Studies of the strong coupling and weak coupling methods in FSI analysis

The weak coupling methods in fluid–structure interaction analysis are newly classified into three types; the weak coupling method for solving structures with interfaces, the weak coupling method for solving fluids with interfaces, and the weak coupling method for solving both fluids and structures with interfaces. The consistent added matrices of these weak coupling methods are derived from the condensation of the strong coupling formulation. Some approximations for the consistent added matrices, which can avoid the matrix coupling, are proposed. The reasons for convergence difficulty in the weak coupling methods are clarified. A number of numerical results are presented to investigate the convergence properties and computational efficiency of these methods. Copyright © 2004 John Wiley & Sons, Ltd.     

A comparison of FE–BE coupling schemes for large‐scale problems with fluid–structure interaction

To predict the sound radiation of structures, both a structural problem and an acoustic problem have to be solved. In case of thin structures and dense fluids, a strong coupling scheme between the two problems is essential, since the feedback of the acoustic pressure onto the structure is not negligible. In this paper, the structural part is modeled with the finite element (FE) method. An interface to a commercial FE package is set up to import the structural matrices. The exterior acoustic problem is efficiently modeled with the Galerkin boundary element (BE) method. To overcome the well‐known drawback of fully populated system matrices, the fast multipole method is applied. Different coupling formulations are investigated. They are either based on the Burton–Miller approach or use a mortar coupling scheme. For all cases, iterative solvers with different preconditioners are used. The efficiency with respect to their memory consumption and computation time is compared for a simple model problem. At the end of the paper, a more complex structure is simulated. Copyright © 2008 John Wiley & Sons, Ltd.     

FE/FMBE coupling to model fluid–structure interaction

In this paper, a finite element (FE)/fast multipole boundary element (FMBE)‐coupling method is presented for modeling fluid–structure interaction problems numerically. Vibrating structures are assumed to consist of elastic or sound absorbing materials. An FE method (FEM) is used for this part of the solution. This structural sub‐domain is embedded in a homogeneous fluid. The case where the boundary of the structural sub‐domain has a very complex geometry is of special interest. In this case, the BE method (BEM) is a more suitable numerical tool than FEM to account for the sound propagation in the homogeneous fluid. The efficiency of the BEM is increased by using FMBEM. The BE‐surface mesh required is directly generated by the FE‐mesh used to discretize the structural sub‐domain and the absorbing material. This FE/FMBE‐coupling method makes it possible to predict the effects of arbitrarily shaped absorbing materials and vibrating structures on the sound field in the surrounding fluid numerically. The coupling method proposed is used to study the acoustic behavior of the lining of an anechoic chamber and that of an entire anechoic chamber in the low‐frequency range. The numerical results obtained are compared with the experimental data. Copyright © 2008 John Wiley & Sons, Ltd.     

Interface‐reduction for the Craig–Bampton and Rubin method applied to FE–BE coupling with a large fluid–structure interface

Component mode‐based model‐order reduction (MOR) methods like the Craig–Bampton method or the Rubin method are known to be limited to structures with small coupling interfaces. This paper investigates two interface‐reduction methods for application of MOR to systems with large coupling interfaces: for the Craig–Bampton method a direct reduction method based on strain energy considerations is investigated. Additionally, for the Rubin method an iterative reduction scheme is proposed, which incrementally constructs the reduction basis. Hereby, attachment modes are tested if they sufficiently enlarge the spanned subspace of the current reduction basis. If so, the m‐orthogonal part is used to augment the basis. The methods are applied to FE–BE coupled systems in order to predict the vibro‐acoustic behavior of structures, which are partly immersed in water. Hereby, a strong coupling scheme is employed, since for dense fluids the feedback of the acoustic pressure onto the structure is not negligible. For two example structures, the efficiency of the reduction methods with respect to numerical effort, memory consumption and computation time is compared with the exact full‐order solution. Copyright © 2008 John Wiley & Sons, Ltd.     

Hot compressive deformation behavior and microstructure evolution of Ti–6Al–2Zr–1Mo–1V alloy at 1073 K

Hot compressive behaviors of Ti–6Al–2Zr–1Mo–1V alloy at 1073 K, as well as the evolution of microstructure during deformation process, were investigated in this paper. The results shows that flow stress increases up to a peak stress, then decease with increasing strain, and forms a stable stage at last. The grain size also shows an decrease at first and increase after a minimum value. Dislocations are observed to produce at the interface of α/β phase, and the phase interface and dislocation circle play an important role in impeding the movement of dislocation. As strain increase, micro-deformation bands with high-density dislocation are founded, and dynamic recrystallization occurs.     

