OBTAINING MULTI-AXIAL ELASTIC POTENTIALS FOR RUBBER-LIKE MATERIALS VIA AN EXPLICIT,EXACT APPROACH BASED ON SPLINE INTERPOLATION

An explicit, exact approach is proposed to obtain multi-axial elastic potentials for isotropic rubber-like materials undergoing large incompressible deformations. By means of two direct, explicit procedures, this approach reduces the problem of determining multi-axial poten- tials to that of determining one-dimensional elastic potentials. To this end, two one-dimensional potentials for uniaxial case and simple shear case are respectively determined via spline inter- polation and, then, the two potentials are extended to generate a multi-axial elastic potential using a novel method based on certain logarithmic invariants. Eventually, each of the multi-axial potentials will exactly match the finite strain data from four benchmark tests.     

Effective enhanced model for a large deformable soft pneumatic actuator

Soft pneumatic actuators have been widely used for implementing sophisticated and dexterous movements,due to numerous fascinating features compared with their rigid counterparts.Relatively speaking,modeling and analysis of an entire soft pneumatic actuator considering contact interaction between two adjacent air chambers is extremely rare,which is exactly what we are particularly interested in.Therefore,in order to establish an accurate mechanical model and analyze the overall configuration and stress distribution for the soft pneumatic actuator with large deflection,we consider the contact interaction of soft materials rather than hard materials,to produce an effective enhanced model for soft contact of a large deformable pneumatic actuator.In this article,a multiple-point contact approach is developed to circumvent the mutual penetration problem between adjacent air chambers of the soft actuator that occurs with the single-point contact approach employed in linear elastic rigid materials.In contrast to the previous simplified rod-based model that did not focus on contact interaction which was adopted to clarify the entire deformation of the actuator,the present model not only elaborates nonlinear large deformation and overall configuration variations,but also accurately delineates stress distribution law inside the chamber structure and the stress concentration phenomenon.By means of a corresponding static experiment,a comparison of the simulation results with experimental data validates the effectiveness and accuracy of this model employing a multiple-point contact approach.Excellent simulation of the actual bending deformation of the soft actuator is obtained,while mutual penetration is successfully circumvented,whereas the model with single-point contact cannot achieve those goals.Finally,as compared with the rod-based model,the results obtained using the proposed model are more consistent with experimental data,and simulation precision is improved.     

Modified virtual internal bond model based on deformable Voronoi particles

In last time, the series of virtual internal bond model was proposed for solving rock mechanics problems. In these models, the rock continuum is considered as a structure of discrete particles connected by normal and shear springs(bonds). It is well announced that the normal springs structure corresponds to a linear elastic solid with a fixed Poisson ratio, namely, 0.25 for threedimensional cases. So the shear springs used to represent the diversity of the Poisson ratio.However, the shearing force calculation is not rotationally invariant and it produce difficulties in application of these models for rock mechanics problems with sufficient displacements. In this letter, we proposed the approach to support the diversity of the Poisson ratio that based on usage of deformable Voronoi cells as set of particles. The edges of dual Delaunay tetrahedralization are considered as structure of normal springs(bonds). The movements of particle's centers lead to deformation of tetrahedrals and as result to deformation of Voronoi cells. For each bond, there are the corresponded dual face of some Voronoi cell. We can consider the normal bond as some beam and in this case, the appropriate face of Voronoi cell will be a cross section of this beam. If during deformation the Voronoi face was expand, then, according Poisson effect, the length of bond should be decrees. The above mechanism was numerically investigated and we shown that it is acceptable for simulation of elastic behavior in 0.1–0.3 interval of Poisson ratio. Unexpected surprise is that proposed approach give possibility to simulate auxetic materials with negative Poisson's ratio in interval from –0.5 to –0.1.     

A method to determine Young＇s modulus of soft gels for cell adhesion

A convenient technique is reported in this note for measuring elastic modulus of extremely soft material for cellular adhesion. Specimens of bending cylinder under gravity are used to avoid contact problem between testing device and sample, and a beam model is presented for evaluating the curvatures of gel beams with large elastic deformation. A self-adaptive algorithm is also proposed to search for the best estimation of gels＇ elastic moduli by comparing the experimental bending curvatures with those computed from the beam model with preestimated moduli. Application to the measurement of the property of polyacrylamide gels indi- cates that the material compliance varies with the concentrations of bis-acrylamide, and the gels become softer after being immersed in a culture medium for a period of time, no matter to what extent they are polymerized.     

