DC1 CFD techniques for IBRA-type discretizations:
Explore the applicability of IBRA-type discretization to problems in solid mechanics.

Abstract:

This individual project investigates advanced isogeometric-analysis (IGA) methods for enhanced geometric-fidelity simulations in fluid and solid mechanics, by drawing on two recent works. The first study, “The Shifted Boundary Method in Isogeometric Analysis”, extends IGA using the shifted boundary method (SBM) to impose Dirichlet and Neumann conditions on unfitted geometries, showing that high-order NURBS plus SBM recover optimal convergence while avoiding small cut-cell instabilities.
The second study, “Isogeometric analysis for non‑Newtonian viscoplastic fluids”, applies high-order IGA to viscoplastic non-Newtonian fluid flows, demonstrating the applicability of IGA to complex rheologies in fluid dynamics. Building on these, this project’s objective is to integrate SBM-type unfitted boundary discretizations with IGA for non-Newtonian fluid flows and fluid‐structure interacting systems. Specifically, we will implement an IGA-SBM coupling for viscoplastic flows, addressing two key challenges: robust imposition of boundary/interface conditions on complex geometries without conforming meshes, and accurate representation of non‐Newtonian constitutive behaviour within a smooth high-order basis. The expected outcomes include a computational framework that supports trimmed and parametric geometries, maintains optimal convergence rates, and provides improved stability in challenging domains. Ultimately the project aims to deliver a validated simulation tool that bridges CAD-geometry and high-fidelity analysis for complex fluid mechanics applications, enabling efficient and accurate predictions in research or industry contexts.

DC2 IBRA-type discretizations in computational solid mechanics:
Explore the applicability of IBRA-type discretization to problems in solid mechanics.

Abstract:

This research project addresses the persistent challenge of integrating design and analysis in computational solid mechanics, particularly for complex geometries encountered in aerospace and automotive applications. Conventional workflows depend on Computer-Aided Design (CAD) for geometry definition and the Finite Element Method (FEM) for analysis, creating a disconnect that requires extensive meshing and pre-processing. Isogeometric Analysis (IGA) offers a unified framework by employing Non-Uniform Rational B-Splines (NURBS)—the mathematical foundation of CAD—directly in numerical simulations. This approach enhances geometric fidelity and smoothness while eliminating the meshing bottleneck. However, the application of IGA to non-linear solid mechanics problems remains challenging, especially when modeling advanced material behaviors such as plasticity, damage, and hyperelasticity, or when dealing with trimmed and irregular geometries. To overcome these limitations, this project explores Immersed Boundary Representation Analysis (IBRA)-type discretizations as an extension of IGA. IBRA enables efficient handling of complex geometries by embedding CAD representations within structured computational domains, avoiding the need for conforming meshes. The combined IGA–IBRA framework aims to improve the stability, accuracy, and computational efficiency of simulations involving non-linear materials and trimmed solids. The ultimate goal is to develop robust, industry-ready computational tools that streamline the design-to-analysis pipeline, reduce costs, and enhance the predictive capability of numerical simulations in advanced engineering applications.

DC3 Application of IBRA-type discretizations in implicit contact mechanics:
Use of smooth CAD discretizations in contact mechanics is known to be beneficial.

Abstract:

This individual project explores advanced isogeometric-analysis (IGA) strategies for accurate and robust simulations in contact mechanics, focusing on extending the Shifted Boundary Method (SBM) to solid–solid interaction problems. Building on recent work that combines IGA with SBM for unfitted boundary representations, the project aims to impose contact constraints efficiently on non-conforming geometries while preserving the smoothness and high-order accuracy of NURBS-based discretizations.
The method reformulates the contact problem within the SBM framework, allowing normal and tangential conditions to be enforced weakly on surrogate boundaries, thus avoiding mesh-dependent instabilities. Emphasis is placed on achieving optimal convergence and improved stability through penalty or Nitsche-type formulations adapted to contact.
The expected outcome is an IGA–SBM contact formulation capable of handling complex, curved, or trimmed geometries with enhanced geometric fidelity and computational robustness—bridging CAD-based design and high-fidelity analysis in solid mechanics.

DC4 Co-simulation strategies involving IBRA for solution of multi-field problems:
Complex technical systems often require a partitioned approach to enable disciplinary modelling and simulation with bestsuited solution approaches and discretization techniques in each domain.

