arXiv subjects

Ivo Steinbrecher

Publications and source records attributed to Ivo Steinbrecher.

14 recordsLinked to original sources

arXiv2026

Braided endovascular implants for intracranial aneurysms: mechanics, hemodynamics, and clinical translation

Endovascular implants prevent intracranial aneurysm rupture by altering the mechanical and hemodynamic environment at the aneurysm neck. Yet many in silico workflows prescribe or reconstruct the post-deployment geometry before computing flow, leaving unresolved the mechanics that create the clinically relevant interface. Here we review braided intraluminal flow diverters, intrasaccular devices, and emerging flow-disruption concepts across deployment mechanics, inter-wire and wire-wall contact, superelasticity, wall apposition, pore geometry, computational fluid dynamics, and fluid-structure interaction. We connect these modeling choices to neck coverage, malapposition, migration, deformation, and durability, and distinguish established evidence from mechanistic inference and prospective hypotheses. We argue that model fidelity should match the clinical question: prescribed or fast placement may support screening, whereas questions of coverage, apposition, compaction, and migration benefit from mechanically plausible deployment states. An interface-resolved mechanics-to-flow framework, supported by measurable validation targets and standardized reporting, could improve device design and enable more reliable patient-specific treatment planning.

physics.comp-ph↗

arXiv2026

Modified augmented Lagrangian preconditioning for mixed-dimensional beam-solid coupling

This paper presents modified augmented Lagrangian block preconditioners for the mixed-dimensional coupling of three-dimensional solid bodies with embedded one-dimensional torsion-free Kirchhoff-Love beams using Lagrange multipliers for constraint enforcement. The finite element discretization of this mixed formulation leads to an indefinite saddle-point system. An augmented Lagrangian formulation is employed to regularize the linear system while maintaining exact enforcement of the coupling constraints. Starting from the corresponding ideal augmented Lagrangian block preconditioner, more practical block-triangular variants are derived in which the solid, beam, and Schur complement blocks can be treated independently. In addition, different variants of Schur complement approximations are introduced. Numerical experiments demonstrate robustness with respect to model parameters, near mesh-independent iteration counts, and favorable strong and weak scalability. These results indicate the suitability of the proposed approach for large-scale simulations of mixed-dimensional models in solid and structural mechanics, as demonstrated by an engineering example involving a composite sandwich plate.

cs.CE↗

arXiv2026

Mechanical Modeling of Braided Neurovascular Flow Diverters using a Beam-to-Beam and Beam-to-Surface Contact Formulation

Braided neurovascular flow diverters are widely used for the endovascular treatment of intracranial aneurysms, where their mechanical response and final deployed configuration are governed by the interaction of many slender, interwoven wires. Accurate numerical modeling of these devices is essential for analyzing their structural behavior during deformation occurring in compression or deployment. This work presents a structural-mechanics-based modeling framework and finite element formulation for the numerical simulation of braided flow diverters. The individual wires are modeled using geometrically exact Simo--Reissner beam theory, allowing a consistent description of large rotations and curved reference configurations. Mechanical interactions between individual wires are described by a beam-to-beam contact formulation, while the interaction with surrounding tubular structures, such as microcatheters, is captured by a beam-to-surface contact formulation. A flexible parametric description of interwoven braided flow diverter geometries is introduced, enabling systematic control of geometric design parameters such as wire count, braiding angle, device length, and radial interweaving pattern. The proposed framework is assessed by means of three representative validation cases from the literature. A tensile test is considered to investigate the length--diameter relation and axial force response of the device, while a radial compression test is used to study the pressure--diameter behavior. Finally, a stepwise compression example is used to evaluate geometry-sensitive quantities, including local wire distance, pitch angle, porosity, and metal coverage ratio. Rooted in structural mechanics and contact mechanics, these examples provide a systematical validation setting for the proposed modeling framework and its application to the mechanical analysis of braided flow diverters.