Spinodal surface instability of soft elastic thin films

When the thicknesses of thin films reduce to microns or even nanometers, surface energy and surface interaction often play a significant role in their deformation behavior and surface morphology. The spinodal surface instability induced by the van der Waals force in a soft elastic thin film perfectly bonded to a rigid substrate is investigated theoretically using the bifurcation theory of elastic structures. The analytical solution is derived for the critical condition of spinodal surface morphology instability by accounting for the competition of the van der Waals interaction energy, elastic strain energy and surface energy. Detailed examinations on the effect of surface energy, thickness and elastic properties of the film show that the characteristic wavelength of the deformation bifurcation mode depends on the film thickness via an exponential relation, with the power index in the range from 0.749 to 1.0. The theoretical solution has a good agreement with relevant experiment results.     

Correlation of powder flow properties to interparticle interactions at ambient and high temperatures

A combination of a continuum approach and a particle–particle approach to describe the multi-scale nature of the mechanical properties of bulk solids may be beneficial to scientific and engineering applications. In this paper, a procedure is proposed to estimate the interparticle forces beginning with the bulk flow properties as measured with standardized techniques. In particular, the relationship between interparticle forces and bulk solid tensile strength is adopted based on the microscale approaches of Rumpf(1970) and Molerus(1975). The flow properties of fluid cracking catalyst(FCC), corundum and glass bead powders were all characterized with a modified Schulze ring shear cell capable of operating at temperatures up to 500℃. The powder test conditions were selected such that the van der Waals forces were the most significant particle–particle interactions. The model equations describe two cases, in which either elastic or plastic deformation of the contact points is assumed. The results indicate that the model provides the correct order of magnitude for the values of the tensile strength when proper values for the mean curvature radius at the contact points are taken into account. A sensitivity analysis for the main parameters in the model was performed. This analysis indicated that the assumption of plastic deformation at contact surfaces coupled with a decrease in porosity justified an increase of the tensile strength with consolidation stress. Furthermore, the effect of temperature on the measured flow behavior can be explained as a change in the strength of the material.     

New expression for collision efficiency of spherical nanoparticles in Brownian coagulation

The collision efficiency of dioctyl phthalate nanoparticles in Brownian coag- ulation has been studied. A set of collision equations is solved numerically to find the relationship between the collision efficiency and the particle radius varying in the range of 50 nm to 500 nm in the presence of Stokes resistance, lubrication force, van der Waals force, and elastic deformation force. The calculated results are in agreement with the experimental data qualitatively. The results show that the collision efficiency decreases with the increase of the particle radii from 50 nm to 500 nm. Based on the numerical data, a new expression for collision efficiency is presented.     

A computational study of a capsule lateral migration in microchannel flow

A numerical method is used to model a capsule migration in a microchannel with small Reynolds number Re ≈ 0 . 01. The capsule is modeled as a liquid drop surrounded by a neo-Hookean elastic membrane. The numerical model combines immersed boundary with lattice Boltzmann method (IB-LBM). The LBM is used to simulate fixed Cartesian grid while the IBM is utilized to implement the fluid-structure interaction by a set of Lagrangian moving grids for the membrane. The effect of shear elasticity and bending stiffness are both considered. The results show the significance of elastic modulus and initial lateral position on deformation and morphological properties of a circular capsule. The wall effect becomes stronger as the capsule initial position gets closer to the channel wall. As the elastic modulus of membrane increases, the capsule undergoes less pronounced deformation and velocity in direction x is decreased, thus, the capsule motion is slower than the background flow. The best agreement between the present model and experiments for migration velocity takes place for the capsule with normal to moderate membrane elastic modulus. The results are in good agreement with experiment study of Coupier et al. and previous numerical studies. Therefore, the IB-LBM can be employed to make prediction in vitro and in vivo studies of capsule deformation.     