Abstract:

This project focuses on improving multi-field simulations of complex technical systems by developing flexible co-simulation strategies that combine different solvers and discretization approaches. In particular, it explores the potential of Isogeometric B-Rep Analysis (IBRA), which provides highly accurate surface representations and smooth continuity across patch boundaries. By integrating IBRA with other methods, such as low- and high-order or embedded discretizations, simulations can achieve higher geometric fidelity without sacrificing flexibility. A central challenge is the accurate and robust transfer of data between different discretizations at coupled interfaces, such as the “wet surface” in fluid-structure interaction (FSI) problems. The project aims to develop novel mapping operators and coupling algorithms that account for IBRA-specific features, including trimming curves and patch-boundary continuities, while enabling stable and efficient multi-field simulations. All implementations are planned within the open-source Kratos-Multiphysics framework to ensure reproducibility and extensibility. Expected outcomes include robust and accurate data transfer methods, effective coupling of diverse solvers, and a demonstration of the advantages of IBRA in surface-coupled problems. Overall, the work seeks to enhance the accuracy, efficiency, and reliability of high-fidelity simulations across multiple engineering fields.

DC5 Large deformation structural elements (beams and shells) modeled with IBRA, including trimming and multiple coupled patches:
Development and systematic assessment of high-accuracy and robust structural mechanics elements for large deformation isogeometric B-Rep analysis.

Abstract:

This research focuses on developing robust and accurate structural mechanics elements for large deformation Isogeometric B-Rep Analysis (IBRA), tackling challenges associated with complex geometries, shell and beam formulations. The project aims to bridge the divide between CAD representations and nonlinear structural simulations, ensuring high continuity, geometric exactness, and numerical stability under demanding loading conditions. The work involves extending the IBRA framework in Kratos Multiphysics, introducing advanced formulations based on Reissner–Mindlin theory and enhanced interpolation schemes to mitigate shear and membrane locking effects. Comprehensive benchmarks will rigorously evaluate the accuracy and stability of the proposed elements in scenarios involving extensive rotations and deformations. By combining the precision of CAD-based modeling with resilient nonlinear analysis, the outcome contributes to a new generation of high-fidelity, scalable structural elements for engineering applications.

DC6 Mathematical tools for immersed IGA:
Development of mathematical tools for immersed IGA, related, in particular, to accurate and efficient integration, multipatch coupling, and dynamics (implicit and/or explicit).

Abstract:

This research project is dedicated to advancing the computational efficiency of simulating complex phase-field interface problems by developing novel tools within the Isogeometric Analysis (IGA) framework. While the phase-field approach is highly robust for modeling phenomena like fracture or cancer growth, it requires a fine spatial resolution to adequately resolve the interfaces. Typically, IGA employs tensor-product constructions for multidimensional basis functions, resulting in non-local refinement that propagates along entire parametric directions. We address this issue by using locally adaptive refinement and coarsening strategies using Truncated Hierarchical B-splines. This approach allows to have local meshing features only where necessary, dynamically following the evolution of the interfaces. To further improve the design-to-analysis streamline, we integrate this methodology with immersed boundary methods, specifically the Finite Cell Method (FEM), to efficiently model geometrically complex domains in the context of interface problems, thereby circumventing the major bottleneck of boundary-conforming meshing that typically hinders the integration between design and analysis.

DC7 Complex Constitutive modelling for immersed and shell discretizations:
Study of structural mechanics problems for immersed 3D or shell discretizations, with a special focus on advanced constitutive modeling, composites, phase-field modeling of brittle fracture, structural dynamics.

Abstract:

