3D fluid–structure-contact interaction based on a combined XFEM FSI and dual mortar contact approach

Abstract

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

Numerical procedure for fluid-structure interaction with structure displacements limited by a rigid obstacle

“…For (12), we can consult [3], Theorem 5.3-1, p. 210. In (12), n(ϕ(X)) is the unit vector normal to Σ 5 at the point ϕ(X) ∈ Σ 5 , oriented to the exterior of D.…”

“…An extension to 3D nonlinear shell which manages non-convex contact constraint is proposed in [1]. An approach combining an extended finite element method (XFEM) and a dual finite deformation mortar contact formulation is proposed in [12].…”

LLM and X-FEM based interface modeling of fluid–thin structure interactions on a non-interface-fitted mesh

“…In particular, recent interest in the non-interface-fitted mesh approaches [1,10,11,13,[17][18][19]21,22,24,25,[27][28][29][32][33][34][35][36][37]40,41,[46][47][48][54][55][56][58][59][60][61][62], in which the fluid and structure are described in general by the Eulerian and Lagrangian coordinates, respectively, is remarkable. One reason for this interest is associated with the practical merit of mesh generation, because the approach using a non-interface-fitted mesh can reduce human and computational costs and difficulties of the mesh generation.…”

“…Further advancements are studied in Refs. [48,54,58,59] with consideration of fluid-solid interactions, stress discontinuity, partitioned iterative schemes, domain integrals [54], FSI contacts [59], etc. The combination of the X-FEM and the IFEM [21] is also given in Ref.…”

The Discontinuity‐Enriched Finite Element Method

“…This flexibility in the analysis, however, comes at a price because the complexity of the conformal mesh generation is transferred to that of the detection of the intersection between elements and a discontinuity, and to related subsidiary implementations. Nevertheless, X/GFEM has proven to outmatch the standard FEM in problems with evolving geometric features such as crack propagation, moving interfaces, topology optimization, and phase/solidification problems . Despite these undeniable advantages, X/GFEM suffers from shortcomings that are either rooted in its theoretical background (the need to enrich all nodes in elements crossed by a discontinuity) or whose solution is still not definitive (the high condition number issue).…”