Equibiaxial Deformation Research Articles

Comparison of the elongational behavior of various polyolefins in uniaxial and equibiaxial flows

For processing operations with a pronounced elongational component, it was found that the uniformity of extruded items is improved by the presence of strain hardening usually measured in uniaxial elongation. Many processing operations such as foaming, film blowing, and blow molding are dominated by biaxial deformations, however, and therefore, the question arises how strain hardening in uniaxial and biaxial deformation compares. Besides a linear and long-chain branched PP, one classical LDPE, an HDPE pipe extrusion grade with a bimodal MMD, and a LCB-mPE were also characterized. For the measurements in uniaxial elongation the Munstedt tensile rheometer (MTR) and the ARES-EVF were used, while the lubricated flow method was applied for equibiaxial deformation. It was found that the strain hardening in uniaxial elongation is more pronounced. The dependence of strain hardening on strain rate is qualitatively the same in both modes. In the range of strain rates, the chosen long-chain branched LDPE and PP exhibit a strain hardening, which is approximately independent of the elongational rates applied, whereas for the HDPE it becomes smaller with increasing rate.

Equibiaxial extensional deformation and stress relaxation of glycerol plasticized wheat gluten at different concentrations

The aim of the present work has been to study the equibiaxial extensional deformation of glycerol plasticized moisture-containing gluten (MG) with different MG volume fractions ranging from 0.56 to 0.75 under lubricated squeezing flow at room temperature. The hyperelastic model with a strain energy potential of the Mooney–Rivlin form is applied to describe the biaxial stress as a function of biaxial strain at low strains. The initial shear modulus as a function of MG volume fraction reveals a particle network of gluten. Analysis of the relaxation modulus at biaxial strain 0.7 on the basis of the Kohlrausch–Williams–Watts (KWW) model reveals that decreasing volume fraction of MG increases the width of the distribution of relaxation times as well as the average relaxation time of wheat proteins.

Mechanical behavior of an acrylic elastomer used in dielectric elastomer actuators

The paper reports on extensive experimental work for the characterization of a dielectric elastomer used as base material for electroactive polymer (EAP) actuators. The mechanical behavior of the acrylic elastomer VHB 4910 is characterized using large strain experiments (uniaxial and equibiaxial deformation) under force and displacement controlled loading conditions. Next to tensile and relaxation tests, experiments were conducted also using the so-called circular actuators. Over 40 actuators were produced (with different in-plane pre-strain levels) and activated with voltages between 2000 and 3500 V. The experimental data are useful for determining constitutive model parameters as well as for validating models and simulation procedures for electromechanical coupling in EAP actuators. A novel approach is proposed for finite element analysis of dielectric elastomer actuator, which has been used in the present work for the evaluation of the experimental observations from circular actuators. Material parameters of different visco-hyperelastic models have been determined from a subset of the experimental data and the predictive capabilities of the models evaluated through comparisons with the remaining data. The prediction of the circular actuator behavior was satisfactory so that the proposed models might be useful for actuator design and optimization purposes. Limitations of the proposed constitutive model formulation are presented.

A New Thermodynamical Approach for the Simulation of Thermoforming Process using the Quasi-static Finite Element Method

The problem of modeling and the quasi-static finite element simulation of thermoforming processes for viscoelastic sheet is considered. To take account of the enclosed gas volume, responsible for inflation of the thermoplastic membrane, which contributes significantly to the strength and stiffness of a thermoplastic structure, the expression of external virtual work is expressed by a closed volume integral. The pressure load used in modeling is thus deduced from the thermodynamic law of ideal gases. The viscoelastic behavior of the Lodge model is considered. The Lagrangian formulation together with the assumption of the membrane theory is used in the finite element implementation. The numerical validation is performed by comparing the theoretical solution for the uniaxial and equibiaxial hencky deformation and free inflation with numerical results. Moreover, the influence of the Lodge constitutive model on the thickness and stress distribution in the thermoforming of containers made of HIPS is presented.

A Relationship between Thermal Diffusivity and Finite Deformation in Polymers

The thermal diffusivity of elastomers (i.e., rubber-like materials) can change substantially with elastic finite deformation. Initially isotropic elastomers may be thermally anisotropic when deformed. Data from several experimental studies demonstrate significant changes in the thermal conductivity or diffusivity tensor with finite deformation. Formulating the thermal diffusivity tensor and deformation in terms of the reference configuration may aid in the development of constitutive relations by use of material symmetry. Illustrated here is a relationship between the diffusivity and deformation of representative materials during uniaxial and equibiaxial deformation. Each component of the diffusivity tensor appears to be related to the deformation in the direction of the component only.

