The effect of fiber recruitment on the swelling of a pressurized anisotropic non-linearly elastic tube

We study the effect of fiber recruitment on the mechanical response of a fiber reinforced non-linearly elastic tube that is both swollen and pressurized. Attention is restricted to cylindrically symmetric tube deformation. The constitutive model permits fibers to support tension, but not compression. While many combinations of pressure and swelling cause all of the fibers to be recruited for load support, both large swelling and large deswelling can give rise to fiber derecruitment at certain locations in the tube. This leads to less channel opening than would be the case if the fibers provided support while contracted. The transition between mechanically active and mechanically inactive fibers can be described in terms of the quasi-static motion of a fiber recruiting interface.     

Fiber Remodeling During Torsion of a Fiber Reinforced Hyperelastic Cylinder��Unloading Behavior

Previous studies introduced a constitutive theory for fiber reinforced hyperelastic materials that allows the fibers to undergo microstructural changes. In this theory, increasing deformation of the matrix leads to increasing stretch of the fibers that causes their gradual dissolution. The dissolving fibers reassemble in the direction of maximum principal stretch of the matrix. The implications of the constitutive theory were first studied for two homogeneous deformations: uniaxial extension along the fibers and simple shear in the direction normal to the fibers. The constitutive theory was then used in treatment of the non-homogeneous deformation of combined axial stretch and twisting. The emphasis was on the determination of the influence of increasing axial stretch and twist on the spatial distribution of fiber dissolution and reassembly within the cylinder and also on the axial force and torque applied to the end faces of the cylinder. The present work is concerned with another aspect of combined axial stretch and twisting of the cylinder, namely unloading following dissolution and reassembly of some of the fibers. In this case, the cylinder is given an initial twist until there is an inner core of original fiber/matrix material and an outer sheath of remodeled fiber/matrix material. A condition is established that determines the combinations of axial stretch and twist that cause no additional dissolution and reassembly of fibers during unloading. It is also shown that there is a residual axial stretch and twist if the axial force and torque become zero. A numerical example illustrates this for a particular choice of matrix and fiber properties.     

A mathematical model for cylindrical,fiber reinforced electro-pneumatic actuators

In recent years, dielectric elastomers have received increasing attention due to their unparalleled large strain actuation response (>100%). The force output, however, has remained a major limiting factor for many applications. To address this limitation, a model for a fiber reinforced dielectric elastomer actuator based on the deformation mechanism of McKibben actuators is presented. In this novel configuration, the outer cylindrical surface of a dielectric elastomer is enclosed by a network of helical fibers that are thin, flexible and inextensible. This configuration yields an axially contractile actuator, in contrast to unreinforced actuators which extend. The role of the fiber network is twofold: (i) to serve as reinforcement to improve the load-bearing capability of dielectric elastomers, and (ii) to render the actuator inextensible in the axial direction such that the only free deformation path is simultaneous radial expansion and axial contraction. In this paper, a mathematical model of the electromechanical response of fiber reinforced dielectric elastomers is derived. The model is developed within a continuum mechanics framework for large deformations. The cylindrical electro-pneumatic actuator is modeled by adapting Green and Adkins’ theory of reinforced cylinders to account for the applied electric field. Using this approach, numerical solutions are obtained assuming a Mooney–Rivlin material model. The results indicate that the relationship between the contractile force and axial shortening is bilinear within the voltage range considered. The characteristic response as a function of various system parameters such as the fiber angle, inflation pressure, and the applied voltage are reported. In this paper, the elastic portion of the modeling approach is validated using experimental data for McKibben actuators.     

角蛋白组织摩擦学性能及其损伤自修复的初步研究

采用纳米压痕/划痕仪和维氏硬度仪,初步研究了2种不同角蛋白材料-指甲和鸡爪的摩擦学性能及其损伤自修复特性.结果表明:指甲和鸡爪微观结构的不同导致其摩擦学性能和自修复能力有较大差异.由于具有更好的纤维取向性,指甲表面的划痕摩擦系数略低于鸡爪.指甲横截面上垂直于纤维方向的划痕摩擦力比平行于纤维方向的大,划痕宽度小;鸡爪内外层结构的不同使得其外层的摩擦力较大,划痕宽度较小.浸泡在水中,指甲和鸡爪上的压痕变形和低载下的划痕变形能够分别在5和30 min内完全恢复.     

Swelling of an internally pressurized nonlinearly elastic tube with fiber reinforcing

We study the effect of swelling on the mechanical response of fiber reinforced tubes within the context of finite elastic deformation. The fibers themselves do not swell, setting up a competition between the matrix, for which swelling tends to open the tube, and the fibers, for which swelling tends to constrict the tube. Balancing these tendencies in the constitutive response can lead to an internal channel opening that remains relatively constant over a wide range of swelling. Further, the hoop stress on the inner wall in such a situation may be compressive, rather than tensile. Both effects may be advantageous in certain settings, including biological organ systems.     

