Morphogenesis of growing soft tissues

Recently, much attention has been given to a noteworthy property of some soft tissues: their ability to grow. Many attempts have been made to model this behavior in biology, chemistry, and physics. Using the theory of finite elasticity, Rodriguez has postulated a multiplicative decomposition of the geometric deformation gradient into a growth-induced part and an elastic one needed to ensure compatibility of the body. In order to fully explore the consequences of this hypothesis, the equations describing thin elastic objects under finite growth are derived. Under appropriate scaling assumptions for the growth rates, the proposed model is of the F?ppl-von Kármán type. As an illustration, the circumferential growth of a free hyperelastic disk is studied.     

Finite element analysis of ionic liquid gel soft actuator

A new type of soft actuator material-ionic liquid gel(ILG),which consists of HEMA,BMIMBF4,and TiO_2,can be transformed into gel state under the irradiation of ultraviolet(UV)light.In this paper,Mooney–Rivlin hyperelastic model of finite element method is proposed for the first time to study the properties of the ILG.It has been proved that the content of TiO_2 has a great influence on the properties of the gel,and Young’s modulus of the gel increases with the increase of its content,despite of reduced tensile deformation.The results in this work show that when the TiO_2 content is 1.0 wt%,a large tensile deformation and a strong Young’s modulus can be obtained to be 325%and 7.8 k Pa,respectively.The material parameters of ILG with TiO_2content values of 0.2 wt%,0.5 wt%,1.0 wt%,and 1.5 wt%are obtained,respectively,through uniaxial tensile tests,including C_(10),C_(01),C_(20),C_(11),C_(02),C_(30),C_(21),C_(12),and C_(03)elements.In this paper,the large-scaled general finite element software ANSYS is used to simulate and analyze the ILG,which is based on SOLID186 element and nonlinear hyperelastic Mooney–Rivlin model.The finite element simulation analysis based stress-strain curves are almost consistent with the experimental stress–strain curves,and hence the finite element analysis of ILG is feasible and credible.This work presents a new direction for studying the performance of soft actuator for the ILG,and also contributes to the design of soft robot actuator.     

Elastic property of multiphase composites with random microstructures

We propose a computational method with no ad hoc empirical parameters to determine the elastic properties of multiphase composites of complex geometries by numerically solving the stress–strain relationships in heterogeneous materials. First the random microstructure of the multiphase composites is reproduced in our model by the random generation-growth method. Then a high-efficiency lattice Boltzmann method is employed to solve the governing equation on the multiphase microstructures. After validated against a few standard solutions for simple geometries, the present method is used to predict the effective elastic properties of real multiphase composites. The comparisons between the predictions and the existing experimental data have shown that the effects of pores/voids in composites are not negligible despite their seemingly tiny amounts. Ignorance of such effects will lead to over-predictions of the effective elastic properties compared with the experimental measurements. When the pores are taken into account and treated as a separate phase, the predicted Young’s modulus, shear modulus and Poisson’s ratio agree well with the available experimental data. The present method provides an alternative tool for analysis, design and optimization of multiphase composite materials.     

A constitutive model of the human vocal fold cover for fundamental frequency regulation

The elastic as well as time-dependent mechanical response of the vocal fold cover (epithelium and superficial layer of the lamina propria) under tension is one key variable in regulating the fundamental frequency. This study examines the hyperelastic and time-dependent tensile deformation behavior of a group of human vocal fold cover specimens (six male and five female). The primary goal is to formulate a constitutive model that could describe empirical trends in speaking fundamental frequency with reasonable confidence. The constitutive model for the tissue mechanical behavior consists of a hyperelastic equilibrium network in parallel with an inelastic, time-dependent network and is combined with the ideal string model for phonation. Results showed that hyperelastic and time-dependent parameters of the constitutive model can be related to observed age-related and gender-related differences in speaking fundamental frequency. The implications of these findings on fundamental frequency regulation are described. Limitations of the current constitutive model are discussed.     

