In-plane Shear Deformation Research Articles

Elastic behavior of a red blood cell with the membrane’s nonuniform natural state: equilibrium shape, motion transition under shear flow, and elongation during tank-treading motion

Direct numerical simulations of the mechanics of a single red blood cell (RBC) were performed by considering the nonuniform natural state of the elastic membrane. A RBC was modeled as an incompressible viscous fluid encapsulated by an elastic membrane. The in-plane shear and area dilatation deformations of the membrane were modeled by Skalak constitutive equation, while out-of-plane bending deformation was formulated by the spring model. The natural state of the membrane with respect to in-plane shear deformation was modeled as a sphere ([Formula: see text]), biconcave disk shape ([Formula: see text]) and their intermediate shapes ([Formula: see text]) with the nonuniformity parameter [Formula: see text], while the natural state with respect to out-of-plane bending deformation was modeled as a flat plane. According to the numerical simulations, at an experimentally measured in-plane shear modulus of [Formula: see text] and an out-of-plane bending rigidity of [Formula: see text] of the cell membrane, the following results were obtained. (i) The RBC shape at equilibrium was biconcave discoid for [Formula: see text] and cupped otherwise; (ii) the experimentally measured fluid shear stress at the transition between tumbling and tank-treading motions under shear flow was reproduced for [Formula: see text]; (iii) the elongation deformation of the RBC during tank-treading motion from the simulation was consistent with that from in vitro experiments, irrespective of the [Formula: see text] value. Based on our RBC modeling, the three phenomena (i), (ii), and (iii) were mechanically consistent for [Formula: see text]. The condition [Formula: see text] precludes a biconcave discoid shape at equilibrium (i); however, it gives appropriate fluid shear stress at the motion transition under shear flow (ii), suggesting that a combined effect of [Formula: see text] and the natural state with respect to out-of-plane bending deformation is necessary for understanding details of the RBC mechanics at equilibrium. Our numerical results demonstrate that moderate nonuniformity in a membrane's natural state with respect to in-plane shear deformation plays a key role in RBC mechanics.

Dry Stone Masonry Walls in Bending—Part II: Analysis

With the objective of developing analytical models for evaluation of the lateral strength of dry-stack masonry (DSM) walls subject to horizontal inertial loading, simple collapse mechanisms are proposed, which include a combination of out-of-plane flexural deformation along the main panel and in-plane shear deformation in the connecting return walls. The lateral strength is calculated using a virtual work approach incorporating moment capacities along different types of crack lines and shear resistance of in-plane panels participating in the mechanisms. The proposed treatment of the active in-plane panels assumes that they undergo frictional shear deformation (versus rigid body rocking), in consistency with the zero tensile strength nature of DSM. Allowance is also made for the presence of either restrained or unrestrained overburden loads at the top of the wall, which can generate either a strengthening or weakening effect, respectively. The accuracy of the analysis is assessed by comparing its predictions to the results of experimental tests on DSM reported in the companion study. These comparisons are favorable with respect to both the predicted values of strength and the critical failure mechanisms.

Decomposition of in-plane shear in thin-walled members

In this paper in-plane (membrane) shear deformations in thin-walled members are discussed. Unlike many earlier works on the effect of shear deformations, the actual work is based on shell model rather than beam model. Thus, the presented work has no intention to develop a new shear-deformable beam theory, by adding some assumed shear deformations to classical beam degrees of freedom, but the actual research considers the thin-walled member as a set of connected flat plates, the displacement field of which is determined by nodal displacements and shape functions. The goal here is to make a full and meaningful modal decomposition within the given displacement field, i.e., to determine sub-fields within the general displacement field so that deformations within the sub-fields would correspond to some desired buckling or deformation modes. The presented work is therefore the direct extension of constraint finite strip method (cFSM), however, this time having a special focus on the shear modes. Though the presented shear modes are initiated by cFSM, and the presentation utilizes the terminology of cFSM, it is to highlight here that the proposed modal decomposition of in-plane shear deformations is not limited to buckling analysis or to the finite strip method. Indeed, the proposed shear space decomposition can be used in any case when the analysed member is thin-walled, built up from flat plates, is modelled by shell-type elements, and the member is prismatic. Since the flexural behaviour of the plates is assumed to follow Kirchhoff thin plate theory, no out-of-plane shear is considered.

