable for 2D and 3D case studies. Includes a document with detailed instructions.

Paper: Hirshikesh, S. Natarajan, R. K. Annabattula, E. Martínez-Pañeda. Phase field modelling of crack propagation in functionally graded materials. Composites Part B: Engineering 169: 239-248 (2019)

ABAQUS user-element subroutine (UEL) for Gudmundson (2004) higher order strain gradient plasticity formulation, including both energetic and dissipative length scales.

Paper: E. Martínez-Pañeda, V.S. Deshpande, C.F. Niordson, N.A. Fleck. The role of plastic strain gradients in the crack growth resistance of metals. Journal of the Mechanics and Physics of Solids, 126: 136-150 (2019)

ABAQUS user-element subroutine (UEL) for the coupled deformation – hydrogen transport – phase field fracture scheme presented in the associated paper.

Paper: E. Martínez-Pañeda, A. Golahmar, C.F. Niordson. A phase field formulation for hydrogen assisted cracking. Computer Methods in Applied Mechanics and Engineering, 342: 742-761 (2018)

ABAQUS user-element subroutine (UEL) with a robust phase field formulation for fracture. Several integration schemes are available, as detailed in the accompanying documentation.

Paper: E. Martínez-Pañeda, A. Golahmar, C.F. Niordson. A phase field formulation for hydrogen assisted cracking. Computer Methods in Applied Mechanics and Engineering, 342: 742-761 (2018)

ABAQUS input files with a control algorithm to overcome convergence problems in cohesive zone modelling of crack propagation. The code is largely inspired by the work by Segurado and Llorca (2004) on particle fracture in composites.

Paper: E. Martínez-Pañeda, S. del Busto, C. Betegón. Non-local plasticity effects on notch fracture mechanics. Theoretical and Applied Fracture Mechanics, 92: 276-287 (2017)

Matlab script to predict the variation with the applied potential of the cracking threshold and the stage II crack growth rate. The model builds on Gerberich’s decohesion dislocation-based model, strain gradient plasticity and advanced electrochemistry. See details in the associated paper.

Paper: E. Martínez-Pañeda, C.F. Niordson, R.P. Gangloff. Strain gradient plasticity-based modeling of hydrogen environment assisted cracking. Acta Materialia, 105: 9-16 (2017)

A toolbox to connect Abaqus and Matlab, enabling the usage of the statistical analysis, image processing, integrated graph-plotting and mathematical optimization capabilities of Matlab to post-process the outcome of advanced finite element calculations. See www.abaqus2matlab.com

Paper: G. Papazafeiropoulos, M. Muñiz-Calvente, E. Martínez-Pañeda. Abaqus2Matlab: a suitable tool for finite element post-processing. Advances in Engineering Software, 105: 9-16 (2017)

ABAQUS USDFLD Subroutine for the implementation of a continuous variation of the material elastic properties between integration points.

Paper: E. Martínez-Pañeda. On the finite element implementation of functionally graded materials. Materials, 12(2): 287 (2019)

Non-linear eXtendend Finite Element code developed in MATLAB including the following material models: linear elasticity, von Mises plasticity and conventional mechanism-based strain gradient (CMSG) plasticity. Particularly appealing to capture the singularity intrinsic to MSG plasticity.

Paper: E. Martínez-Pañeda, S. Natarajan, S. Bordas. Gradient plasticity crack tip characterization by means of the extended finite element method. Computational Mechanics, 59: 831-842 (2017)

Finite Element implementation of Gurtin (2004) Distortion Gradient Plasticity (DGP) theory by following and extending the Minimum Principles established by Fleck and Willis (2009). Code developed entirely in Fortran.

Paper: E. Martínez-Pañeda, C.F. Niordson, L. Bardella. A finite element framework for distortion gradient plasticity with applications to bending of thin foils. International Journal of Solids and Structures, 96: 288-299 (2016)

ABAQUS user-element subroutine (UEL) with a cohesive zone formulation. Includes the dependence of the cohesive strength on the total hydrogen concentration and the effect of cyclic loading.

Paper: S. del Busto, C. Betegón, E. Martínez-Pañeda. A cohesive zone framework for environmentally assisted fatigue. Engineering Fracture Mechanics, 185: 210-226 (2017)

ABAQUS User Material (UMAT) subroutine with the constitutive formulation of the conventional mechanism-based strain gradient (CMSG) plasticity theory.

Paper: E. Martínez-Pañeda and C. Betegón. Modeling damage and fracture within strain-gradient plasticity. International Journal of Solids and Structures, 59: 208-215 (2015)