In silico modeling of transcatheter heart valve oversizing and ellipticity, Part I: Establishing credibility of an advanced model Sam Boxwell, Dylan Armfield, Rachel M.E. Cahalane, William Hickey, Scott Cook, Patricia Kelly, Philip Cardiff, Laoise M. McNamara Computer Methods and Programs in Biomedicine, 2026 Abstract Background and Objectives Transcatheter aortic valve implantation (TAVI) is the most common modality of treatment for aortic stenosis. However, transcatheter heart valves (THVs) can be prone to early failure and an increase in thrombogenic events, yet the risk factors associated with these failure modes remain poorly understood. Computational modeling may be used to predict biomechanical indices associated with degeneration and thrombogenicity, however existing models do not fully account for complex stent and leaflet material behavior, and establishing model credibility according to ASME VV-40 is required. Methods In this study, we developed an advanced structural and hemodynamic in silico framework to predict the in vitro performance of a supra-annular, self-expanding THV across a range of clinically-relevant expansion and ellipticity indices. The THV was modelled by incorporating a novel 3-fibre material model for pericardium tissue leaflets and a super-elastic nitinol stent. Results Calculation verification was conducted and, on this basis, we provide recommendations on mesh density, element integration and target time increment. Following verification, we validated our models with radial force, structural camera and hemodynamic particle image velocimetry testing across multiple THV deployment configurations. In the ‘min-oversizing, circular’ case, we predicted a similar geometric orifice area (4.35 vs 4.02cm 2 ), pinwheeling index (2.6% vs 2.7%), stent deflection (1.95 vs 1.76mm) and flow velocity (1.33 vs 1.27m/s) to in vitro data. Conclusion Thus, we validated a novel structural and hemodynamic in silico framework for studying THVs, which will be applied to understand deployment factors contributing to structural degeneration and thrombogenicity. This framework also holds potential for guiding next-generation THV design and predictive procedural modeling.
In silico modeling of transcatheter heart valve oversizing and ellipticity, Part II: Effects on leaflet mechanics, hemodynamics, and stent deflection contributing to thrombogenic risk and structural degeneration Sam Boxwell, Rachel M.E. Cahalane, Dylan Armfield, William Hickey, Scott Cook, Patricia Kelly, Philip Cardiff, Laoise M. McNamara Computer Methods and Programs in Biomedicine, 2026 BACKGROUND AND OBJECTIVES: Transcatheter aortic valve implantation (TAVI) is the leading treatment for aortic stenosis. Self-expanding transcatheter heart valves (THVs) are oversized to prevent paravalvular leakage and then deployed over the diseased native valve. However, this can result in incomplete expansion and elliptical deployment, which may influence thrombogenic risk and structural degeneration, although this is not fully understood. METHODS: In this study, we utilized a validated in silico framework to assess the impact of THV oversizing and ellipticity on leaflet mechanics, hemodynamic shear stress and stent deformation, which are indicators of structural degeneration and thrombogenicity. We simulated self-expansion of a deformable THV stent within an idealized aortic annulus, applied pulsatile loading conditions representative of the cardiac cycle and then evaluated post-deployment frame deformation, leaflet mechanics, hemodynamics and stent fatigue. RESULTS: We predicted stent-frame decoupling of the supra-annular THV, with increased expansion and circularity at the functional valve level compared to the inflow. THV oversizing reduced valve expansion at the supra-annular valve level (< 90% expansion), which increased leaflet coaptation and pinwheeling, but reduced peak leaflet stresses and stent deflection compared to nominal sizing. Oversizing also altered hemodynamics, causing early mainstream flow separation, which increased leaflet oscillatory shear and viscous shear stress downstream of the THV, potentially increasing thrombogenic risk and promoting tissue degeneration. THV ellipticity induced heterogenous stent deflections, leading to variable leaflet stress distributions and coaptation mismatch. CONCLUSION: We propose that flexible THV stents may mitigate adverse effects of elliptical deployment and emphasize the importance of assessing THV expansion through fluoroscopy and considering post-TAVI balloon-dilatation to increase expansion and improve long-term functional valve performance.