A new ferromagnetic hysteresis model for soft magnetic composite materials

A new ferromagnetic hysteresis model for soft magnetic composite materials based on their specific properties is presented. The model relies on definition of new anhysteretic magnetization based on the Cauchy-Lorentz distribution describing the maximum energy state of magnetic moments in material. Specific properties of soft magnetic composite materials (SMC) such as the presence of the bonding material, different sizes and shapes of the Fe particles, level of homogeneity of the Fe particles at the end of the SMC product treatment, and achieved overall material density during compression, are incorporated in both the anhysteretic differential magnetization susceptibility and the irreversible differential magnetization susceptibility. Together they form the total differential magnetization susceptibility that defines the new ferromagnetic hysteresis model. Genetic algorithms are used to determine the optimal values of the proposed model parameters. The simulated results show good agreement with the measured results.     

Amplitude equations for non-linear Rayleigh waves

We investigate asymptotic equations describing small amplitude surface elastic waves in the half-plane (Rayleigh waves). For hyperelastic materials such model equations are Hamiltonian systems, and are seen to lead to the formation of singularities in the surface elastic displacement. At the time of singularity formation the Fourier spectra of the solutions exhibit power law decay, and the observed exponents suggest the existence of both differentiable and non-differentiable singular profiles.     

玻璃-橡胶混合颗粒体系的弹性行为研究

废旧橡胶制品颗粒与砂土颗粒混合物作为建筑填充材料具有环保、轻质、减震效果好等特点.软硬组分的混合比例可以调制体系力学性能从而实现兼顾材料柔韧性与强度的需求,但细观层面上材料性能改变的原因尚不明确.本文主要研究玻璃-橡胶混合颗粒体系的弹性行为及其微观机制.利用飞行时间法测量混合材料等效动弹性模量,发现随着橡胶颗粒增加,体系逐渐从类玻璃刚性行为转变为类橡胶柔性行为.离散元模拟结果与实验结果类似.此外,模拟显示低橡胶颗粒占比样品内主要由玻璃颗粒构成主力链结构,而橡胶颗粒基本不参与强力链的构成.当橡胶颗粒占比较大时,玻璃颗粒和橡胶颗粒共同构成主力链网络结构,但颗粒间法向接触力分布相对更为均匀,可视为玻璃颗粒悬浮于橡胶颗粒中.基于上述结果,提出了改进的等效介质理论,用于描述混合颗粒体系的弹性行为.研究认为:橡胶颗粒占比较小时内部颗粒的变形相对均匀,材料近似满足等应变假设,视为并联弹簧模型;橡胶颗粒占比较大时混合材料近似满足等应力假设,视为串联弹簧模型.两种模型得到的结果与模拟结果一致.上述结果有利于从微观角度揭示混合颗粒材料弹性行为的变化机制.     

Stress field and interaction forces of dislocations in anisotropic multilayer thin films

Utilizing Fourier transforms, the elastic field of three-dimensional dislocation loops in anisotropic multilayer materials is developed. Green's functions and their derivatives, obtained first in the Fourier domain and then in the real domain by numerical inversion, are used in integrals to determine the elastic field of dislocation loops. The interaction forces between dislocations and free surfaces or interfaces in multilayer thin films are then investigated. The developed method is based on rigorous elasticity solutions for dislocations approaching to within one to two atomic planes from the interface. For a dislocation in one layer, the interface image force is determined mainly by the elastic moduli and thicknesses of neighbouring layers. When a dislocation approaches an interface between two layers, within 10–20 atomic planes, the image force changes rapidly. Interaction forces are then kept constant up to the interface. The model shows that, when a dislocation crosses an interface from a soft to a hard layer, additional external forces must be applied to overcome an elastic mismatch barrier. The developed method extends the concept of the Kohler barrier in 2D, and shows that the interface force barrier not only depends on the relative ratio of the elastic moduli of neighbouring layers, but also on the 3D shape of the dislocation, the number of interacting adjacent layers, and on layer thicknesses.     