An augmented Cartesian grid method for Stokes–Darcy fluid–structure interactions

A new finite difference method based on Cartesian meshes is proposed for solving the fluid–structure interaction between a fluid flow modeled by the Stokes equations and a porous media modeled by the Darcy's law. The idea is to introduce several augmented variables along the interface between the fluid flow and the porous media so that the problem can be decoupled as several Poisson equations. The augmented variables should be chosen so that the Beavers–Joseph–Saffman and other interface conditions are satisfied. In the discretization, the augmented variables have co‐dimension one compared with that of the primitive variables and are solved through the Schur complement system. A non‐trivial analytic solution with a circular interface is constructed to check second‐order convergency of the proposed method. Numerical examples with various interfaces and parameters are also presented. Some simulations show interesting behaviors of the fluid–structure interaction between the fluid flow and the porous media. The computational framework can be applied to other multi‐phase and multi‐physics problems. Copyright © 2015 John Wiley & Sons, Ltd.     

Generalized Robin–Neumann explicit coupling schemes for incompressible fluid‐structure interaction: Stability analysis and numerics

We introduce a new class of explicit coupling schemes for the numerical solution of fluid‐structure interaction problems involving a viscous incompressible fluid and an elastic structure. These methods generalize the arguments reported in [Comput. Methods Appl. Mech. Engrg., 267:566–593, 2013, Numer. Math., 123(1):21–65, 2013] to the case of the coupling with thick‐walled structures. The basic idea lies in the derivation of an intrinsic interface Robin consistency at the space semi‐discrete level, using a lumped‐mass approximation in the structure. The fluid–solid splitting is then performed through appropriate extrapolations of the solid velocity and stress on the interface. Based on these methods, a new, parameter‐free, Robin–Neumann iterative procedure is also proposed for the partitioned solution of implicit coupling. A priori energy estimates, guaranteeing the stability of the schemes and the convergence of the iterative procedure, are established within a representative linear setting. The accuracy and performance of the methods are illustrated in several numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of space mapping algorithms for application to partitioned fluid–structure interaction problems

Fluid–structure interactions (FSI) play a crucial role in many engineering fields. However, the computational cost associated with high‐fidelity aeroelastic models currently precludes their direct use in industry, especially for strong interactions. The strongly coupled segregated problem—that results from domain partitioning—can be interpreted as an optimization problem of a fluid–structure interface residual. Multi‐fidelity optimization techniques can therefore directly be applied to this problem in order to obtain the solution efficiently. In previous work, it is already shown that aggressive space mapping (ASM) can be used in this context. In this contribution, we extend the research towards the use of space mapping for FSI simulations. We investigate the performance of two other approaches, generalized space mapping and output space mapping, by application to both compressible and incompressible 2D problems. Moreover, an analysis of the influence of the applied low‐fidelity model on the achievable speedup is presented. The results indicate that output space mapping is a viable alternative to ASM when applied in the context of solver coupling for partitioned FSI, showing similar performance as ASM and resulting in reductions in computational cost up to 50% with respect to the reference quasi‐Newton method. Copyright © 2015 John Wiley & Sons, Ltd.     

A rheological interface model and its space–time finite element formulation for fluid–structure interaction

This contribution discusses extended physical interface models for fluid–structure interaction problems and investigates their phenomenological effects on the behavior of coupled systems by numerical simulation. Besides the various types of friction at the fluid–structure interface the most interesting phenomena are related to effects due to additional interface stiffness and damping. The paper introduces extended models at the fluid–structure interface on the basis of rheological devices (Hooke, Newton, Kelvin, Maxwell, Zener). The interface is decomposed into a Lagrangian layer for the solid‐like part and an Eulerian layer for the fluid‐like part. The mechanical model for fluid–structure interaction is based on the equations of rigid body dynamics for the structural part and the incompressible Navier–Stokes equations for viscous flow. The resulting weighted residual form uses the interface velocity and interface tractions in both layers in addition to the field variables for fluid and structure. The weak formulation of the whole coupled system is discretized using space–time finite elements with a discontinuous Galerkin method for time‐integration leading to a monolithic algebraic system. The deforming fluid domain is taken into account by deformable space–time finite elements and a pseudo‐structure approach for mesh motion. The sensitivity of coupled systems to modification of the interface model and its parameters is investigated by numerical simulation of flow induced vibrations of a spring supported fluid‐immersed cylinder. It is shown that the presented rheological interface model allows to influence flow‐induced vibrations. Copyright © 2010 John Wiley & Sons, Ltd.     