Solid Mechanics Segregated Solver Acceleration With Jacobian-Free Newton-Krylov Andry Monlon, Alessandro Scolaro, Philip Cardiff, Ivor Clifford, Oskari Pakari, Mathieu Hursin International Journal for Numerical Methods in Engineering, 2026 The segregated algorithm is a common approach for finite volumes solvers in solid mechanics, providing a memory‐efficient and straightforward implementation. Due to the inter‐coupling of the components through the source terms, it suffers from a slow convergence behavior in specific scenarios, such as geometries with significantly uneven dimensions. Examples of attempts to improve the performance of the segregated algorithm in such cases are available in the literature, for instance, with machine learning or with multigrid acceleration. On the other hand, Newton solvers and Jacobian‐Free Newton‐Krylov method have been successfully applied as standalone solvers for fluid mechanics applications, or even for multi‐physics coupling in nuclear codes. Complementing recent work on Newton‐Krylov as a standalone solver for solid mechanics, this paper proposes a novel approach to tackle the slow convergence issue by coupling the segregated algorithm with a Jacobian‐Free Newton‐Krylov method. The targeted advantage being the performance improvements for pure mechanical simulations with almost no parametrization from the code user. In the article, the method is introduced and benchmarked against the original segregated algorithm and the Anderson acceleration. 2D and 3D steady‐state cases are considered, including small and large deformations, from linear to nonlinear mechanical behaviors. The OpenFOAM Fuel Behavior Analysis Tool (OFFBEAT) is a multidimensional fuel performance code developed jointly by the Paul Scherrer Institute (PSI) and the École Polytechnique Fédérale de Lausanne (EPFL). Using the PETSc library, the innovative coupling with the segregated algorithm has been implemented into OFFBEAT to produce the benchmarks. Still relying on the OpenFOAM framework and the segregated algorithm, the proposed method benefits from the validation of the existing code base. The results, obtained for serial executions, exhibit a promising reduction in computational time and number of iterations to convergence, paving the way for further development in solid mechanics solvers and a possible extension to other physics.
A Jacobian-Free Newton-Krylov Method for Cell-Centred Finite Volume Solid Mechanics Philip Cardiff, Dylan Armfield, Željko Tuković, Ivan Batistić International Journal for Numerical Methods in Engineering, 2026 This study proposes a Jacobian‐free Newton‐Krylov approach for finite‐volume solid mechanics. Traditional Newton‐based approaches require explicit Jacobian matrix formation and storage, which can be computationally expensive and memory‐intensive. In contrast, Jacobian‐free Newton‐Krylov methods approximate the Jacobian's action using finite differences, combined with Krylov subspace solvers such as the generalised minimal residual method (GMRES), enabling seamless integration into existing segregated finite‐volume frameworks without major code refactoring. This work proposes and benchmarks the performance of a compact‐stencil Jacobian‐free Newton‐Krylov method against a conventional segregated approach on a suite of test cases that span varying geometric dimensions, nonlinearities, dynamic responses and material behaviours. Key metrics, including computational cost, memory efficiency and robustness, are evaluated, along with the influence of preconditioning strategies and stabilisation scaling. Results show that the proposed Jacobian‐free Newton‐Krylov method outperforms the segregated approach in all linear and nonlinear elastic cases, achieving order‐of‐magnitude speedups in many instances; however, divergence is observed in elastoplastic cases, highlighting areas for further development. It is found that preconditioning choice affects performance: a LU direct solver is fastest for small to moderately sized cases, while a multigrid method is more effective for larger problems. The findings demonstrate that Jacobian‐free Newton‐Krylov methods are promising for advancing finite‐volume solid mechanics simulations, particularly for existing segregated frameworks where minimal modifications enable their adoption. The described implementations are available in the solids4foam toolbox for OpenFOAM, inviting the community to explore, extend and compare these procedures.