EXPERIMENTAL ANALYSIS ON SOFT MATERIAL CONTACT PROBLEMS BY DIGITAL MOIR AND EMBEDDED-GRATING METHODS

Soft material is becoming increasingly important to many industries, which leads to the demand for a better understanding of its mechanical properties under large deformation. In this paper, a technique of integrating the digital moiré method and embedded-grating approach is presented for investigating mechanical behaviors of a vulcanized silicone rubber in contact with a wedge-shaped indenter. Two distinct deformation sectors are observed from the experimental result. A simple way of computing strain is also presented by analysing grid deformation within the framework of geometrical nonlinearity. Three regions were observed from strain distribution along the horizontal direction: the contact region, the sink-in region and the far-field region.Moreover, the extent of the sticky region and that of the slippy region within the contact interface are distinguished, which can provide realistic data for theoretical modelling. Based on the finite deformation elasticity theory, the distribution of contact pressure and shear stress over the contact interface are derived for prediction of possible cracks.     

Dynamic analysis on generalized linear elastic body subjected to large scale rigid rotations

The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine- matics through translational and rotational deformations, and a modified constitutive relation for the rotational deformation is proposed between the couple stress and the curvature tensor. Thus, the balance equations of momentum and moment are used for the motion equations of the body. The floating frame of reference formulation is applied to the elastic body that conducts rotations about a fixed axis. The motion-deformation coupled model is developed in which three types of inertia forces along with their incre- ments are elucidated. The finite element governing equations for the dynamic analysis of the elastic body under large rotations are subsequently formulated with the aid of the constrained variational principle. A penalty parameter is introduced, and the rotational angles at element nodes are treated as independent variables to meet the requirement of C1 continuity. The elastic body is discretized through the isoparametric element with 8 nodes and 48 degrees-of-freedom. As an example with an application of the motion- deformation coupled model, the dynamic analysis on a rotating cantilever with two spatial layouts relative to the rotational axis is numerically implemented. Dynamic frequencies of the rotating cantilever are presented at prescribed constant spin velocities. The maximal rigid rotational velocity is extended for ensuring the applicability of the linear model. A complete set of dynamical response of the rotating cantilever in the case of spin-up maneuver is examined, it is shown that, under the ultimate rigid rotational velocities less than the maximal rigid rotational velocity, the stress strength may exceed the material strength tolerance even though the displacement and rotational angle responses are both convergent. The influence of the cantilever layouts on their responses and the multiple displacement trajectories observed in the floating frame is simultaneously investigated. The motion-deformation coupled model is surely expected to be applicable for a broad range of practical applications.     

A Strain Energy Function for Vulcanized Rubbers

A three-parameter strain energy function is developed to model the nonlinearly elastic response of rubber-like materials. The development of the model is phenomenological, based on data from the classic experiments of Treloar, Rivlin and Saunders, and Jones and Treloar on sheets of vulcanized rubber. A simple two-parameter version, similar to the Mooney-Rivlin and Gent-Thomas strain energies, provides an accurate fit with all of the data from Rivlin and Saunders and Jones and Treloar, as well as with Treloar’s data for deformations for which the principal deformation invariant I ₁ has values in the range 3≤I ₁≤20.     

Antiplane elastic wave propagation in pre-stressed periodic structures; tuning,band gap switching and invariance

The effect of nonlinear elastic pre-stress on antiplane elastic wave propagation in a two-dimensional periodic structure is investigated. The medium consists of cylindrical annuli embedded on a periodic square lattice in a uniform host material. An identical inhomogeneous deformation is imposed in each annulus and the theory of small-on-large is used to find the incremental wave equation governing subsequent small-amplitude antiplane waves. The plane-wave-expansion method is employed in order to determine the permissable eigenfrequencies. It is found that pre-stress significantly affects the band gap structure for Mooney–Rivlin and Fung type materials, allowing stop bands to be switched on and off. However, it is also shown that for a specific class of materials, their phononic properties remain invariant under nonlinear deformation, permitting some rather interesting behaviour and leading to the possibility of phononic cloaks.     