Tension of a cylindrical membrane partially stretched over a rigid cylinder

We study a contact problem with friction for a hyperelastic long thin-walled tube. One end of the tube is placed over an immovable, rough, rigid cylinder and an axial force is applied to another end. We assume the deformation of the tube is finite and axisymmetric. The tube is modeled by a semi-infinity cylindrical membrane. The axial force tends to a constant value at large distances from the inclusion. The membrane is made of an incompressible, homogeneous, isotropic elastic material. A contact between the membrane and the rigid cylinder is with a dry friction. The membrane will not slide off the cylinder only by friction and at a sufficient contact area. The friction is described by Coulomb’s law. We study a minimum length of the membrane which is in contact with the rigid cylinder and is needed to hold the membrane on the rigid cylinder. We obtain an explicit solution for the Bartenev–Khazanovich (Varga) strain–energy function and numerical results for the Mooney–Rivlin and Fung models.     

Investigation of fiber motion near solid boundaries in simple shear flow

In this paper, fiber motion near a planar wall was investigated using a planar shear flow apparatus. Fibers were placed (one at a time) perpendicular to the flow direction at various locations throughout the flow field. The location and orientation of each fiber versus time was measured, using an image processing system, until the fiber aligned with the flow direction. When the centroid of the fiber was located at distances greater than a fiber length from the wall, Jeffery's equations governing particle motion were verified. For distances less than a fiber length and greater than a fiber diameter from the wall, the fiber experienced an increased rate of rotation. In this regime, the motion of the fiber could be described by Jeffery's equations if an increased effective shear rate was used. The effective shear rate was found to increase logarithmically with decreasing separation distance. The wall effect was higher for longer aspect ratio fibers and was also a function of orientation; fibers oriented perpendicular to the wall rotated faster than those oriented parallel to the wall at the same separation distance. Once the fiber aligned with the flow direction, it ceased to rotate within the field of view. In this orientation, the wall had a stabilizing effect on the fiber. In efforts to relate the increase in shear rate to the aspect ratio of the fiber and the separation distance between the fiber and a solid wall, a translation model based on the work of De Mestre and Russel was explored. This model allows one to quantify the increase in shear rate experienced by the fiber due to the presence of a wall or obstruction in the flow field. However, the model has its limitations and care should be taken when applying this model outside its realm of validity. When compared to experimental data, the translation model provides a very good estimate of the increased shear rate experienced by the fiber when it is located less than 2/3 of a fiber length from a planar wall. Received: 20 April 2000 Accepted: 28 September 2000     

Influence on fiber inclination and interfacial conditions on fracture in composite materials

Dynamic photoelasticity has been used to study the effect of the fiber-matrix interface and fiber orientation on dynamic crack growth in fiber composites. Two types of fiber-matrix interfaces are considered: well bonded and partly debonded. The fiber-matrix interface is characterized by conducting fiber pullout tests. Partly debonded fibers aligned with the loading direction, result in higher fiber debonded lengths, lower dynamic stress-intensity factorK _ID and lower fracture surface roughness compared to well bonded fibers. Orientation of brittle fibers, with respect to the loading direction, impairs their ability to lowerK _ID , while oriented ductile fibers produce no significant change inK _ID . Misalignment of fibers from the loading direction reduces the fiber debonded length due to kinding of the fiber at the crack face.     

Spherical indentation of composite laminates with controlled gradients in elastic anisotropy

Three-dimensional elastic analyses and experiments of indentation of thick laminated plates of carbon fiber reinforced epoxy are presented. Pointwise, the material is characterized as a linear elastic orthotropic material. The in-plane orientation of the carbon fibers is systematically varied as a function of depth. The influence of fiber orientation as a function of depth on the indentation response is considered along with the relationship between the indenter force vs depth. The fiber orientation profiles considered are those of a continuous linear variation between 90° at the outer surfaces and 0° at the center plane of the laminate, and a cross ply laminate involving alternating 90° and 0° layers through thickness. Experimentally, it is found that for the case of a cross-ply laminate, the indentation produces delaminations localized at the interfaces that separate planes of dissimilar orientation. For this case, stress concentrations at interfaces between plies of dissimilar orientation coincide with the observed sites of delamination. For the graded case, evidence of enhanced nonlinear deformation is found, without the nucleation of cracks. Computations show that for the graded material, tensile stresses perpendicular to fibers are suppressed significantly, possibly explaining the absence of matrix cracks in this material. Measured and computed indenter force-depth variations were found to be in good agreement. Experiments and computations also reveal that the orientation-graded material is more compliant when subjected to indentation than the conventional cross-ply laminate.     

