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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.

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.

The present article proposes a novel computational method for coupling 1D fibers with the 2D surface of a 3D solid. 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 solid surface. This strategy requires a consistent description of the solid 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 representative for the local orientation within a Boltzmann continuum has been considered in a previous contribution. In the present work, this coupling approach will be extended by constructing rotation tensors that are representative for 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.

Contact and related phenomena, such as friction, wear or elastohydrodynamic lubrication, remain as one of the most challenging problem classes in nonlinear solid and structural mechanics. In the context of their computational treatment with finite element methods (FEM) or isogeometric analysis (IGA), the inherent non-smoothness of contact conditions, the design of robust discretization approaches as well as the implementation of efficient solution schemes seem to provide a never ending source of hard nuts to crack. This is particularly true for the case of beam-to-solid interaction with its mixed-dimensional 1D-3D contact models. Therefore, this contribution gives an overview of current steps being taken, starting from state-of-the-art beam-to-beam (1D) and solid-to-solid (3D) contact algorithms, towards a truly general 1D-3D beam-to-solid contact formulation., Comment: 10 pages, 4 figures

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., Comment: 32 pages, 28 figures

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.

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.