cs.CE↗

arXiv2026

An Embedded Mesh Approach for Isogeometric Boundary Layers in Contact Mechanics

This paper proposes a novel discretization workflow for contact problems in which the discretization of the contact interface is decoupled from that of the bulk domain. This separation enables independently tailored meshes for the contact interface and the bulk volume, allowing local requirements--such as element type and mesh resolution--to be addressed efficiently. Exploiting the boundary representation of CAD models, the contact interface of each body is discretized using a NURBS-based boundary layer mesh. This provides a smooth geometric description of the contact surface and enhanced inter-element continuity. The bulk domain is discretized using a structured Cartesian grid. To couple the resulting non-matching discretizations, an embedded mesh approach based on a mortar-type constraint formulation is employed. The paper describes in detail the proposed discretization workflow for generating both the isogeometric boundary layer and the structured Cartesian grid, and presents several strategies for constructing NURBS-based boundary layer meshes. Finally, a set of numerical examples is provided to validate the proposed approach.

cs.CE↗

arXiv2026

A variationally consistent beam-to-beam point coupling formulation for geometrically exact beam theories

Slender beam-like structures frequently occur in engineering applications and often interact at discrete locations through joints or connectors. Accurate modeling of such interactions is particularly challenging when different numerical formulations are involved in terms of underlying beam theory, interpolation schemes, and rotation parametrization. In this work, a versatile formulation-independent beam-to-beam point coupling approach is proposed within the framework of the geometrically exact beam theory discretized by the finite element method. The coupling constraints are expressed solely in terms of cross-section kinematics, namely centroid positions and orientations. Suitable generalized deformation measures for positional and rotational coupling are introduced, allowing for general coupling configurations, including relative rotations and non-coincident cross-section centroids in the reference configuration. The contribution of the coupling conditions to the weak form of the balance equations is derived in a variationally consistent manner and can be incorporated directly into the weak form of existing beam finite element models. Constraint enforcement is formulated using a Lagrange multiplier method and a penalty regularization. The proposed approach satisfies key properties such as objectivity, symmetry, and consistency with an stress-free reference configuration. Numerical examples demonstrate the robustness and flexibility of the method for coupling beams with different formulations and discretizations, even when the interaction points are located at arbitrary positions within beam elements.

cs.CE↗

arXiv2026

Contact-resolved deployment of the Contour Neurovascular System in patient-specific intracranial aneurysms

While intrasaccular flow disruptors are widely used to treat wide-neck intracranial aneurysms, state-of-the-art patient-specific computational models routinely neglect the deployment mechanics by prescribing a pre-seated geometry. This shortcut oversimplifies the true physics and misrepresents the Contour Neurovascular System (CNS), whose critical biomechanical features, such as neck coverage, wall apposition, and migration resistance, are highly path-dependent. To resolve this limitation, we present a contact-resolved finite-element framework that explicitly computes the structural mechanics of implant deployment within patient-specific vascular environments. The device is discretized as a dual-layer interwoven Nitinol braid using geometrically exact beams, while the vascular wall is represented as a deformable hyperelastic shell. Non-linear frictional contact formulations govern complex wire-wire and wire-wall interactions under a staged release protocol. Evaluating three anatomical phenotypes reveals that the final equilibrium morphology is highly sensitive to tangential slip resistance and vertical release depth. Frictionless assumptions permit excessive post-contact sliding, whereas near-stick conditions enhance anchoring but restrict local compliance. Crucially, conventional geometric fast placement fails to capture these critical contact interactions and wall-supported mechanical equilibrium. This deployment-resolved framework establishes a biomechanically grounded foundation for downstream hemodynamics, fluid-structure interaction, and mechanobiological thrombus-formation modeling.

physics.comp-ph↗

arXiv2026

Mixed Finite Elements for Geometrically Exact Beams using Discontinuous Rotations and Discrete Curvature