Simulation of fiber reinforced composite materials mold filling process and mechanical properties analysis

A dynamic simulation of fiber reinforced composite materials mold filling process with double inlets is presented based on the gas–solid–liquid model proposed by Yang et al. [B.X. Yang, J. Ouyang, J. Tao, C.T. Liu, Modeling and simulation of fiber reinforced polymer mold filling process by level set method, CMES – Computer Modeling in Engineering and Sciences 63 (3) (2010) 191–222]. Numerical results show that the fibers far away from the melt interface are in skin-core-skin structure, while those near the interface are almost parallel to the arc of the interface. When the two streams of melts meet, the weld line will be formed, where the orientation of fibers is perpendicular to the flow direction. The orientation of fibers of the numerical result shows well agreement with the experimental results. Finally, the mechanical properties of fiber reinforced composite materials are analyzed. The composite materials with skin-core-skin structure are regarded as laminated orthogonal plywood and the elastic modulus, the shear modulus and Poisson’s ratio are predicted under different slenderness ratios and fiber volume fractions.     

泡沫铝夹芯双圆管结构的准静态轴向压缩性能研究

对泡沫铝夹芯双圆管结构的准静态轴压性能进行了实验研究,发现该新型结构的比质量吸能效率远远高于传统的泡沫铝夹芯单管,并接近甚至超过相应的空管结构;其内外管变形模式均与空管不同且受内外管组合的影响.本文讨论了它的变形机理,分析了外管壁厚对其压缩行为的影响,发现增大外管壁厚有利于增大结构的行程利用率,提高结构的比质量能量吸收...     

Strain gradient elasticity and stress fibers

Since stress fibers have micro-size dimensions, their biomechanical behavior should demand mechanical models conforming with gradient strain deformation theories. In particular, the torsion and the stretching of stress fibers are discussed into the context of strain gradient elasticity theory and their size effects. It is proven for the torsion problem that the torsion moment varies with the axial length of the bar for constant twist angle, whereas for the simple tension problem, the strain is non-uniform along the stress fiber. The proposed theory is supported by experimental evidence.     

EFFECTS OF TENSOR CLOSURE MODELS AND 3-D ORIENTATION ON THE STABILITY OF FIBER SUSPENSIONS IN A CHANNEL FLOW

IntroductionFlowoffibresuspensionshasbeenveryfamiliarinmanyindustrialfields.Fibreadditivesplayanimportantroleindragreductioninmanytypesofflow[1- 3].Inthesuspensions,somebehavioroftheflowmaybealteredbythefibres.Oneoftheimportantexamplesisthehydrodynamicsta…     

Mechanical model for fiber-laden membranes

An integrated mechanical model for fiber-laden membranes is presented and representative predictions of relevance to cellulose ordering and orientation in the plant cell wall are presented. The model describes nematic liquid crystalline self-assembly of rigid fibers on an arbitrarily curved fluid membrane. The mechanics of the fluid membrane is described by the Helfrich bending-torsion model, the fiber self-assembly is described by the 2D Landau-de Gennes quadrupolar Q-tensor order parameter model, and the fiber-membrane interactions (inspired by an extension of the 2D Maier-Saupe model to curved surfaces) include competing curvo-philic (curvature-seeking) and curvo-phobic (curvature-avoiding) effects. Analysis of the free energy reveals three fiber orientation regimes: (a) along the major curvature, (b) along the minor curvature, (c) away from the principal curvatures, according to the competing curvo-philic and curvo-phobic interactions. The derived shape equation (normal stress balance) now includes curvature-nematic ordering contributions, with both bending and torsion renormalizations. Integration of the shape and nematic order equations gives a complete model whose solution describes the coupled membrane shape/fiber order state. Applications to cylindrical membranes, relevant to the plant cell wall, shows how growth decreases the fiber order parameter and moves the fibers’ director from the axial direction towards the azimuthal orientation, eventually leading to a state of stress predicted by pure membranes. The ubiquitous 54.7° cellulose fibril orientation with respect to the long axis in a cylindrical plant cell wall is shown to be predicted by the preset model when the ratio of curvo-phobic and curvo-philic interactions is in the range of the cylinder radius.     

Simulation of crack propagation in fiber-reinforced bulk metallic glasses

Based on a phase-field model for deformation in bulk metallic glasses (BMGs), shear band formation and crack propagation in the fiber-reinforced BMG are investigated. Ideal unbroken fibers embedded in the BMG matrix are found to significantly influence the shear banding and crack propagation in the matrix. The crack propagation affected by fibers’ length and orientation is quantitatively characterized and is described by micromechanics models for composite materials. Furthermore, fractures in some practical fiber-reinforced BMG composites such as tungsten-reinforced Zr-based BMG are simulated. The relation between the enhanced fracture toughness and the mechanical properties of fiber reinforcements is determined. Different fracture modes of BMG-matrix composites are identified from the systematic simulation studies, which are found to be consistent with experiments. The simulation results suggest that the phase-field modeling approach could be a useful tool to assist the fabrication and design of BMG composites with high fracture toughness and ductility.     