A finite volume Simo–Reissner beam method for moored floating body dynamics Amirhossein Taran, Seevani Bali, Željko Tuković, Vikram Pakrashi, Philip Cardiff Applied Ocean Research, 2025 This paper presents a novel finite volume mooring line model based on the geometrically exact Simo–Reissner beam model for analysing the interaction between a floating rigid body and its mooring lines. The coupled numerical model is implemented entirely within a finite volume-based discretisation framework using a popular computational fluid dynamics C++ toolbox, OpenFOAM. Unlike existing methods for modelling mooring lines, which rely on lumped mass models or finite element-based approaches, this work simulates the mooring cables using non-linear beam models implemented in a finite volume framework to account for bending, tensile, and torsional loading. This advancement makes the current work particularly valuable for simulating extreme sea conditions. The coupled model developed in this study has been validated and verified using experimental and numerical data for a floating box moored with four catenary mooring lines under regular wave conditions featuring different wave heights and periods. The results demonstrate strong agreement with both experimental and numerical data, highlighting the model’s accuracy in capturing mooring dynamics and floating body motion. • A finite volume-based mooring line model based on Simo–Reissner beam theory. • A unified FV framework in OpenFOAM models the floating body and mooring lines. • The model accurately captures bending, tensile, and torsional loads. • Validation of a Coupled Model for a Catenary-Moored Floating Box in Waves.
One-step SelfSim algorithm: Formulating material models from measured strain fields with machine learning Simon Rodriguez, Philip Cardiff Computers and Structures, 2025 This article introduces a method to formulate material models from measured strain fields using machine learning, termed One-step SelfSim. Unlike the original SelfSim algorithm, which requires two simulations—one with measured displacements and another with measured loads—One-step SelfSim only performs the simulation with the measured loads. The training dataset is created by coupling the simulation’s stress results with a measured strain field. The method is applied to an elastoplastic problem, using a recurrent neural network initially trained on linear elastic data to model the behaviour of a steel plate undergoing elastoplastic deformation. Results demonstrate that the machine learning model effectively captures the elastoplastic behaviour, with good agreement between simulation outcomes and expected data, particularly for the displacement field. The model is further tested on a plate with a hole, confirming its applicability in scenarios distinct from the training phase. Two additional contributions are presented. First, the SelfSim algorithm is implemented within a finite volume framework, extending its application beyond finite element simulations. Second, a recurrent neural network is employed to represent history-dependent behaviour, replacing the nested modular neural networks commonly used in earlier studies. • Introduced One-Step SelfSim, a novel machine learning-based approach to derive material models from measured strain fields, bypassing displacement-driven simulations. • Demonstrated the algorithm’s effectiveness in modelling elastoplastic behaviour, utilising recurrent neural networks for history-dependent material responses. • Extended the application of the SelfSim algorithm from finite element methods to the finite volume framework, implemented via OpenFOAM. • Verified the method through test cases, including elastoplastic deformation of a steel plate and its generalisation to a plate with a hole. • Showed significant computational efficiency and improved accuracy over traditional SelfSim, enabling direct integration of modern experimental strain data.
Offshore renewable energies: exploring floating modular energy islands—materials, construction technologies, and life cycle assessment Enzo Marino, Michaela Gkantou, Abdollah Malekjafarian, Seevani Bali, Charalampos Baniotopoulos, Jeroen van Beeck, Ruben Paul Borg, Niccolo Bruschi, Philip Cardiff, Eleni Chatzi, Ivan Čudina, Florea Dinu, Evangelos Efthymiou, Giulio Ferri, Helena Gervásio, Junlin Heng, Zhiyu Jiang, Stefano Lenci, Ivan Lukačević, Lance Manuel, Angela Meyer, Mariela Méndez-Morales, Adnan Osmanović, Vikram Pakrashi, Amiya Pandit, Giuseppe Rega, Davor Skejić, Luana Tesch, Viorel Ungureanu, Tarik Uzunović, Amrit Shankar Verma Journal of Ocean Engineering and Marine Energy, 2025 Floating modular energy islands (FMEIs) are modular, interconnected floating structures designed to collectively produce, store, convert, and transport renewable energy. This review aims to establish a foundation for developing innovative approaches to sustainably harness multi-energy sources in offshore environments. It leverages existing technological expertise while exploring new solutions to address specific challenges associated with FMEIs. The review initially presents existing technologies for floating energy structures and assesses their applicability to FMEI. The structural materials that could be utilised for the construction of a floating energy island are subsequently reviewed. Next, the offshore construction technologies suitable for FMEI are reviewed. Finally, studies on the life cycle assessment of hybrid energy systems are examined, highlighting the environmental advantages of integrating multiple renewable energy sources, thereby underscoring the potential of FMEIs.