Wrinkling of Sandwich Materials with Nonorthogonal Plain Woven Composite Facesheets

Fabric is often attached on lightweight core to form a sandwich plate. When complex sandwich structure is manufactured, the fabric facesheets are in a state of in-plane tension or shear deformation, and the angle between the warp and weft yarns is altered. An analytical model to calculate the wrinkling load of sandwich plates with nonorthogonal plain woven composite facesheets is established, and the effects of various parameters are demonstrated. Analysis results indicate that the core modulus and thickness, fiber modulus, and yarn orientation of facesheets can influence the facesheets’ wrinkling behavior of sandwich plate on different levels.

Mechanical behaviors of Kevlar 49 fabric subjected to uniaxial, biaxial tension and in-plane large shear deformation

Woven fabrics are used in many applications, including ballistic armors, propulsion engine containment systems and fabric reinforced composites. In order to facilitate the design and improvement of such applications, this paper investigates the stress–strain response in warp and fill directions, the apparent Poisson’s ratio, and the in-plane shear response of Kevlar 49 fabric including the possible effects of specimen size and pre-loading on the mechanical responses of the fabric. Full-field image analysis of the fabric under shear deformation is used to better understand the mechanisms related to in-plane shear. The experimental results show that the fabric exhibits non-linear and orthogonal behavior in tension, and can deform up to 20% before complete failure. It has identical Young’s modulus (pre-peak elastic stiffness) in warp and fill directions, but has different crimp strain, tensile strength and ultimate strain. The apparent Poisson’s ratio is a nonlinear function of strain and dependent upon the levels of pre-loading. It increases with strain quickly at the beginning and decreases gradually until the fabric fails. The shear response is highly nonlinear and has four distinct regions: linear elastic rotation region, dissipative rotation region, yarn compression region and shear locking region, and it is not dependent upon specimen size after normalization.

Finite element model for NCF composite reinforcement preforming: Importance of inter-ply sliding

A semi-discrete model is proposed for the simulation of non-crimp fabric reinforcement preforming. This approach is based on experimental observations of in-plane shear deformations of the reinforcement, out-of-plane bending and inter-ply sliding during the non-crimp fabric preforming. The experiment highlights strong sliding between the two plies of the non-crimp fabric during forming. The two plies of fibers composing the reinforcement are modeled by two layers of shell elements; the stitches are modeled by bar elements. The relationship between bar and shell elements is managed with a specific contact and anisotropic friction law associated to sliding threshold. This meso-macroscopic approach allows the simulation of industrial part forming in a reasonable computational time. The model shows a good prediction of deformations during the forming on a hemispherical shape. In particular sliding between the two fiber layers of the NCF obtained by the simulation is in good agreement with that measured during the preforming experiment.

Behaviour of cold-formed steel shear wall panels under monotonic and reversed cyclic loading

This paper presents the results of an experimental study on the behaviour and strength of the cold-formed steel shear wall panel (CFSSWP) with calcium silicate board as sheathing, when subjected to monotonically increasing and reversed cyclic in-plane shear deformation. These specimens were specifically designed to reach the strength as governed by the strength of the screw connection between the board and the CFS framing and avoid all other modes of failure, ahead of this. The main objectives of the experimental study are (a) to study the influence of board thicknesses and the distance of the screws from the nearest free edge of the board on the wall panel behaviour and strength; (b) to study the behaviour of different wall board configurations normally used in construction practice (c) to develop the values of the important parameters that determine the load-deformation behaviour of the wall panels under in-plane shear and (d) to determine the different limit states in the failure of the screws connecting the board and the CFS framing in such CFSSWP. In addition, a simplified design equation is proposed to evaluate the ultimate shear strength of CFSSWP based on the strength of the screw connection obtained from a sub assemblage shear strength test.