Numerical prediction of fiber motion in a branching channel flow of fiber suspensions

Fiber orientation and dispersion in the dilute fiber suspension that flows through a T-shaped branching channel are simulated numerically based on the slender-body theory. The simulated results are consistent qualitatively with the experimental data available in the literature. The results show that the spatial distribution of fibers is dependent on the fiber aspect ratio, but has no relation with the volume fraction of fiber. The content ratio of fibers near the upper wall increases monotonically with an increasing Re number, and the situation is reverse for the region near the bottom wall. The orientation of fibers depends on Re number, however, the function of fiber volume fraction and aspect ratio is negligible. The fibers near the wall and in the central region of the channel align along the flow direction at all times, but the fibers in the other parts of the channel tend to align along the flow direction only in the downstream region.The project supported by the National Natural Science Foundation of China (10372090) and Doctoral Program of Higher Education in China (20030335001)The English text was polished by Ron Marshall     

Cylindrical membrane partially stretched on a rigid cylinder

We consider the equilibrium problem of a hyperelastic thin-walled tube. One end of the tube is placed over an immovable, rough, rigid cylinder. We assume that the deformation of the tube is finite and axisymmetric. The tube is modeled by a cylindrical membrane. The membrane is composed of an incompressible, homogeneous, isotropic elastic material. We use Bartenev–Khazanovich (Varga) strain energy function. A contact between the membrane and the rigid cylinder is with a dry friction. The membrane will not slide off the cylinder only by a friction and at a sufficient contact area. The friction is described by Coulomb's law. We study a minimum length of the membrane which is in contact with the rigid cylinder and is needed to the equilibrium of the membrane.     

Finite elastic deformations of transversely isotropic circular cylindrical tubes

We consider the finite radially symmetric deformation of a circular cylindrical tube of a homogeneous transversely isotropic elastic material subject to axial stretch, radial deformation and torsion, supported by axial load, internal pressure and end moment. Two different directions of transverse isotropy are considered: the radial direction and an arbitrary direction in planes normal locally to the radial direction, the only directions for which the considered deformation is admissible in general. In the absence of body forces, formulas are obtained for the internal pressure, and the resultant axial load and torsional moment on the ends of the tube in respect of a general strain-energy function. For a specific material model of transversely isotropic elasticity, and material and geometrical parameters, numerical results are used to illustrate the dependence of the pressure, (reduced) axial load and moment on the radial stretch and a measure of the torsional deformation for a fixed value of the axial stretch.     

Debonding and fiber pull-out in reinforced composites

In order to evaluate the strength of fiber-reinforced composites, there is first the need to investigate the interfacial debonding and the pull-out of fibers in a fractured composite with intact fibers. This type of problem in crack bridging has been investigated by several authors based on different models and assumptions [1–7]. In this study, we will consider a three-dimensional model of a single fiber of finite length bonded by a finite cylindrical matrix with an initial crack existing in a portion of the interface. In the model, one end of the cylinder is so constrained that the axial component of displacement vanishes. A tensile stress is applied to the fiber at the other end. The aim is to determine the pull-out of the fiber and the critical condition for interfacial debonding. Both the fiber and the matrix are treated as elastic materials. Analysis is made based on a method using Papkovich-Neuber displacement potential functions for the problem of an elastic solid subjected to axisymmetrical boundary conditions. Solutions are found by means of the technique of trigonometrical series. Effects of initial misfit strains and frictional sliding between the fiber and the matrix over the interfacial crack are also included in the study.     

Dynamic neck development in a polymer tube under internal pressure loading

The initiation and growth of necks in polymer tubes subjected to rapidly increasing internal pressure is analyzed numerically. Plane strain conditions are assumed to prevail in the axial direction. The polymer is characterized by a finite strain elastic–viscoplastic constitutive relation and the calculations are carried out using a dynamic finite element program. Numerical results for neck development are illustrated and discussed for tubes of various thicknesses. The sensitivity to the wave number of the thickness imperfections is studied with a focus on comparing a long wave length imperfection and a short wave length imperfection. After some thinning down at the necks, the mode of deformation switches to neck propagation along the circumference of the tube. A case is shown in which the necks have propagated along the entire tube wall, so that network locking in the polymer results in high stiffness against further expansion of the tube. The rate dependence of the necking behavior gives noticeable differences in neck development for slow loading versus fast loading.