3-D Nanomechanics of an Erythrocyte Junctional Complex in Equibiaxial and Anisotropic Deformations

The erythrocyte membrane skeleton deforms constantly in circulation, but the mechanics of a junctional complex (JC) in the network is poorly understood. We previously proposed a 3-D mechanical model for a JC (Sung, L. A., and C. Vera. Protofilament and hexagon: A three-dimensional mechanical model for the junctional complex in the erythrocyte membrane skeleton. Ann Biomed Eng 31:1314-1326, 2003) and now developed a mathematical model to compute its equilibrium by dynamic relaxation. We simulated deformations of a single unit in the network to predict the tension of 6 alphabeta spectrin (Sp) (top, middle, and bottom pairs), and the attitude of the actin protofilament [pitch (theta), yaw (phi) and roll (psi) angles]. In equibiaxial deformation, 6 Sp would not begin their first round of "single domain unfolding in cluster" until the extension ratio (lambda) reach approximately 3.6, beyond the maximal sustainable lambda of approximately 2.67. Before Sp unfolds, the protofilament would gradually raise its pointed end away from the membrane, while phi and psi remain almost unchanged. In anisotropic deformation, protofilaments would remain tangent but swing and roll drastically at least once between lambda(i) = 1.0 and approximately 2.8, in a deformation angle- and lambda(i)-dependent fashion. This newly predicted nanomechanics in response to deformations may reveal functional roles previous unseen for a JC, and molecules associated with it, during erythrocyte circulation.

An in vitro model of traumatic brain injury utilising two-dimensional stretch of organotypic hippocampal slice cultures

Traumatic brain injury (TBI) is caused by rapid deformation of the brain, resulting in a cascade of pathological events and ultimately neurodegeneration. Understanding how the biomechanics of brain deformation leads to tissue damage remains a considerable challenge. We have developed an in vitro model of TBI utilising organotypic hippocampal slice cultures on deformable silicone membranes, and an injury device, which generates tissue deformation through stretching the silicone substrate. Our injury device controls the biomechanical parameters of the stretch via feedback control, resulting in a reproducible and equi-biaxial deformation stimulus. Organotypic cultures remain well adhered to the membrane during deformation, so that tissue strain is 93 and 86% of the membrane strain in the x- and y-axis, respectively. Cell damage following injury is positively correlated with strain. In conclusion, we have developed a unique in vitro model to study the effects of mechanical stimuli within a complex cellular environment that mimics the in vivo environment. We believe this model could be a powerful tool to study the acute phases of TBI and the induced cell degeneration could provide a good platform for the development of potential therapeutic approaches and may be a useful in vitro alternative to animal models of TBI.

Finite Element Analysis of Transversely Isotropic Viscoelastic Material for Thermoforming Process

In this work, a dynamic finite element method is used in the modeling and numerical simulation of the transversely viscoelastic behavior of a thin, isotropic, and incompressible thermoplastic membrane. The transversely isotropic viscoelastic functional based on the kinetic theory of rubber elasticity is presented. The model is expressed in terms of four material parameters and equations relating these parameters. The thermoforming of the sheet is performed under the action of perfect gas flows. The Lagrangian formulation, together with the assumption of the membrane theory, is used in the finite element implementation. The numerical validation is performed by comparing the theoretical solution for the uniaxial and equibiaxial Hencky deformation with numerical results. Moreover, the influence of fiber direction in the transversely viscoelastic material on the thickness and on the stress distribution in the thermoforming sheet are analyzed.

Analysis of Long Fibers Direction of Transversely Isotropic Hyperelastic Material for Thermoforming Application

In this work, we present the modeling and numerical simulation using the explicit dynamic finite element method for the hyperelastic behavior of a thin, transversely isotropic and incompressible thermoplastic membrane. The Lagrangian formulation together with the assumption of the membrane theory is used. The numerical validation is performed by comparing the theoretical solution for the uniaxial and equibiaxial Hencky deformation with the numerical results. Moreover, the effect of the transversely hyperelastic material on the thickness and on the stress distribution, for the membrane inflation, are analyzed for three different fibers orientations. Finally, a simple example of thermoforming part is presented.

