Effect of membrane bending stiffness on the deformation of capsules in simple shear flow

2001 ◽  
Vol 440 ◽  
pp. 269-291 ◽  
Author(s):  
C. POZRIKIDIS
Keyword(s):  
Curvature Tensor ◽  
Deformation Gradient ◽  
Bending Stiffness ◽  
Boundary Element Methods ◽  
Simple Shear Flow ◽  
Normal Vector ◽  
Membrane Thickness ◽  
Bending Moments ◽  
Balance Equations ◽  
Capsule Deformation

The effect of interfacial bending stiffness on the deformation of liquid capsules enclosed by elastic membranes is discussed and investigated by numerical simulation. Flow-induced deformation causes the development of in-plane elastic tensions and bending moments accompanied by transverse shear tensions due to the non-infinitesimal membrane thickness or to a preferred configuration of an interfacial molecular network. To facilitate the implementation of the interfacial force and torque balance equations involving the hydrodynamic traction exerted on either side of the interface and the interfacial tensions and bending moments developing in the plane of the interface, a formulation in global Cartesian coordinates is developed. The balance equations involve the Cartesian curvature tensor defined in terms of the gradient of the normal vector extended off the plane of the interface in an appropriate fashion. The elastic tensions are related to the surface deformation gradient by constitutive equations derived by previous authors, and the bending moments for membranes whose unstressed shape has uniform curvature, including the sphere and a planar sheet, arise from a constitutive equation that involves the instantaneous Cartesian curvature tensor and the curvature of the resting configuration. A numerical procedure is developed for computing the capsule deformation in Stokes flow based on standard boundary-element methods. Results for spherical and biconcave resting shapes resembling red blood cells illustrate the effect of the bending modulus on the transient and asymptotic capsule deformation and on the membrane tank-treading motion.

Explicit Analytical Solutions for a Complete Set of the Eshelby Tensors of an Ellipsoidal Inclusion

2016 ◽  
Vol 83 (12) ◽  
Author(s):  
Xiaoqing Jin ◽  
Ding Lyu ◽  
Xiangning Zhang ◽  
Qinghua Zhou ◽  
Qian Wang ◽  
...  
Keyword(s):  
Deformation Gradient ◽  
Elastic Field ◽  
Analytical Form ◽  
Ellipsoidal Inclusion ◽  
Normal Vector ◽  
Full Field ◽  
Practical Applications ◽  
Starting Point ◽  
Complete Set ◽  
Outward Unit

The celebrated solution of the Eshelby ellipsoidal inclusion has laid the cornerstone for many fundamental aspects of micromechanics. A well-known difficulty of this classical solution is to determine the elastic field outside the ellipsoidal inclusion. In this paper, we first analytically present the full displacement field of an ellipsoidal inclusion subjected to uniform eigenstrain. It is demonstrated that the displacements inside inclusion are linearly related to the coordinates and continuous across the interface of inclusion and matrix. The exterior displacement, which is less detailed in existing literatures, may be expressed in a more compact, explicit, and simpler form through utilizing the outward unit normal vector of an auxiliary confocal ellipsoid. Other than many practical applications in geological engineering, the displacement solution can be a convenient starting point to derive the deformation gradient, and subsequently in a straightforward manner to accomplish the full-field solutions of the strain and stress. Following Eshelby's definition, a complete set of the Eshelby tensors corresponding to the displacement, deformation gradient, strain, and stress are expressed in explicit analytical form. Furthermore, the jump conditions to quantify the discontinuities across the interface are discussed and a benchmark problem is provided to validate the present formulation.

Numerical simulation of capsule deformation in simple shear flow

2010 ◽  
Vol 39 (2) ◽  
pp. 242-250 ◽  
Author(s):  
Y. Sui ◽  
X.B. Chen ◽  
Y.T. Chew ◽  
P. Roy ◽  
H.T. Low
Keyword(s):  
Numerical Simulation ◽  
Shear Flow ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Capsule Deformation

Dynamics of capsules enclosing viscoelastic fluid in simple shear flow

2018 ◽  
Vol 840 ◽  
pp. 656-687 ◽  
Author(s):  
Zheng Yuan Luo ◽  
Bo Feng Bai
Keyword(s):  
Shear Flow ◽  
Viscoelastic Fluid ◽  
Simple Shear ◽  
Deformation Behaviour ◽  
Three Dimensional ◽  
High Viscosity ◽  
Deborah Number ◽  
Simple Shear Flow ◽  
Capsule Deformation ◽  
Internal Fluid