We propose a novel mixed finite-element formulation for geometrically exact (Simo--Reissner) beams that introduces the moment vector as additional independent field. The specific mixed form allows for an element-local, discontinuous approximation of rotations, which is key to a simple and efficient discretization framework. The concept of discrete curvature provides a mathematically consistent treatment of rotation discontinuities. For linear constitutive laws, the mixed form is derived via a Legendre transform of the curvature-related strain energy. Objectivity is retained at the discrete level by interpolating relative rotations through a multiplicative split of the rotation field; path-independence is inherent to the total Lagrangian setting and verified numerically. Several benchmarks demonstrate optimal rates of convergence and accuracy, irrespective of the beam's slenderness and order of approximation. Notably, the lowest-order element entirely avoids rotation interpolation by employing element-constant rotations only.

math.NA↗

arXiv2026

Influence of coronary plaque morphology on local mechanical states and associated in-stent restenosis

In-stent restenosis (ISR) after percutaneous coronary intervention is a multi-factorial process. Specific morphological lesion characteristics were observed to contribute to the occurrence of ISR. Local mechanical factors, such as stresses and strains, are known to influence tissue adaptation after stent implantation. However, the influence of morphological features on those local mechanical states and, hence, on the occurrence of ISR remains understudied. This work explores how local mechanical quantities relate to ISR by evaluating the stress distributions in the artery wall during and after stent implantation for morphology-informed lesion examples. We perform computational simulations of the stenting procedure with physics-based patient-specific coronary artery models. Different morphologies are assessed using the spatial plaque composition information from high-resolution coronary computed tomography angiography data. In the sample cases, elevated local tensile stresses were consistently found at sites corresponding to ISR. We found that specific morphological characteristics like circumferential or asymmetric block calcifications result in higher stresses in the surrounding tissue. These findings show that for the observed connection between plaque morphology and ISR, the local mechanical state may represent a relevant link. This study provides a mechanistic, illustrative insight for the examined cases. Future work with larger cohorts and systematic follow-up can establish statistically robust associations.

cs.CE↗

arXiv2025

A consistent mixed-dimensional coupling approach for 1D Cosserat beams and 2D surfaces in 3D space

The present article proposes a novel computational method for coupling arbitrarily curved 1D fibers with a 2D surface as defined, e.g., by the 2D surfaces of a 3D solid body or by 2D shell formulations. The fibers are modeled as 1D Cosserat continua (beams) with six local degrees of freedom, three positional and three rotational ones. A kinematically consistent 1D-2D coupling scheme for this problem type is proposed considering the positional and rotational degrees of freedom along the beams. The positional degrees of freedom are coupled by enforcing a constant normal distance between a point on the beam centerline and a corresponding point on the surface. This strategy requires a consistent description of the surface normal vector field to guarantee fundamental mechanical properties such as conservation of angular momentum. Coupling of the rotational degrees of freedom of the beams and a suitable rotation tensor representing the local orientation within a solid volume has been considered in a previous contribution. In the present work, this coupling approach will be extended by constructing rotation tensors that are representative of local surface orientations. Several numerical examples demonstrate the consistency, robustness and accuracy of the proposed method. To showcase its applicability to multi-physics systems of practical relevance, the fluid-structure interaction example of a vascular stent is presented.

cs.CE↗

arXiv2025

Patient-specific coronary angioplasty simulations -- a mixed-dimensional finite element modeling approach

Coronary angioplasty with stent implantation is the most frequently used interventional treatment for coronary artery disease. However, reocclusion within the stent, referred to as in-stent restenosis, occurs in up to 10% of lesions. It is widely accepted that mechanical loads on the vessel wall strongly affect adaptive and maladaptive mechanisms. Yet, the role of procedural and lesion-specific influence on restenosis risk remains understudied. Computational modeling of the stenting procedure can provide new mechanistic insights, such as local stresses, that play a significant role in tissue growth and remodeling. Previous simulation studies often featured simplified artery and stent geometries and cannot be applied to real-world examples. Realistic simulations were computationally expensive since they featured fully resolved stenting device models. The aim of this work is to develop and present a mixed-dimensional formulation to simulate the patient-specific stenting procedure with a reduced-dimensional beam model for the stent and 3D models for the artery. In addition to presenting the numerical approach, we apply it to realistic cases to study the intervention's mechanical effect on the artery and correlate the findings with potential high-risk locations for in-stent restenosis. We found that high artery wall stresses develop during the coronary intervention in severely stenosed areas and at the stent boundaries. Herewith, we lay the groundwork for further studies towards preventing in-stent restenosis after coronary angioplasty.