Ductile tearing analyses of cracked TP304 pipes using the multiaxial fracture strain energy model and the Gurson–Tvergaard–Needleman model

Ductile crack growth behaviours of TP304 pipes containing different circumferential defects were investigated in the study. Finite element (FE) damage analysis of the ductile fracture was carried out based on an uncoupled multiaxial fracture strain energy (MFSE) model with only two model parameters, which can be calibrated by data from tensile tests and fracture toughness tests. For the purpose of comparison, the Gurson–Tvergaard–Needleman (GTN) model was also employed in the FE damage analysis. It is observed that the MFSE model can reproduce the ductile tearing experiments as excellently as the GTN model does. Despite its simplicity, the MFSE model can reasonably predict the magnitudes of the crack initiation load and maximum load, the load‐line displacement, the crack mouth opening displacement, the crack extension and the crack profiles in the full‐scale cracked pipe tests.     

Identification of Johnson–Cook's Viscoplastic Model Parameters Using the Virtual Fields Method: Application to Titanium Alloy Ti6Al4V

Abstract: The identification of viscoplastic material parameters is addressed using a new powerful method: the virtual fields method (VFM). Contrary to classical procedures that are statically determined, the VFM is applied to heterogeneous mechanical fields. Without any hypotheses of homogeneity required, the exploitation of tests with the VFM is not limited to small levels of strains anymore and it can be taken advantage of the large amount of information available thanks to full‐field measurements. In the case of viscoplastic models, the characterisation of strain‐rate sensitivity with the VFM is attempted in this paper using only one test under high‐speed loading conditions, whereas several tests performed at different constant strain‐rates are required for the classical procedures. This article focuses on the development of the VFM for the characterisation of Johnson–Cook's (JC) viscoplastic model. To his aim a return‐mapping algorithm was developed according to the JC's model with an implicit Euler scheme implemented to integrate the constitutive relations. The whole viscoplastic behaviour of a Titanium alloy (Ti6Al4V) is successfully characterised by the VFM using only two tensile tests on notched flat specimens, with full‐field strain measurements by digital image correlation.     

The weak substitution method – an application of the mortar method for patch coupling in NURBS‐based isogeometric analysis

In this contribution, a mortar‐type method for the coupling of non‐conforming NURBS (Non‐Uniform Rational B‐spline) surface patches is proposed. The connection of non‐conforming patches with shared degrees of freedom requires mutual refinement, which propagates throughout the whole patch due to the tensor‐product structure of NURBS surfaces. Thus, methods to handle non‐conforming meshes are essential in NURBS‐based isogeometric analysis. The main objective of this work is to provide a simple and efficient way to couple the individual patches of complex geometrical models without altering the variational formulation. The deformations of the interface control points of adjacent patches are interrelated with a master‐slave relation. This relation is established numerically using the weak form of the equality of mutual deformations along the interface. With the help of this relation, the interface degrees of freedom of the slave patch can be condensated out of the system. A natural connection of the patches is attained without additional terms in the weak form. The proposed method is also applicable for nonlinear computations without further measures. Linear and geometrical nonlinear examples show the high accuracy and robustness of the new method. A comparison to reference results and to computations with the Lagrange multiplier method is given. Copyright © 2015 John Wiley & Sons, Ltd.     