Comparative Analysis of Stress Distribution of Braided Composites under Different Load Conditions

In this paper, a comparative analysis of microscopic stress distribution in braided composites under different load conditions has been performed using a numerical method. The complexity of the architecture in non-orthogonally braided composites leads to the difficulty in the study of microscopic stress field. A geometric model which is suitable for the description of the stress distribution has been established. The location and magnitude of stress peak under different loads were investigated and the stress concentrations were subsequently discussed. For in-plane load, the maximum stress appears at ‘joint part’ of main bearing tow; for out-plane load, at ‘overlapped part’. These results are beneficial to detecting the damage initiation regions. The effect of braid angle on in-plane shear deformation is more intensive relative to the in-plane tension, whereas the influence is inconspicuous for the out-plane load. The comparative analysis is help for a thorough understanding of the mechanical properties of braided composites.

Effect of shear strain on the deflection of a clamped magnetostrictive film–substrate system

The effect of in-plane shear strain of a clamped bimorph on the deflection produced by magnetization of the film is investigated. The deflection is found by minimizing the Gibbs free energy with respect to four parameters, strains and curvatures along x and y directions at the interface, by assuming that the curvature in the y direction varies as a function of aspect ratio w/l along x. A set of standard linear equations of four parameters are obtained and the deflection is expressed in terms of the four parameters by solving the equations using Cramer rules. The inconsistencies pointed out by previous authors are also reviewed. For actuators made of thick and short clamped film–substrate system, the in-plane shear deformation should not be omitted. The present calculation model can give a relatively simple and accurate prediction of deflection for thick and short specimens of aspect ratio w/l<10, which supports the results obtained by finite element modeling.

Intra/inter-ply shear behaviors of continuous fiber reinforced thermoplastic composites in thermoforming processes

The thermoforming of continuous fiber reinforced thermoplastic (CFRTP) composite panels generally involves significant in-plane shear deformation. In the present work, the in-plane shear behavior of woven thermoplastic composites (Carbon/Polyphenylene Sulfide) over a range of processing temperatures is studied by bias-test experiments at different velocities. The experimental data of force versus displacement and force versus shear strain are presented for different extension velocities and temperatures. A thermo-visco-elastic model for numerical simulations of woven thermoplastic composite forming is proposed considering the influences of temperature and of strain rate. We applied a large displacement three-dimensional cohesive element with eight nodes which has been used for crack analysis in fracture mechanics by other authors, to investigate the inter-ply shear mechanism of woven thermoplastic composites. Applying three-dimensional cohesive elements, multi-plies forming simulations are performed to show inter-ply slip behaviors at different temperatures. The proposed models can be useful to predict from the properties of reinforcement and resin the intra/inter-ply shear behaviors of woven thermoplastic composites at high temperatures if experimental characterization of composite laminate behaviors is difficult to conduct.

Hyperelastic Constitutive Modeling of Hexagonal Honeycombs Subjected to In-Plane Shear Loading

The in-plane flexible shear property of hexagonal honeycombs may be useful for the compliant structural applications. In this paper, hyperelastic strain energy functions are developed for a finite in-plane shear deformation of hexagonal honeycombs over a constituent material’s elastic range. Effective shear stress-strain curves of hexagonal structures and local cell wall deformation are investigated using the finite element based homogenization method. The hyperelastic models, which are only related to the effective properties of a honeycomb, may not be good enough to capture the nonlinear behavior at a high macroscopic shear strain level. The primary microscopic cell wall deformation mode under macroscopic in-plane shear loading was identified to be the bending of the vertical cell wall h, which is perpendicular to the macroscopic loading direction. The re-entrant hexagonal structures having a negative Poisson’s ratio shows a high macroscopic shear flexible property associated with the high h when the honeycombs are designed to have the same macroscopic shear modulus.

Effect of fiber, matrix and interface properties on the in-plane shear deformation of carbon-fiber reinforced composites

The effect of fiber, matrix and interface properties on the in-plane shear response of carbon-fiber reinforced epoxy laminates was studied by means of a combination of experiments and numerical simulations. Two cross-ply laminates with the same epoxy matrix and different carbon fibers (high-strength and high-modulus) were tested in shear until failure according to ASTM standard D7078, and the progressive development of damage was assessed by optical microscopy in samples tested up to different strains. The composite behavior was also simulated through computational micromechanics, which was able to account for the effect of the constituent properties (fiber, matrix and interface) on the macroscopic shear response. The influence of matrix, fiber and interface properties on each region and on the overall composite behavior was assessed from the experimental results and the numerical simulations. After the initial elastic region, the shear behavior presented two different regions, the first one controlled by matrix yielding and the second one by the elastic deformation of the fibers. It was found that in-plane shear behavior of cross-ply laminates was controlled by the matrix yield strength and the interface strength and was independent of the fiber properties.