Performance of a vertex-centred block-coupled finite volume methodology for small-strain static elastoplasticity[Figure presented] Federico Mazzanti, Philip Cardiff Computers and Mathematics with Applications, 2025 This article assesses the performance of a vertex-centred block-coupled finite volume methodology for static small-strain elastoplasticity based on a Newton-Raphson algorithm. The proposed coupled solution algorithm is compared with vertex-centred and cell-centred segregated solution procedures in terms of accuracy, efficiency and robustness for quasi-static problems. This coupled methodology is then verified on four test cases: a patch test to check its ability to reproduce first-order polynomials; the method of manufactured solutions to check the order of convergence of displacement and stress; a 2-D perforated plate and a 3-D narrow T-member under elastoplastic conditions to examine the accuracy of the solutions on non-trivial test cases. The proposed methodology demonstrates high accuracy and a computational efficiency of up to 28× speedups over the standard cell-centred segregated approach.
A Finite Volume Framework for Damage and Fracture Prediction in Wire Drawing Andrew Whelan, Tian Tang, Vikram Pakrashi, Philip Cardiff International Journal for Numerical Methods in Engineering, 2025 This article presents the implementation of the canonical Lemaitre and Gurson–Tvergaard–Needleman (GTN) damage models and a more recent phase‐field type model within a Lagrangian, geometrically nonlinear, cell‐centred finite volume framework. The proposed segregated solution procedure uses Picard‐type defect (deferred) outer corrections, where the primary unknowns are cell‐centre displacements and pressures. Spurious zero‐energy modes (numerical oscillations in displacement and pressure) are avoided by introducing stabilisation (smoothing) diffusion terms to the pressure and momentum equations. Appropriate scaling of the momentum “Rhie–Chow” stabilisation term is shown to be important in regions of plasticity and damage. To accurately predict damage and fracture in wire drawing where hydrostatic pressure is high, novel variants of the Lemaitre model with crack‐closure and triaxiality effects are proposed. The developed methods are validated against the notched round bar and flat notched bar experimental cases and subsequently applied to the analysis of axisymmetric wire drawing. It is shown that the proposed finite volume approach provides a robust basis for predicting damage in wire drawing, where the proposed novel Lemaitre model with crack‐closure effects was shown to be the most suitable for predicting experimentally observed fracture.
Simulation of a ship advancing in floating ice floes Proceedings of the International Conference on Port and Ocean Engineering Under Arctic Conditions POAC, 2019
A 3-D poro-elasto-plastic model for sand production around open-hole and cased & perforated wellbores 50th US Rock Mechanics Geomechanics Symposium 2016, 2016
A new reservoir scale model for fracture propagation and stress reorientation in injection wells 50th US Rock Mechanics Geomechanics Symposium 2016, 2016
Evolving an aircraft using a parametric design system Jonathan Byrne, Philip Cardiff, Anthony Brabazon, Michael O’Neill Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2014
High-order cell-centred finite-volume solid mechanics using a Jacobian-free Newton-Krylov method I Batistić, P Castrillo, P Cardiff Journal of Computational Physics, 115056 , 2026 2026
In Silico Modeling of Transcatheter Heart Valve Oversizing and Ellipticity, Part I: Establishing Credibility of an Advanced Model S Boxwell, D Armfield, RME Cahalane, W Hickey, S Cook, P Kelly, ... Computer Methods and Programs in Biomedicine, 109404 , 2026 2026