cs.CE↗

arXiv2024

An approximate block factorization preconditioner for mixed-dimensional beam-solid interaction

This paper presents a scalable physics-based block preconditioner for mixed-dimensional models in beam-solid interaction and their application in engineering. In particular, it studies the linear systems arising from a regularized mortar-type approach for embedding geometrically exact beams into solid continua. Due to the lack of block diagonal dominance of the arising 2 x 2 block system, an approximate block factorization preconditioner is used. It exploits the sparsity structure of the beam sub-block to construct a sparse approximate inverse, which is then not only used to explicitly form an approximation of the Schur complement, but also acts as a smoother within the prediction step of the arising SIMPLE-type preconditioner. The correction step utilizes an algebraic multigrid method. Although, for now, the beam sub-block is tackled by a one-level method only, the multi-level nature of the computationally demanding correction step delivers a scalable preconditioner in practice. In numerical test cases, the influence of different algorithmic parameters on the quality of the sparse approximate inverse is studied and the weak scaling behavior of the proposed preconditioner on up to 1000 MPI ranks is demonstrated, before the proposed preconditioner is finally applied for the analysis of steel-reinforced concrete structures in civil engineering.

cs.CE↗

arXiv2021

Fluid-beam interaction: Capturing the effect of embedded slender bodies on global fluid flow and vice versa

This work addresses research questions arising from the application of geometrically exact beam theory in the context of fluid-structure interaction (FSI). Geometrically exact beam theory has proven to be a computationally efficient way to model the behavior of slender structures while leading to rather well-posed problem descriptions. In particular, we propose a mixed-dimensional embedded finite element approach for the coupling of one-dimensional geometrically exact beam equations to a three-dimensional background fluid mesh, referred to as fluid-beam interaction (FBI) in analogy to the well-established notion of FSI. Here, the fluid is described by the incompressible isothermal Navier-Stokes equations for Newtonian fluids. In particular, we present algorithmic aspects regarding the solution of the resulting one-way coupling schemes and, through selected numerical examples, analyze their spatial convergence behavior as well as their suitability not only as stand-alone methods but also for an extension to a full two-way coupling scheme.

cs.CE↗

arXiv2021

Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes

This article proposes a mortar type finite element formulation for consistently embedding curved, slender beams, i.e. 1D Cosserat continua, into 3D solid volumes. A consistent 1D-3D coupling scheme for this problem type is proposed, which enforces both positional and rotational constraints. Since Boltzmann continua exhibit no inherent rotational degrees of freedom, suitable definitions of orthonormal triads are investigated that are representative for the orientation of material directions in the 3D solid. The rotation tensor defined by the polar decomposition of the deformation gradient is demonstrated to represent these material directions in a L2-optimal manner. Subsequently, objective rotational coupling constraints between beam and solid are formulated and enforced in a variationally consistent framework. Eventually, finite element discretization of all primary fields results in an embedded mortar formulation for rotational and translational constraint enforcement. Based on carefully chosen numerical test cases, the proposed scheme is demonstrated to exhibit a consistent spatial convergence behavior and to offer the up-scaling potential for studying real-life engineering applications such as fiber-reinforced composite materials.

cs.CE↗

arXiv2019

A mortar-type finite element approach for embedding 1D beams into 3D solid volumes

In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly efficient 1D geometrically exact beam finite elements, based on various types of geometrically nonlinear beam theories. The surrounding solid volume is modeled with 3D continuum (solid) elements. An embedded mortar-type approach is employed to enforce the kinematic coupling constraints between the beam elements and solid elements on non-matching meshes. This allows for very flexible mesh generation and simple material modeling procedures in the solid, since it can be discretized without having to capture for the reinforcements, while still being able to account for complex nonlinear effects due to the embedded fibers. Several numerical examples demonstrate the consistency, robustness and accuracy of the proposed method, as well as its applicability to rather complex fiber-reinforced structures of practical relevance.

cs.CE↗