Paracrine stimulation of surfactant secretion by extracellular ATP in response to mechanical deformation

We developed a heterologous system to study the effect of mechanical deformation on alveolar epithelial cells. First, isolated primary rat alveolar type II (ATII) cells were plated onto silastic substrata coated with fibronectin and maintained in culture under conditions where they become alveolar type I-like (ATI) cells. This was followed by a second set of ATII cells labeled with the nontransferable, vital fluorescent stain 5-chloromethylfluorescein diacetate to distinguish them from ATI cells. By morphometric analysis, equibiaxial deformation (stretch) of the silastic substratum induced comparable changes in cell surface area for both ATII and ATI cells. Surfactant lipid secretion was measured using cells metabolically labeled with [(3)H]choline. In response to 21% tonic stretch for 15 min, ATII cells seeded with ATI cells secreted nearly threefold more surfactant lipid compared with ATII cells seeded alone. ATI cells did not secrete lipid in response to stretch. The enhanced lipid secretion by ATII plus ATI cocultures was inhibited by treatment with apyrase and adenosine deaminase, suggesting that ATP release by ATI cells enhanced surfactant lipid secretion at 21% stretch. This was confirmed using a luciferase assay where, in response to 21% stretch, ATI cells released fourfold more ATP than ATII cells. Because ATI cells release significantly more ATP at a lower level of stretch than ATII cells, this supports the hypothesis that ATI cells are mechanosensors in the lung and that paracrine stimulation of ATII cells by extracellular ATP released from ATI cells plays a role in regulating surfactant secretion.

Thermodynamic approach of inflation process of K-BKZ polymer sheet with respect to thermoforming

The problem of modeling and the dynamic finite element simulation of thermoforming process for viscoelastic sheet are considered. The pressure load used in modeling is thus deduced from the thermodynamic law of ideal gases. The viscoelastic behavior of the K-BKZ model is considered. The Lagrangian formulation together with the assumption of the membrane theory is used in the finite element implementation. The numerical validation is performed by comparing the theoretical solution for the uniaxial and equibiaxial hencky deformation with numerical results. Moreover, the influence of the K-BKZ constitutive model, for three linear time distribution of airflow rate loading, on the thickness and on the stress distribution in thermoforming of containers made of HDPE are analyzed. POLYM. ENG. SCI., 45:1319–1335, 2005. © 2005 Society of Plastics Engineers

Superplastic gas pressure forming of fine-grained AZ61 magnesium alloy sheet

Abstract Superplastic deformation behavior of fine-grained AZ61 magnesium alloy sheet during equi-biaxial tensile deformation has been investigated. Thin circular diaphragms were successfully deformed into the hemispherical domes at 673 K in applied gas pressure range of 0.46–1.20 MPa. In this pressure range, average shell stress in range of 7–23 MPa and average deformation rate in range of 2×10−4 to 5×10−3 s−1 were imposed on the deforming hemisphere. The thickness profile of the resulting shape, which is sensitive to strain-rate sensitivity (m) and the extent of deformation, was examined and compared with the analytical model. For the low pressure condition (0.46 MPa) the forming process obeyed the model but not at high pressures (0.8 and 1.2 MPa). In the latter cases, according to the deformation mechanism map for Mg, the rate-controlling deformation mechanism changes from lattice diffusion (DL) controlled GBS to DL-controlled dislocation climb creep during the forming process due to dynamic grain growth. The extent of uniformity in thickness distribution is less than predicted by the theoretical model. The reduction of m-value resulted from this change of deformation mechanism.

Simultaneous biaxial deformation behavior of isotactic polypropylene films

AbstractThe simultaneous biaxial deformation behavior of isotactic polypropylene films was investigated using a novel laboratory film stretcher. A detailed description of the apparatus and its measurement capabilities is presented. The effects of drawing temperature and ratio, strain rate, and deformation modes on the macroscopic equibiaxial deformation and its relation to film dimension uniformity were studied. The strain rate was found to have a large influence on biaxial deformation homogeneity. For temperatures 15°C to 5°C below the melting point, it could be concluded that a homogeneous biaxial deformation was achieved if the Hencky strain rate was higher than 0.1 s−1. Additionally, it was found that the nominal biaxial yield stresses were linearly dependent on temperature in the range under investigation.

An in vitro model of neural trauma: device characterization and calcium response to mechanical stretch.

An in vitro model for neural trauma was characterized and validated. The model is based on a novel device that is capable of applying high strain rate, homogeneous, and equibiaxial deformation to neural cells in culture. The deformation waveform is fully arbitrary and controlled via closed-loop feedback. Intracellular calcium ([Ca2+]i) alterations were recorded in real time throughout the imposed strain with an epifluorescent microscopy system. Peak change in [Ca2+]i recovery of [Ca2+]i and percent responding NG108-15 cells were shown to be dependent on strain rate (1(-1) to 10(-1)) and magnitude (0.1 to 0.3 Green's Strain). These measures were also shown to depend significantly on the interaction between strain rate and magnitude. This model for neural trauma is a robust system that can be used to investigate the cellular tolerance and response to traumatic brain injury.