Previous studies on capsule dynamics in shear flow have dealt with Newtonian fluids, while the effect of fluid viscoelasticity remains an unresolved fundamental question. In this paper, we report a numerical investigation of the dynamics of capsules enclosing a viscoelastic fluid and which are freely suspended in a Newtonian fluid under simple shear. Systematic simulations are performed at small but non-zero Reynolds numbers (i.e. $Re=0.1$) using a three-dimensional front-tracking finite-difference model, in which the fluid viscoelasticity is introduced via the Oldroyd-B constitutive equation. We demonstrate that the internal fluid viscoelasticity presents significant effects on the deformation behaviour of initially spherical capsules, including transient evolution and equilibrium values of their deformation and orientation. Particularly, the capsule deformation decreases slightly with the Deborah number De increasing from 0 to $O(1)$. In contrast, with De increasing within high levels, i.e. $O(1{-}100)$, the capsule deformation increases continuously and eventually approaches the Newtonian limit having a viscosity the same as the Newtonian part of the viscoelastic capsule. By analysing the viscous stress, pressure and viscoelastic stress acting on the capsule membrane, we reveal that the mechanism underlying the effects of the internal fluid viscoelasticity on the capsule deformation is the alterations in the distribution of the viscoelastic stress at low De and its magnitude at high De, respectively. Furthermore, we find some new features in the dynamics of initially non-spherical capsules induced by the internal fluid viscoelasticity. Particularly, the transition from tumbling to swinging of oblate capsules can be triggered at very high viscosity ratios by increasing De alone. Besides, the critical viscosity ratio for the tumbling-to-swinging transition is remarkably enlarged with De increasing at relatively high levels, i.e. $O(1{-}100)$, while it shows little change at low De, i.e. below $O(1)$.

scholarly journals Homogenized Balance Equations for Nonlinear Poroelastic Composites

2021 ◽  
Vol 11 (14) ◽  
pp. 6611
Author(s):  
Laura Miller ◽  
Raimondo Penta
Keyword(s):  
Deformation Gradient ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Type Model ◽  
Nonlinear Behaviour ◽  
Pore Scale ◽  
Balance Equations ◽  
The Matrix ◽  
Elastic Composites ◽  
Porous Composites

Within this work, we upscale the equations that describe the pore-scale behaviour of nonlinear porous elastic composites, using the asymptotic homogenization technique in order to derive the macroscale effective governing equations. A porous hyperelastic composite can be thought of as being comprised of a matrix interacting with a number of subphases and percolated by a fluid flowing in the pores (which is chosen to be Newtonian and incompressible here). A general nonlinear macroscale model is derived and is then specified for a particular choice of strain energy function, namely the de Saint-Venant function. This leads to a macroscale system of PDEs, which is of poroelastic type with additional terms and transformations to account for the nonlinear behaviour of the material. Our new porohyperelastic-type model describes the effective behaviour of nonlinear porous composites by prescribing the stress balance equations, the conservation of mass and Darcy’s law. The coefficients of these macroscale equations encode the detailed microstructure of the material and are to be found by solving pore-scale differential problems. The model reduces to the following limit cases of (a) linear poroelastic composites when the deformation gradient approaches the identity, (b) nonlinear composites when there are no pores and (c) nonlinear poroelasticity when only the matrix–fluid interaction is considered. This model is applicable when the interactions between various hyperelastic solid phases occur at the pore-scale, as in biological tissues such as artery walls, the myocardium, lungs and liver.

Influence of internal viscosity on the large deformation and buckling of a spherical capsule in a simple shear flow

2011 ◽  
Vol 672 ◽  
pp. 477-486 ◽  
Author(s):  
É. FOESSEL ◽  
J. WALTER ◽  
A.-V. SALSAC ◽  
D. BARTHÈS-BIESEL
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Viscosity Ratio ◽  
Fluid Motion ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Simple Shear Flow ◽  
Flow Strength ◽  
Capsule Deformation ◽  
Internal Viscosity

The motion and deformation of a spherical elastic capsule freely suspended in a simple shear flow is studied numerically, focusing on the effect of the internal-to-external viscosity ratio. The three-dimensional fluid–structure interactions are modelled coupling a boundary integral method (for the internal and external fluid motion) with a finite element method (for the membrane deformation). For low viscosity ratios, the internal viscosity affect the capsule deformation. Conversely, for large viscosity ratios, the slowing effect of the internal motion lowers the overall capsule deformation; the deformation is asymptotically independent of the flow strength and membrane behaviour. An important result is that increasing the internal viscosity leads to membrane compression and possibly buckling. Above a critical value of the viscosity ratio, compression zones are found on the capsule membrane for all flow strengths. This shows that very viscous capsules tend to buckle easily.

scholarly journals Osserman Lightlike Hypersurfaces on a Foliated Class of Lorentzian Manifolds