Integral representations of constitutive equations

This paper is concerned with constitutive equations in which the stress at an instant of time,t, say, is a functional of the deformation gradient history up to and includingt. It is assumed that the deformation gradient histories are of bounded variation and are continuous, or piece-wise continuous with a countable number of salti. It is shown that if the stress functional isn times Fréchet differentiable in the sense of the supremum norm, it can be represented by a series of multiple integrals in the deformation gradient history, with an error or ordern + 1 in the displacement gradients. The relation of this type of integral representation to that of Green and Rivlin is discussed.     

超弹性橡胶材料的改进Rivlin模型

讨论了不可压缩橡胶材料的超弹性唯象本构模型。针对典型实验,给出选择应变能函数的原则。从物理机理上,分析了Neo-Hookean模型、Mooney模型、三阶Rivlin模型及Ogden模型的优缺点。在此基础上,将Rivlin模型改进成为 ,这种新形式具有三个优点：①若取前三项（N=1）,则其结果与不可压缩线弹性的应变能相等,能够近似满足剪切的线性关系,但拉伸及压缩的线性关系是精确满足的。②当N≥2时,简单剪切中的应变能及剪应力τxy在小应变情况下是以剪应变γxy为等比的多项式展开;而Rivlin模型只能保证简单剪切实验中的应变能及剪应力τxy是以(γxy)2为等比的级数展开的形式,当取前两项的情况下,Rivlin模型只能精确保证常剪切,拉伸及压缩的线性关系无法得到保证。针对典型实验数据,若取同阶次多项式,本文模型的同类实验数据预测及不同类实验数据间相互预测的精度都比Rivlin模型的高。     

Effective balance equations for elastic composites subject to inhomogeneous potentials

We derive the new effective governing equations for linear elastic composites subject to a body force that admits a Helmholtz decomposition into inhomogeneous scalar and vector potentials. We assume that the microscale, representing the distance between the inclusions (or fibers) in the composite, and its size (the macroscale) are well separated. We decouple spatial variations and assume microscale periodicity of every field. Microscale variations of the potentials induce a locally unbounded body force. The problem is homogenizable, as the results, obtained via the asymptotic homogenization technique, read as a well-defined linear elastic model for composites subject to a regular effective body force. The latter comprises both macroscale variations of the potentials, and nonstandard contributions which are to be computed solving a well-posed elastic cell problem which is solely driven by microscale variations of the potentials. We compare our approach with an existing model for locally unbounded forces and provide a simplified formulation of the model which serves as a starting point for its numerical implementation. Our formulation is relevant to the study of active composites, such as electrosensitive and magnetosensitive elastomers.     

Viscoelastic flow simulation of polytetrafluoroethylene (PTFE) paste extrusion

Polytetrafluoroethylene (PTFE) is known to be a polymer that shows inherent microstructure formation during cold processing such as paste extrusion. To model such a complex flow, a viscoelastic constitutive equation is proposed that takes into account the continuous change of the paste microstructure during flow, through fibril formation. The mechanism of fibrillation is captured through a microscopic model for a structural parameter ξ that represents the percentage of fibrillated domains of the paste. The proposed viscoelastic constitutive equation consists of a viscous shear-thinning term (Carreau model) and an elastic term (modified Mooney–Rivlin model), the relative contribution of the two depending on ξ. The viscous and elastic parameters of the model are determined by using shear and extensional rheometry on the paste. Finite element simulations based on the proposed constitutive relation with the measured model parameters predict reasonably well the variations of the extrusion pressure with the apparent shear rate and the die geometrical characteristics.     