The Mullins effect in equibiaxial deformation

Common experience teaches that the pressure required to inflate a balloon is noticeably reduced by prestretching it several times prior to its primary inflation. This preconditioning phenomenon is known as stress-softening and often is called the Mullins effect. A theory of stress-softening in incompressible isotropic materials is applied to study this effect in an equibiaxial extension for which some general results are presented. It is shown, for example, that effects of stress-softening in a simple uniaxial compression can be adduced from those demonstrated for equibiaxial extension under plane stress. The general equibiaxial results are applied to study the Mullins effect in the inflation of a spherical membrane. The stress-softening phenomenon in cyclic inflation and deflation of the balloon is investigated for Mooney-Rivlin and biotissue parent material models. It is shown analytically that the effect of preconditioning in uniaxial extension is to significantly reduce the pressure required to first inflate a balloon to an equivalent strain intensity. This result characterizes the familiar softening phenomenon associated with balloon inflation.

Cavitation characteristics of a superplastic 8090 Al alloy during equi-biaxial tensile deformation

Cavitation behavior of a superplastic 8090 Al alloy during equi-biaxial tensile deformation has been investigated by deforming the sheet into a right cylindrical die. Cavitation characteristics could be separated into two stages. In stage I, the sheet deformed freely as part of a spherical dome, and the cavity volume increased exponentially with deformation. The evolution of cavity volume was due to both nucleation and growth of cavities. In the second stage, the surface friction would restrict thinning of the sheet, and the cavity volume first increased and then decreased with forming time for all test strain rates. Decrease in cavity volume in the later stage could be related to the cavity shrinkage that resulted from the sintering effect. A higher imposed pressure during forming leaded to a greater average cavity shrinkage rate. The cavitation level could be effectively reduced by a post-sintering procedure.

Instability of an internally constrained hyperelastic material

The wave speed criterion is applied to discuss restrictions on the material response functions of an isotropic, Bell constrained material in order that small amplitude, plane waves may propagate in the material with real-wave speeds. The case of a body subjected to a biaxial stress is related to the elastic stability of a Bell constrained slab. We show that two cases among five reported by Beatty and Pan in study of the elastic stability of a thick plate cannot support such waves. These cases, therefore, are not possible and must be excluded as potential solutions. The question of the stability of the equibiaxial deformations of a Bell constrained material under an all-around Cauchy stress, suggested in primary work of Beatty and Hayes on homogeneous deformations of Bell materials, is investigated. It is shown that for a general Bell material model, the state of equibiaxial deformation under an all-around Cauchy stress is materially unstable, unless all stretches are equal to one, their value in the initial undistorted state.

Mechanical properties of a poly(methyl acrylate) nanocomposite containing regularly-arranged silica particles

In an earlier investigation, poly(methyl acrylate) nanocomposites containing silica particles were found to have novel optical properties when the particles were regularly spaced rather than randomly located. The availability of these materials was used to determine whether there was any difference in the particles' reinforcing ability between ordered and random arrangements. The two types of composites were compared using near-equilibrium mechanical property measurements in uniaxial or equi-biaxial deformation, and dynamic mechanical properties measurements. It was found that having the filler particles regularly arranged had little effect on these properties, and that there was no anisotropy in their mechanical behavior. Related experiments could possibly be used to clarify the long-standing question of the importance of particle aggregation in elastomer reinforcement.

Axisymmetric elastic membranes subjected to fluid loading

We consider axisymmetric isotropic elastic membranes that are loaded by an incompressible liquid. The resulting deformation which contains the liquid is assumed to be axisymmetric. We consider undeformed plane disks of varying thickness and also hemispherical cups. We show how the resulting deformation can be controlled by the initial thickness variation of the disk. In all cases there is a critical loading where the membrane undergoes a very rapid change of shape, from being almost concave to having an hourglass shape. For a hemispherical cup, the deformation produces a wrinkled region which diminishes with increased loading but briefly reappears as the membrane traverses the unstable region. The onset of instability appears to be governed by the equibiaxial deformation at the apex of the deformed container. Instability is initiated when the deformation reaches the corresponding value of the first bifurcation point for a spherical membrane.

Plastic instability in equi-biaxial deformation of aluminium alloy sheet

Plastic instability, which results in the localization and failure of sheet metals, has been studied in the equi-biaxial stretching of AA 8014 aluminium alloy sheet. Attention was focussed on two main industrial conditions of the material: these were representative of materials that could be processed by the commercial batch-annealing process (slow heating, long time) or by a continuous annealing process (fast heating, short time). The instability strains were measured experimentally and compared with those predicted by different instability criteria. The results have been analyzed on the basis of the mechanical characteristics of the material under different conditions. It is concluded that pressure instability can not be used as the extreme limit of forming and thus there is a considerable amount of useful deformation after the instability strain has been reached.