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SUMMARYThis paper presents a new approach for imposing Dirichlet conditions weakly on non-fitting finite element meshes. Such conditions, also called embedded Dirichlet conditions, are typically, but not exclusively, encountered when prescribing Dirichlet conditions in the context of the eXtended finite element method (XFEM). The method's key idea is the use of an additional stress field as the constraining Lagrange multiplier function. The resulting mixed/hybrid formulation is applicable to 1D, 2D and 3D problems. The method does not require stabilization for the Lagrange multiplier unknowns and allows the complete condensation of these unknowns on the element level. Furthermore, only non-zero diagonal-terms are present in the tangent stiffness, which allows the straightforward application of state-of-the-art iterative solvers, like algebraic multigrid (AMG) techniques. Within this paper, the method is applied to the linear momentum equation of an elastic continuum and to the transient, incompressible Navier-Stokes equations. Steady and unsteady benchmark computations show excellent agreement with reference values.

SUMMARYWe have developed a new crack tip element for the phantom node method. In this method, a crack tip can be placed inside an element. Therefore cracks can propagate almost independent of the finite element mesh. We developed two different formulations for the three-node triangular element and four-node quadrilateral element, respectively. Although this method is well suited for the one-point quadrature scheme, it can be used with other general quadrature schemes. We provide some numerical examples for some static and dynamic problems.

Abstract. This contribution focusses on computational approaches for fluid structure interaction problems from several perspectives. Common driving force is the desire to handle even the large deformation case in a robust, efficient and straightforward way. In order to meet these requirements main subjects are on the one hand necessary improvements on coupling issues as well as on Arbitrary Lagrangian able fixed grid approaches and start the development of new such approaches. Some numerical examples are provided along the paper.

Finite deformation contact of flexible solids embedded in fluid flows occurs in a wide range of engineering scenarios. We propose a novel three-dimensional finite element approach in order to tackle this problem class. The proposed method consists of a dual mortar contact formulation, which is algorithmically integrated into an eXtended finite element method (XFEM) fluid-structure interaction approach. The combined XFEM fluid-structure-contact interaction method (FSCI) allows to compute contact of arbitrarily moving and deforming structures embedded in an arbitrary flow field. In this paper, the fluid is described by instationary incompressible Navier-Stokes equations. An exact fluid-structure interface representation permits to capture flow patterns around contacting structures very accurately as well as to simulate dry contact between structures. No restrictions arise for the structural and the contact formulation. We derive a linearized monolithic system of equations, which contains the fluid formulation, the structural formulation, the contact formulation as well as the coupling conditions at the fluid-structure interface. The linearized system may be solved either by partitioned or by monolithic fluid-structure coupling algorithms. Two numerical examples are presented to illustrate the capability of the proposed fluid-structure-contact interaction approach.Keywords Finite deformation contact · Contact of solids in fluid · EXtended finite element method · Fluid-structure interaction · Dual mortar contact approach · Partitioned and monolithic fluid-structure coupling

This paper presents two domain decomposition techniques for fixed grid fluid-structure interaction simulations that can be applied to the interaction of general structures with incompressible flows. One approach is based on an overlapping domain decomposition idea while the other uses non-overlapping domains. The first technique combines a fixed grid Chimera approach with arbitrary Lagrangean Eulerian based methods, the second one is based on an eXtended Finite Element Method (XFEM) strategy. Both techniques are used in a partitioned and strong coupling fluid -structure framework. The usage of such fixed-grid methods considerably increases the range of possible applications. Several test examples demonstrate key features of both methods.

Three-dimensional higher-order eXtended finite element method (XFEM)-computations still pose challenging computational geometry problems especially for moving interfaces. This paper provides a method for the localization of a higher-order interface finite element (FE) mesh in an underlying three-dimensional higher-order FE mesh. Additionally, it demonstrates, how a subtetrahedralization of an intersected element can be obtained, which preserves the possibly curved interface and allows therefore exact numerical integration.The proposed interface algorithm collects initially a set of possibly intersecting elements by comparing their 'eXtended axis-aligned bounding boxes'. The intersection method is applied to a highly reduced number of intersection candidates. The resulting linearized interface is used as input for an elementwise constrained Delaunay tetrahedralization, which computes an appropriate subdivision for each intersected element. The curved interface is recovered from the linearized interface in the last step. The output comprises triangular integration cells representing the interface and tetrahedral integration cells for each intersected element.Application of the interface algorithm currently concentrates on fluid-structure interaction problems on low-order and higher-order FE meshes, which may be composed of any arbitrary element types such as hexahedra, tetrahedra, wedges, etc. Nevertheless, other XFEM-problems with explicitly given interfaces or discontinuities may be tackled in addition. Multiple structures and interfaces per intersected element can be handled without any additional difficulties. Several parallelization strategies exist depending on the desired domain decomposition approach. Numerical test cases including various geometrical exceptions demonstrate the accuracy, robustness and efficiency of the interface handling.