Electro-elastomers: Large deformation analysis of silicone membranes

Electro-elastomers are large strain smart materials capable of both sensing and actuation. Typical electro-elastomer setups consist of either a silicone or acrylic membrane sandwiched between two compliant grease electrodes. Silicone electro-elastomers have maximum elastic strains between 200% and 350%. Acrylic electro-elastomers are more widely employed due to larger actuation strains but are softer than silicone and have a lower force output [Goulbourne, N.C., Frecker, M., Mockensturm, E.M., Snyder, A.J., 2003. Modeling of a dielectric elastomer diaphragm for a prosthetic blood pump. In: Proceedings of SPIE, Smart Structures and Materials: EAPAD, San Diego; Goulbourne, N.C., Mockensturm, E.M., Frecker, M., 2005b. Quasi-static and dynamic inflation of a dielectric elastomer membrane. In: Proceedings of SPIE, Smart Structures and Materials: EAPAD, San Diego]. A numerical formulation for the large deformation response of electro-elastomer membranes subject to electromechanical loading is derived in this paper. The approach is based on modifying the elastic membrane theory of Green, Adkins, and Rivlin [Adkins, J.E., Rivlin, R.S., 1952. Large elastic deformations of isotropic materials IX. The deformation of thin shells. Philosophical Transactions of the Royal Society of London. Series A Mathematical and Physical Sciences 244, 505–531; Green, A.E., Adkins, J.E., 1970. Large Elastic Deformations. Oxford University Press, London]. The electro-elastic stress state is defined as the combination of the electrical Maxwell stress and the mechanical stress for hyperelastic materials [Goulbourne, N.C., Mockensturm, E.M., Frecker, M., 2005a. A nonlinear model for dielectric elastomer membranes. ASME Journal of Applied Mechanics 72, (6) 899–906]. This paper augments our previous work by presenting a mathematical solution procedure for simulating the field responsive behavior of silicone electro-elastomers configured for both in-plane and out-of-plane deformation. Thin axisymmetric membranes subject to electromechanical loads are the focus of this investigation. The numerical analysis shows that there is a delicate balance between the electrical and the mechanical portions of the stress, which must be maintained for the overall stress to remain tensile and by extension the electro-elastomer to remain stable. It is shown that at very high voltages the stress can become negative ultimately leading to transducer failure. For sensing applications, the varying capacitive behavior of electro-elastomers is used to extract information about the membrane’s deformed state.     

Inhomogeneous shearing of strain-stiffening rubber-like hollow circular cylinders

The purpose of this paper is to investigate the effects of strain-stiffening for the classical problems of axial and azimuthal shearing of a hollow circular cylinder composed of an incompressible isotropic non-linearly elastic material. For some specific strain-energy densities that give rise to strain-stiffening in the stress–stretch response, the stresses and resultant axial forces are obtained in explicit closed form. While such results are well known for classical constitutive models such as the Mooney–Rivlin and neo-Hookean models, our main focus is on materials that undergo severe strain-stiffening in the stress–stretch response. In particular, we consider in detail two phenomenological constitutive models that reflect limiting chain extensibility at the molecular level and involve constraints on the deformation. The amount of shearing that tubes composed of such materials can sustain is limited by the constraint. Numerical results are also obtained for an exponential strain-energy that exhibits a less abrupt strain-stiffening effect. Potential applications of the results to the biomechanics of soft tissues are indicated.     

An approach for prediction of the elasto-plastic behavior of particulate reinforced composites

A numerical approach is presented in this paper for the calculation of the elasto-plastic deformation behavior of particulate reinforced composites. The effect of shape and arrangement of particulate on the elastic modulus and tensile deformation behavior were estimated. The approach presented can consider the shape and arrangement effect of reinforcement particulate via a simple parameter called the geometrical factor (Gf). Elastic moduli and tensile deformation estimations for the particulate reinforced composites were studied. The results of proposed approach were in very good agreement with the results of finite element analysis.     

Role of elasticity in elastic–plastic fracture: Analytical bi-linear crack-tip fields and finite element analysis

A solution for Model-I plane strain crack tip fields in a bi-linear elastic–plastic material is presented. The elastic–plastic Poisson's ratio is introduced to characterize the influence of elastic deformation on the near tip constraint. Attention is focused on the distribution of elastic/plastic strain energy in the sensitive region of the forward sector ahead of a crack tip. The present study shows that the elastic strain energy can be higher than the plastic strain energy in this sensitive sector while large amount of the plastic strain energy develops outside this sector around the crack tip. The effect of elastic deformation in this sensitive region on the structure of crack-tip fields is considerable and the assumption in some important solutions for crack-tip fields reported in literature that the elastic deformation is small and can be ignored is therefore not physically reasonable. Besides, finite element analysis is carried out to validate the analytical solution and good agreement between them is found. It is seen that the present solution with T-stress can properly describe the crack-tip fields under various constraints for different specimens and an analytical relation is established between the critical value of J-integral, J_c, and T-stress for elastic–plastic fracture.