Magnetic and magnetoelastic properties of epitaxialSmFe2 thin film

We report on magnetic and magnetoelastic measurements for a 5000 Å (110)SmFe2 thin film, which was successfully analyzed by means of a point charge modelfor describing the effect of the epitaxial growth in this kind of system. Some ofthe main conclusions of the Mössbauer and magnetoelastic results and the newmagnetization results up to 5 T allow us to get a full description of the crystalelectric field, exchange, and magnetoelastic behavior in this compound. So, newsingle-ion parameters are obtained for the crystal field interaction of samarium ions,A4⟨r4⟩ = +755 K/ion andA6⟨r6⟩ = −180 K/ion, and new single-ion magnetoelastic coupling MPa and MPa, which represent the tetragonal and the in-plane shear deformations, respectively.Moreover, the new thermal behavior of the samarium magnetic moment, the exchangecoupling parameter, and the magnetocrystalline anisotropy of the iron sublattice areobtained too. From these, the softening of the spin reorientation transition with respect tothe bulk case could be accounted for.

Osteocyte calcium signaling response to bone matrix deformation

Osteocytes embedded in calcified bone matrix have been widely believed to play important roles in mechanosensing to achieve adaptive bone remodeling in a changing mechanical environment. In vitro studies have clarified several types of mechanical stimuli such as hydrostatic pressure, fluid shear stress, and direct deformation influence osteocyte functions. However, osteocyte response to mechanical stimuli in the bone matrix has not been clearly understood. In this study, we observed the osteocyte calcium signaling response to the quantitatively applied deformation in the bone matrix. A novel experimental system was developed to apply deformation to cultured bone tissue with osteocytes on a microscope stage. As a mechanical stimulus to the osteocytes in bone matrix, in-plane shear deformation was applied using a pair of glass microneedles to bone fragments, obtained from 13-day-old embryonic chick calvariae. Deformation of bone matrix and cells was quantitatively evaluated using an image correlation method by applying for differential interference contrast images of the matrix and fluorescent images of immunolabeled osteocytes, together with imaging of the cellular calcium transient using a ratiometric method. As a result, it was confirmed that the newly developed system enables us to apply deformation to bone matrix and osteocytes successfully under the microscope without significant focal plane shift or deviation from the observation view field. The system could be a basis for further development to investigate the mechanosensing mechanism of osteocytes in bone matrix through examination of various types of rapid biochemical signaling responses and intercellular communication induced by matrix deformation.

Mechanisms of shear deformation in fiber-reinforced polymers: experiments and simulations

The mechanisms of in-plane shear deformation in a cross-ply glass fiber-epoxy laminate were studied through a combination of experiments and simulations. Shear deformation parallel and perpendicular to the fibers led to very different deformation and fracture patterns. Deformation was localized in a matrix shear band parallel to the fibers in the former, while fiber rotation and widespread plastic deformation in the matrix were dominant in the latter. The differences in the mechanical response between both orientations increased with the applied strain and it was shown that the cross-ply laminate response was given by the averaged contribution of both. The relevance of this behavior for the development of continuum damage mechanics models is noted.