Isogeometric analysis (IGA) offers several advantages compared to conventional Finite Element Analysis (FEA). In particular, the effect of higher-order inter-element continuity due to the smoothness of its spline-based basis functions improves spectral accuracy over standard FEA, establishing IGA as a strong alternative in the field of structural dynamics. The focus of the current reserach project is mainly placed on immersed IGA, where the presence of small cut elements can produce very large maximum discrete eigenfrequencies. In explicit schemes this forces infinitesimal critical time steps to ensure stability, and thus simulation times become infeasible. Immersed IGA is an alternative that can provide stability and efficiency by leveraging higher continuity together with a lumped mass matrix, the reduction of the largest eigenfrequency is substantial, enabling much larger time steps, although there is a negative effect on accuracy, clearly visible on problems dominated by linear behavior. Resolving that would require the use of consistent mass matrix with α-stabilization, although that would reduce efficiency but still keep simulation times feasible. Depending on the application the appropriate approach should be chosen although it is evident that there is room for improvement in both directions. In order to further understand better the underlying mechanisms, as well as investigate potential improvements, this project establishes a unified procedure to assess time-domain accuracy in explicit dynamics and applies it across four representative structural elements. Starting from the simplest bar problem, the study extends to membranes (2D, second-order) and to Bernoulli–Euler beams and Kirchhoff–Love plates (fourth-order). The aim is to quantify the stability–efficiency–fidelity balance of lumping versus stabilized consistent mass in an immersed setting, using standardized approaches for the problem setup and metrics. Understunding the existing behavior is crucial for proposing novel approaches that would potentially mitigate the negarive effects present at the currenct state of the art. In parallel, we investigate two complementary directions. First, a quadtree rotated-square study shows that adverse spectral behavior is not governed by tiny element presence (mass) alone; connectivity and basis-support adjacencies are decisive too, further complicating the process of targeted treatment of the problematic areas. Second, we explore selective mass scaling for IGA, and benchmark it against conventional FE, with a goal of investigating and exploiting potential advantages due to the specific features unique to IGA.

DC8 Efficient unbounded acoustic analysis starting from CAD:
Combine the IGA BEM method and recent model order reduction strategies that have been applied in a pure BEM-context.

Abstract:

This research tries to integrate Isogeometric Analysis (IGA)-type workflows with model order reduction (MOR) frameworks for numerical transient solution of acoustic problems. Specifically utilizing time domain boundary element method (TD-BEM) for external noise emission problems and utilizing finite element method (FEM) for internal problems with moving or generic transient noise problems. These methods will be further improved with the integration of MOR to become applicable to industrial scale problems where each solution method also requires different MOR technique. By employing nonuniform B-spline (NURBS) basis function for the aforementioned problems, the smallest element size can be contained while still resolving the geometric details of the geometry which improves stability and convergence characteristics of the numerical solution.

DC9 Model Order Reduction of coupled vibro-acoustic systems:
DC9 will work towards efficient model order reduction schemes for one-way coupled and fully coupled vibro-acoustic analysis where the acoustic domain is described using a boundary discretisation.

Abstract:

The project focuses on developing advanced model order reduction techniques for coupled vibroacoustic systems, essential for controlling noise and vibration in automotive and aerospace engineering. It combines Finite Element Methods (FEM) for structural analysis with Boundary Element Methods (BEM) for acoustic modeling, enabling high-fidelity simulations while reducing computational cost and memory requirements. The research explores efficient reduction strategies, including Krylov- and modal-based approaches, and extends to isogeometric analysis (IGA) integrated with BEM to achieve smoother and more accurate representations of complex geometries. Furthermore, fast assembly techniques such as Fast Multipole and H-matrix methods are investigated to accelerate computations and make large-scale vibroacoustic analyses feasible. The overall objective is to provide scalable, precise, and efficient simulation tools for vibroacoustic systems, supporting the optimization of design and performance in complex engineering applications.

DC10 Implementation of IGA in the design and analysis workflow of machine elements and systems:
Although the basic principles of IGA are known for some decades, its application in industry is less spread than one would expect considering its fundamental advantage: the representation of real surfaces in a well-defined mathematical way instead of a discrete non-smooth finite element mesh.

Abstract:

This study presents an integrated IGA-based approach for the modeling, simulation, and analysis of contact behavior in machine elements and systems, with a particular focus on 3D helical gears. By directly employing NURBS-based geometric representations from CAD, the proposed CATIA-Rhino-IGA workflow eliminates the process of geometry representation and mesh generation, thus improving computational accuracy and efficiency. The proposed workflow is expected to accurately capture the complex 3D contact interactions under realistic loading conditions, and reveal stress concentrations beneath the contact surface consistent with Hertzian contact theory, which are known to be the primary origin of pitting fatigue damage on gear tooth flanks. Furthermore, ISO standards are used to validate the IGA-based computed stress results, to confirm the reliability of the proposed approach. The study will investigate the contact behavior between mating helical gear teeth, including the computation of pressure distribution and contact stresses within the contact zone. Emphasis is placed on the accurate representation of tooth geometry and the precise evaluation of the local contact area, which are critical for predicting gear performance and durability. Overall, this research will contributes to advancing the engineering workflow for mechanical systems, enable more geometrically accurate and reliable simulations of machine elements such as gears, bearings, and other contact-driven components.