In silico modeling of transcatheter heart valve oversizing and ellipticity, Part II: Effects on leaflet mechanics, hemodynamics, and stent deflection contributing to … S Boxwell, RME Cahalane, D Armfield, W Hickey, S Cook, P Kelly, ... Computer Methods and Programs in Biomedicine, 109361 , 2026 2026 Citations: 1
A Jacobian‐Free Newton‐Krylov Method for Cell‐Centred Finite Volume Solid Mechanics P Cardiff, D Armfield, Ž Tuković, I Batistić International Journal for Numerical Methods in Engineering 127 (3), e70268 , 2026 2026 Citations: 3
A Jacobian-free Newton-Krylov method for high-order cell-centred finite volume solid mechanics I Batistic, P Castrillo, P Cardiff arXiv preprint arXiv:2601.18417 , 2026 2026
Towards Coupling a 3D Heart Model with a 0D Closed-Loop Circulation in OpenFOAM D Kelly, P Cardiff 2026
Estimation of Wall Thickness in Middle Cerebral Artery Aneurysms Using Fluid-Structure Interaction Simulations J Nagy, W Fenz, M Giretzlehner, V Mazanec, Z Major, A Gruber, ... Engineering Modelling, Analysis and Simulation 3 (1) , 2026 2026
beamFoam: A Cell-Centred Finite Volume Solver for Nonlinear Geometrically-Exact Beams in OpenFOAM S Bali, A Taran, Ž Tuković, V Pakrashi, P Cardiff OpenFOAM® Journal 5, 180-210 , 2025 2025
Version 3.0-laserbeamFoam: Laser ray-tracing and thermally induced state transition simulation toolkit T Flint, P Ćosić, G Parivendhan, SA Rodriguez, I Bunaziv, P O’Toole, ... SoftwareX 32, 102419 , 2025 2025 Citations: 2
A finite volume Simo–Reissner beam method for moored floating body dynamics A Taran, S Bali, Ž Tuković, V Pakrashi, P Cardiff Applied Ocean Research 165, 104845 , 2025 2025 Citations: 2
Offshore renewable energies: exploring floating modular energy islands—materials, construction technologies, and life cycle assessment E Marino, M Gkantou, A Malekjafarian, S Bali, C Baniotopoulos, ... Journal of Ocean Engineering and Marine Energy 11 (4), 1157-1182 , 2025 2025 Citations: 19
One-step SelfSim algorithm: Formulating material models from measured strain fields with machine learning S Rodriguez, P Cardiff Computers & Structures 318, 107944 , 2025 2025
Performance of a vertex-centred block-coupled finite volume methodology for small-strain static elastoplasticity F Mazzanti, P Cardiff Computers & Mathematics with Applications 195, 212-238 , 2025 2025
Numerical modelling of phase changes in laser materials processing using OpenFOAM I Bunaziv, T Flint, P Cardiff, X Ren, M Eriksson IOP Conference Series: Materials Science and Engineering 1332 (1), 012006 , 2025 2025 Citations: 2
Validation of a finite volume Simo-Reissner beam method for moored floating solar platforms C McAlister, A Taran, M Campell, S Bali, M Karimirad, V Pakrashi, ... The 20th OpenFOAM Workshop (OFW20) , 2025 2025 Citations: 1
solids4foam: A toolbox for performing solid mechanics and fluid-solid interaction simulations in OpenFOAM P Cardiff, I Batisti Journal of Open Source Software 10 (108), 7407 , 2025 2025 Citations: 9
Analysis of Coupling Strategies for Conjugate Heat Transfer Problems E Tandis, P Cardiff, A Ashrafizadeh OpenFOAM® Journal 5, 38-58 , 2025 2025 Citations: 1
A finite volume framework for damage and fracture prediction in wire drawing A Whelan, T Tang, V Pakrashi, P Cardiff International Journal for Numerical Methods in Engineering 126 (1), e7640 , 2025 2025 Citations: 4
A finite volume adaptation of beam-to-beam contact interactions implemented for geometrically exact Simo–Reissner beams S Bali, Ž Tuković, P Cardiff, A Ivanković, V Pakrashi Computational mechanics 75 (1), 237-263 , 2025 2025 Citations: 6
Offshore renewable energies: A review towards floating modular energy islands—monitoring, loads, modelling and control E Marino, M Gkantou, A Malekjafarian, S Bali, C Baniotopoulos, ... Ocean engineering 313, 119251 , 2024 2024 Citations: 44
MOST CITED SCHOLAR PUBLICATIONS
Mechanical behaviour of additively-manufactured polymeric octet-truss lattice structures under quasi-static and dynamic compressive loading C Ling, A Cernicchi, MD Gilchrist, P Cardiff Materials & Design 162, 106-118 , 2019 2019 Citations: 336