Extrinsic cohesive modelling of dynamic fracture and microbranching instability in brittle materials

Dynamic crack microbranching processes in brittle materials are investigated by means of a computational fracture mechanics approach using the finite element method with special interface elements and a topological data structure representation. Experiments indicate presence of a limiting crack speed for dynamic crack in brittle materials as well as increasing fracture resistance with crack speed. These phenomena are numerically investigated by means of a cohesive zone model (CZM) to characterize the fracture process. A critical evaluation of intrinsic versus extrinsic CZMs is briefly presented, which highlights the necessity of adopting an extrinsic approach in the current analysis. A novel topology‐based data structure is employed to enable fast and robust manipulation of evolving mesh information when extrinsic cohesive elements are inserted adaptively. Compared to intrinsic CZMs, which include an initial hardening segment in the traction–separation curve, extrinsic CZMs involve additional issues both in implementing the procedure and in interpreting simulation results. These include time discontinuity in stress history, fracture pattern dependence on time step control, and numerical energy balance. These issues are investigated in detail through a ‘quasi‐steady‐state’ crack propagation problem in polymethylmethacrylate. The simulation results compare reasonably well with experimental observations both globally and locally, and demonstrate certain advantageous features of the extrinsic CZM with respect to the intrinsic CZM. Copyright © 2007 John Wiley & Sons, Ltd.     

On nucleation and propagation of PLC bands in an Al–3Mg alloy

The processes of nucleation and propagation of Portevin–LeChatelier deformation bands during tensile deformation of the alloy AA5754 have been investigated by a special optical technique for local strain measurements, combining both a line-scan and a CMOS camera to record the changes of surface strain, applying digital image correlation. Examples for bands of types A and B are observed and discussed with respect to the micro-mechanisms of their nucleation and propagation, emphasizing local stress concentrations in addition to the well-known effects of dynamic strain aging and dislocation interactions for explaining the PLC behavior. Finally the nucleation and propagation of PLC bands are simulated by computations based on a simple constitutive model.     

Experimental Investigations on Deformation and Fracture Behavior of Glass Sphere Filled Epoxy Functionally Graded Materials

In this paper, deformation and fracture behavior of glass sphere filled epoxy functionally graded materials (FGM) are numerically evaluated and experimentally studied. The fabrication of the FGM is described in detail, and the spatial gradation of elastic modulus and the microscopic structure in FGM are measured and analyzed. The deformation and fracture characterization of the FGM specimen with a crack oriented along the direction of the elastic gradient under three point bend are studied by the experimental and the finite element method. The influences of crack location at both the stiff and the compliant sides of the FGM specimen on crack initiation, deformation field and stress intensity factor are analyzed. The results are: (a) The neutral-axis in the FGM specimen under three-point-bending will shift toward the stiffer side; (b) The initial fracture load increases with the increase of elastic modulus at the crack tip; (c) The elastic gradients shield a crack on the compliant side and lower the stress intensity factor when compared to the one with crack on the stiff side. These results will be useful for better design and reliable evaluation of FGM.     

Analysis of transient flow in pipelines with fluid–structure interaction using method of lines

A mathematical model is presented for transient flow in a pipeline with fluid–structure interaction. Water hammer theory and equations of axial motion for the pipeline are employed and the Poisson, junction and transient shear stress couplings are taken into account, which give rise to four coupled non‐linear, first‐order hyperbolic partial differential equations governing the fluid flow and pipe motion. These equations are discretized in space using the Keller box scheme and the method of lines is employed to reduce the partial differential equations to a system of ordinary differential equations. The resulting system is solved using a backward differentiation formulation method. The effect of transient shear stress on transient flow is investigated and the mechanisms underlying this effect are explored. The results revealed that the influence of transient shear stress can be significant and varies considerably, depending on the boundary conditions, viz, valve closure time. Copyright © 2005 John Wiley & Sons, Ltd.     

Crack evolution law and failure mode of red sandstone under fatigue–creep interaction

To explore the fracture characteristics of rock under the interaction of fatigue load and creep load, fatigue–creep interactive loading experiments were performed on red sandstone with prefabricated cracks. The crack evolution process and failure mode were analyzed using acoustic emission technology and digital image correlation. The results showed that crack growth mainly occurred in the fatigue loading stage; the crack evolution of the sample could be divided into three stages: nucleation and initiation ( ), stable expansion ( ), and unstable fracture ( ). There were distinct differences in the crack propagation modes of the rock samples with different prefabricated crack angles. The relationship between the crack initiation angle and prefabricated crack angle was analyzed based on the maximum circumferential stress theory. Moreover, with an increase in the prefabricated crack angle, the rock sample gradually changed from compression–shear failure to tension–shear failure.