2016 ◽  
Vol 8 (2) ◽  
pp. 55
Author(s):  
C. Atindogbe ◽  
K. L. Duggal
Keyword(s):  
Curvature Tensor ◽  
Constant Curvature ◽  
Open Subset ◽  
Normal Vector ◽  
Lorentzian Manifolds ◽  
Schwarzschild Spacetime ◽  
Osserman Manifold ◽  
The Family ◽  
Characterization Theorems ◽  
Lightlike Hypersurfaces

This paper deals with a family of Osserman lightlike hypersurfaces $(M_u)$ of a  class of Lorentzian manifolds $\bar{M}$ such that its each null normal vector is defined on some open subset of $\bar{M}$ around $M_u$.  We prove that a totally umbilical family of lightlike hypersurfaces of a connected Lorentzian pointwise Osserman manifold of constant curvature is locally Einstein and pointwise ${\cal F}-$Osserman, where our foliation approach provides the required algebraic symmetries of the induced curvature tensor. Also we prove two new characterization theorems for the family  of Osserman lightlike hypersurfaces, supported by a physical example of Osserman lightlike hypersurfaces of the Schwarzschild spacetime.

scholarly journals Experimental Analysis of Bending Stiffness Characteristics of Grouted Double Mortise-Tenon Joint for Prefabricated Metro Station Structure

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Xiuren Yang ◽  
Fang Lin ◽  
Meiqun Huang
Keyword(s):  
Variable Stiffness ◽  
Bending Stiffness ◽  
Bending Moments ◽  
Underground Structures ◽  
Axial Loads ◽  
Characteristic Analysis ◽  
Metro Station ◽  
Prototype Test ◽  
Stiffness Characteristics ◽  
Station Structure

The grouted mortise-tenon joint, invented as the connection between the large prefabricated components, is the key to the prefabricated underground structures, and the double-tenon joint is most widely used in the prefabricated metro station structure. This paper conducts characteristic analysis of bending stiffness with a 1 : 1 prototype test in key working direction of different joint types for grouted double mortise-tenon joint. The results show that the double-tenon joint is characteristic of variable stiffness under different loads. Change laws of double-tenon joint bending stiffness without and with auxiliary pretightening device in tension side and compression side are also discussed. The correlations for calculating double-tenon joint bending stiffness with various axial loads and bending moments are derived at last, which offers the theory foreshadowing of similar joints.

On Beltrami-Michell-Like Equations for Nonlinear Elastic Dielectrics

1986 ◽  
Vol 10 (3) ◽  
pp. 167-173
Author(s):  
S. Dost ◽  
P.G. Glockner
Keyword(s):  
Stress Field ◽  
Deformation Gradient ◽  
Polarization Vector ◽  
Balance Equations ◽  
Independent Field ◽  
Polarization Gradient ◽  
Nonlinear Elastic

Beltrami-Michell-like equations for nonlinear elastic dielectrics are obtained by choosing the deformation gradient, the polarization gradient and the polarization vector as independent field variables, so as to yield linear compatibility equations. The corresponding stress field also yields linear balance equations. Two simple examples for the case of semilinear isotropic elastic dielectrics are solved to illustrate the theory.

scholarly journals Nonlinear morphoelastic plates I: Genesis of residual stress

2011 ◽  
Vol 16 (8) ◽  
pp. 812-832 ◽  
Author(s):  
Joseph McMahon ◽  
Alain Goriely ◽  
Michael Tabor
Keyword(s):  
Residual Stress ◽  
Elastic Body ◽  
Response Function ◽  
Deformation Gradient ◽  
Global Constraint ◽  
Balance Equations ◽  
Multiplicative Decomposition ◽  
Rigorous Analysis ◽  
Volumetric Growth ◽  
Residual Strains

Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis is given of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate. Balance equations are derived via the Global Constraint Principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed, and the existence of residually stressed states is established.

Effects of Ambipolar Diffusion on Prominence Thread Models

1994 ◽  
Vol 144 ◽  
pp. 315-321 ◽  
Author(s):  
M. G. Rovira ◽  
J. M. Fontenla ◽  
J.-C. Vial ◽  
P. Gouttebroze
Keyword(s):  
Energy Balance ◽  
Transition Region ◽  
Ambipolar Diffusion ◽  
Line Profiles ◽  
Balance Equations ◽  
Model Calculations ◽  
Partial Frequency ◽  
Frequency Redistribution ◽  
Partial Frequency Redistribution ◽  
Theoretical Structure

AbstractWe have improved previous model calculations of the prominence-corona transition region including the effect of the ambipolar diffusion in the statistical equilibrium and energy balance equations. We show its influence on the different parameters that characterize the resulting prominence theoretical structure. We take into account the effect of the partial frequency redistribution (PRD) in the line profiles and total intensities calculations.

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