OpenFOAM finite volume solver for fluid-solid interaction Ž Tuković, A Karač, P Cardiff, H Jasak, A Ivanković Transactions of FAMENA 42 (3), 1-31 , 2018 2018 Citations: 175
Ship resistance when operating in floating ice floes: A combined CFD&DEM approach L Huang, J Tuhkuri, B Igrec, M Li, D Stagonas, A Toffoli, P Cardiff, ... Marine Structures 74, 102817 , 2020 2020 Citations: 157
Thirty Years of the Finite Volume Method for Solid Mechanics: P. Cardiff, I. Demirdžić P Cardiff, I Demirdžić Archives of Computational Methods in Engineering 28 (5), 3721-3780 , 2021 2021 Citations: 143
An open-source finite volume toolbox for solid mechanics and fluid-solid interaction simulations P Cardiff, A Karač, P De Jaeger, H Jasak, J Nagy, A Ivanković, Ž Tuković arXiv preprint arXiv:1808.10736 , 2018 2018 Citations: 137
A block-coupled finite volume methodology for linear elasticity and unstructured meshes P Cardiff, Ž Tuković, H Jasak, A Ivanković Computers & structures 175, 100-122 , 2016 2016 Citations: 126
Fluid-structure interaction of a large ice sheet in waves L Huang, K Ren, M Li, Ž Tuković, P Cardiff, G Thomas Ocean Engineering 182, 102-111 , 2019 2019 Citations: 118
On finite volume method implementation of poro‐elasto‐plasticity soil model T Tang, O Hededal, P Cardiff International journal for numerical and analytical methods in geomechanics … , 2015 2015 Citations: 99
A large strain finite volume method for orthotropic bodies with general material orientations P Cardiff, A Karač, A Ivanković Computer Methods in Applied Mechanics and Engineering 268, 318-335 , 2014 2014 Citations: 94
Strategies for effective stimulation of multiple perforation clusters in horizontal wells R Manchanda, EC Bryant, P Bhardwaj, P Cardiff, MM Sharma SPE Production & Operations 33 (03), 539-556 , 2018 2018 Citations: 87
A review on the modelling of wave-structure interactions based on OpenFOAM L Huang, Y Li, D Benites-Munoz, CW Windt, A Feichtner, S Tavakoli, ... OpenFOAM® Journal 2, 116-142 , 2022 2022 Citations: 72
Deformation response of EPS foam under combined compression-shear loading. Part I: Experimental design and quasi-static tests C Ling, J Ivens, P Cardiff, MD Gilchrist International Journal of Mechanical Sciences 144, 480-489 , 2018 2018 Citations: 71
Development of a finite volume contact solver based on the penalty method P Cardiff, A Karač, A Ivanković Computational Materials Science 64, 283-284 , 2012 2012 Citations: 69
A Lagrangian cell‐centred finite volume method for metal forming simulation P Cardiff, Ž Tuković, PD Jaeger, M Clancy, A Ivanković International journal for numerical methods in engineering 109 (13), 1777-1803 , 2017 2017 Citations: 65
Three-dimensional fluid–structure interaction simulation with a hybrid RANS–LES turbulence model for applications in transonic flow domain B Šekutkovski, I Kostić, A Simonović, P Cardiff, V Jazarević Aerospace Science and Technology 49, 1-16 , 2016 2016 Citations: 58
Development of the finite volume method for hip joint stress analysis P Cardiff University College Dublin , 2012 2012 Citations: 58
Evolving parametric aircraft models for design exploration and optimisation J Byrne, P Cardiff, A Brabazon Neurocomputing 142, 39-47 , 2014 2014 Citations: 56
A numerical study of processing parameters and their effect on the melt-track profile in Laser Powder Bed Fusion processes G Parivendhan, P Cardiff, T Flint, Ž Tuković, M Obeidi, D Brabazon, ... Additive manufacturing 67, 103482 , 2023 2023 Citations: 55
OpenFOAM library for fluid structure interaction Z Tukovic, P Cardiff, A Karac, H Jasak, A Ivankovic 9th OpenFOAM workshop 710 , 2014 2014 Citations: 46
Wind-induced phenomena in long-span cable-supported bridges: a comparative review of wind tunnel tests and computational fluid dynamics modelling Y Zhang, P Cardiff, J Keenahan Applied Sciences 11 (4), 1642 , 2021 2021 Citations: 45