MULTISCALE PROGRESSIVE FAILURE ANALYSIS OF PLAIN-WOVEN COMPOSITE MATERIALS

The paper presents an overview of multiscale modeling of advanced fibrous composite materials. Following the review, a nonlinear, fully three-dimensional, numerical model is proposed which is suitable for multiscale elastic and progressive failure analysis of plain-woven composite materials. The proposed model is developed for implementation into the Finite Element code ABAQUS/Explicit as a user-defined subroutine for constant stress (one integration point) solid elements. The multiscale strategy applied in this paper uses a closed-form solution approach for homogenization of the mesoscale properties of a woven composite. A mosaic model of the woven composite's Representative Volume Element (RVE) is used for deriving the micromechanical relations used for homogenization. The composite RVE model used herein is composed of UD interlacing yarns (fill and warp yarns) and matrix-rich regions. For failure and damage analysis, the following features are implemented in this work: material nonlinearity for pure in-plane shear deformation; physically-based failure criteria for matrix failure in the UD yarns; maximum stress failure criteria for failure of fibers in the UD yarns and of the pure matrix in the resin-rich regions and energy-based damage mechanics. The proposed strategy, which has been implemented and tested for a special case of an in-plane damage, has some evident advantages compared to the other approaches, especially for application to full-scale simulations, i.e., component and structural scales. A comparison of the proposed model with experimental data shows a good correlation can be achieved.

Large Shear Deformation of E-glass/ Polypropylene Woven Fabric Composites at Elevated Temperatures

Stamping operation of textile composite sheets in industry involves a process of heating and cooling of the material. In the present article, the in-plane large shear deformation of woven fabric composite sheets at elevated temperatures is studied. Using the modified ‘picture frame’ test, the effects of temperature on the shear behavior of the material and the onset of wrinkling were investigated. In addition to the reduction in yarn width, the change of physical and mechanical properties of polypropylene (PP) fibers with temperature also plays a significant role. The initial shear stiffness of the composite sheets and the onset of wrinkling are reasonably explained by inter-yarn friction measurement. To simply consider the temperature effect, the introduction of a temperature-dependent factor for the simulation of stamping operation is suggested.

Simulation and tomography analysis of textile composite reinforcement deformation at the mesoscopic scale

The preforming stage of the RTM composite manufacturing process leads to fibrous reinforcement deformations which may be very large especially for double curvature shapes. The knowledge of the mesoscopic deformed geometry is important for reinforcement permeability computations and for damage prediction analyses of the composite. A simulation method for woven composite fabric deformation at mesoscopic scale is presented in this paper. A specific continuum hypo-elastic constitutive model is proposed for the yarn behavior. The associated objective derivative is based on the fiber rotation. Spherical and deviatoric parts of the transverse behavior are uncoupled. X-ray tomography is used to obtain experimental undeformed and deformed 3D geometries of the textile reinforcements. It provides, in particular, fiber distribution within the yarn. A comparison between deformed geometries obtained by mesoscopic simulation and by tomography is presented for biaxial tension and in-plane shear deformation.

A nonlinear theory for electroelastic shells with relatively large in-plane shear deformation and its implications in nonlinear mode coupling

A set of nonlinear two-dimensional equations for thin electroelastic shells in vibrations with moderately large shear deformation in the tangent plane are obtained from the three-dimensional equations of nonlinear electroelasticity. As an example for application, the equations are used to study nonlinear torsional vibration of a circular cylindrical piezoelectric shell. It is shown that torsion is nonlinearly coupled to axial extension and circumferential extension. The results of this paper emphasize the need for further study of mode coupling induced by nonlinearity.

Large deformation analysis of fibrous materials using rate constitutive equations

Rate constitutive equations (or hypoelastic constitutive equations) are frequently used in finite element software for finite strain analyses. For instance the material user subroutines of softwares such as ABAQUS ® are based on such approaches in the case of large deformations. Among these approaches, most of them use the standard Green Naghdi or Jaumann objective derivatives. The mechanical behaviour at finite strains of fibrous media (fabrics, composite reinforcements, NCF, etc.) is specific because of the possible sliding between fibres. The rate constitutive equations can be used if the fibrous medium is considered as a continuum. In this case, some approaches use the standard Green Naghdi or Jaumann objective derivatives and the associated rotated frame. The constitutive matrix in the rotated frame is obtained from the one in the fibre frame, which is the only frame where the specificities of the fibrous medium are exhibited. An alternative consists in defining and using an objective derivative and a rotated frame from the rotation of the fibre. The aim of this paper is to show that only the second approach leads to satisfying results for some tests and to explain the reasons why this second approach is preferable. This approach is also used to analyse at mesoscopic scale, in-plane shear deformation of a woven unit cell.