Large deformation frictional contact analysis with immersed boundary method

Navarro‐Jiménez, José Manuel; Tur, M.; Albelda, José Luis; Ródenas, Juan José

doi:10.1007/s00466-017-1533-x

Cited by 8 publications

(16 citation statements)

References 45 publications

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“…The total force ( ) acting on the -th vertex of the immersed surface is evaluated in time accounting for both internal, Eq.s (11), (13), and (14), and external stresses, Eq.s (15) and (16); then, the position of the vertices is updated at each Newtonian dynamic time step considering the membrane mass uniformly distributed over the vertices [50,51]:…”

Section: Deformable Structures Motionmentioning

confidence: 99%

Kinematic and dynamic forcing strategies for predicting the transport of inertial capsules via a combined lattice Boltzmann – Immersed Boundary method

et al. 2019

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Modeling the transport of deformable capsules under different flow regimens is crucial in a variety of fields, including oil rheology, blood flow and the dispersion of pollutants.The aim of this study is twofold. Firstly, a combined Lattice Boltzmann -Immersed Boundary (LBM -IB) approach is developed for predicting the transport of inertial deformable capsules. A Moving Least Squares (MLS) scheme has been implemented to correlate the pressure, velocity and force fields of the fluid domain with the capsule dynamics. This computational strategy has been named LBM -Dynamic IB. Secondly, this strategy is directly compared with a more conventional approach, named LBM -Kinematic IB, where capsules move with the same velocity of the surrounding fluid.Multiple test cases have been considered for assessing the accuracy and efficiency of the Dynamic over Kinematic IB scheme, including the stretching of circular capsules in shear flow, the transport in a plane Poiseuille flow of circular and biconcave capsules, with and without inertia. By monitoring the capsule geometry over time, the two schemes have been documented to be in excellent agreement, especially for low Capillary numbers (Ca ≤ 10 -2 ), in the case of non-inertial capsules. Despite a moderate increase in computational burden, the presented LBM -Dynamic IB scheme is the sole capable of predicting the dynamics of both non-inertial and inertial deformable capsules.The proposed approach can be efficiently employed for studying the transport of blood cells, cancer cells and nano/micro capsules within a capillary flow. 3 INTRODUCTIONThe coupling between fluid and structure dynamics is of great relevance in different disciplines. Biophysicists are investing increasingly more efforts into modeling the flow of complex fluids, such as whole blood, to better understand the mechanisms underlying the development of diseases and their possible cure. [1][2][3][4] In a wide range of engineering problems, there is a growing demand to investigate the rheology of active fluids, oils, polymeric suspension, or colloidal mixtures moving into tortuous channels, with either fixed or variable geometries. This is specifically the case of enhanced oil recovery, trickle bed reactors, and microfluidics devices. [5][6][7][8][9][10][11][12] Regardless of the application, it is easy to recognize that immersed structures may be dragged away downstream by large distances, far from their original locations, or significantly deformed due to an incoming flux. On this premise, it is crucial to have access to computational tools capable of efficiently handle the variation in time of immersed geometries without any loss of accuracy. [13][14][15][16] One of the most suitable computational technique to deal with the motion and deformation of particles into fluids is the Immersed Boundary (IB) method, which was originally developed by Peskin in 1972 to simulate cardiac mechanics [17]. This technique prescribes the evolution of the fluid on an Eulerian Cartesian grid, which is not conforming to the geomet...

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Section: Deformable Structures Motionmentioning

confidence: 99%

Kinematic and dynamic forcing strategies for predicting the transport of inertial capsules via a combined lattice Boltzmann – Immersed Boundary method

et al. 2019

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“…Matrix C iee and a vector iee are built such that each row represents the enforced constraint (15), that is:…”

Section: Spr-c Constraints Enforcementmentioning

confidence: 99%

“…The cgFEM features an efficient hierarchical data structure based on the use of nested Cartesian grids together with a special numerical integration procedure that enables one to capture the exact boundary definition through the use of NURBS. This method has been recently extended to solve 3D frictional contact problems with a stabilized Lagrangian formulation in which the stabilization term is calculated with the SPR stress field. Moreover, the cgFEM features an h ‐adaptive refinement strategy based on the ZZ estimator and the SPR technique .…”

Section: Introductionmentioning

confidence: 99%

Superconvergent patch recovery with constraints for three‐dimensional contact problems within the Cartesian grid Finite Element Method

Navarro‐Jiménez

Navarro-García

Tur

et al. 2019

Numerical Meth Engineering

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Summary The superconvergent patch recovery technique with constraints (SPR‐C) consists in improving the accuracy of the recovered stresses obtained with the original SPR technique by considering known information about the exact solution, like the internal equilibrium equation, the compatibility equation or the Neumann boundary conditions, during the recovery process. In this paper the SPR‐C is extended to consider the equilibrium around the contact area when solving contact problems with the Cartesian grid Finite Element Method. In the proposed method, the Finite Element stress fields of both bodies in contact are considered during the recovery process and the equilibrium is enforced by means of the continuity of tractions along the contact surface.

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Section: Introductionmentioning

confidence: 99%

“…In [26] the deformed surface is defined as a combination of the undeformed CAD geometry and the finite element displacement field. This paper can be considered as an extension of [26], where we study the effect of the surface definition (hence the contact gap) when solving frictionless contact problems with cgFEM. In addition to the previous approaches, linear facets and a combination of FE solution and NURBS surface, in this work we propose a new method in which the deformed configuration is defined as a NURBS surface, i.e., the control points of the original CAD surface are updated such that the new configuration fits the finite element displacement field of the contact surface.…”

Section: Introductionmentioning

confidence: 99%

On the effect of the contact surface definition in the Cartesian grid finite element method

Navarro‐Jiménez

Tur

Fuenmayor

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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The definition of the surface plays an important role in the solution of contact problems, as the evaluation of the contact force is based on the measure of the gap between the solids. In this work three different methods to define the surface are proposed for the solution of contact problems within the framework of the 3D Cartesian grid finite element method. A stabilized formulation is used to solve the contact problem and details of the kinematic description for each surface definition are provided. The three methods are compared solving some numerical tests involving frictionless contact with finite and small deformations.

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Large deformation frictional contact analysis with immersed boundary method

Cited by 8 publications

References 45 publications

Kinematic and dynamic forcing strategies for predicting the transport of inertial capsules via a combined lattice Boltzmann – Immersed Boundary method

Kinematic and dynamic forcing strategies for predicting the transport of inertial capsules via a combined lattice Boltzmann – Immersed Boundary method

Superconvergent patch recovery with constraints for three‐dimensional contact problems within the Cartesian grid Finite Element Method

On the effect of the contact surface definition in the Cartesian grid finite element method

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