Mechanically tunable band gaps in compressible soft phononic laminated composites with finite deformation

We propose a compressible soft periodic structure to study the real time control ability or tunability of longitudinal elastic waves in it by applying a mechanical biasing field. The simple and nonlinear neo-Hookean material model for compressible elastic materials is employed to theoretically investigate the mechanically tunable properties of band structures. The effective acoustic impedance difference is first introduced in the Letter which seems to be the dominating parameter in tuning the acoustic band gaps.     

Structural phase transitions in isotropic magnetic elastomers

Magnetic elastomers represent a new type of materials that are “soft” matrices with “hard” magnetic granules embedded in them. The elastic forces of the matrix and the magnetic forces acting between granules are comparable in magnitude even under small deformations. As a result, these materials acquire a number of new properties; in particular, their mechanical and/or magnetic characteristics can depend strongly on the polymer matrix filling with magnetic particles and can change under the action of an external magnetic field, pressure, and temperature. To describe the properties of elastomers, we use a model in which the interaction of magnetic granules randomly arranged in space with one another is described in the dipole approximation by the distribution function of dipole fields, while their interaction with the matrix is described phenomenologically. A multitude of deformation, magnetic-field, and temperature effects that are described in this paper and are quite accessible to experimental observation arise within this model.     

A general 3-D nonlinear magnetostrictive constitutive model for soft ferromagnetic materials

In this paper, a new general nonlinear magnetostrictive constitutive model is proposed for soft ferromagnetic materials, and it can predict magnetostrictive strain and magnetization curves under various pre-stresses. From the viewpoint of magnetic domain, it is based on the important physical fact that a nonlinear part of the elastic strain produced by magnetic domain wall motion under a pre-stress is responsible for the change of the maximum magnetostrictive strain in accordance with the pre-stress. Then the reduction of magnetostrictive strain from the maximum is caused by the domain rotation. Meanwhile, the magnetization under various pre-stresses in this model is introduced by magnetostrictive effect under the same pre-stress. A simplified 3-D model is put forward by means of linearizing the nonlinear function, i.e. the nonlinear part of the elastic strain produced by domain wall motion, and by using the quartic of magnetization to describe domain rotation. Besides, for the convenience of engineering applications, two-dimensional (plate or film) and one-dimensional (rod) models are also given for isotropic materials and their application ranges are discussed too. In comparison with the experimental data of Kuruzar and Jiles, it is found that this model can predict magnetostrictive strain and magnetization curves under various pre-stresses. The numerical simulation further illustrates that the new model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves. Additionally, this model can be degenerated to the existing magnetostrictive constitutive model for giant magnetostrictive materials (GMM), i.e. a special soft ferromagnetic material.     

Elastic constants measurement of anisotropic Olivier wood plates using air-coupled transducers generated Lamb wave and ultrasonic bulk wave

A hybrid elastic wave method is applied to determine the anisotropic constants of Olive wood specimen considered as an orthotropic solid. The method is based on the measurements of the Lamb wave velocities as well as the bulk ultrasonic wave velocities. Electrostatic, air-coupled, ultrasonic transducers are used to generate and receive Lamb waves which are sensitive to material properties. The variation of phase velocity with frequency is measured for several modes propagating parallel and normal to the fiber direction along a thin Olivier wood plates. A numerical model based mainly on an optimization method is developed; it permits to recover seven out of nine elastic constants with an uncertainty of about 15%. The remaining two elastic constants are then obtained from bulk wave measurements. The experimental Lamb phase velocities are in good agreement with the calculated dispersion curves. The evaluation of Olive wood elastic properties has been performed in the low frequency range where the Lamb length wave is large in comparison with the heterogeneity extent. Within the interval errors, the obtained elastic tensor doesn’t reveal a large deviation from a uniaxial symmetry.     

Simulation of domain patterns in BaTiO3

Computer simulations of domain structure were performed within the continuous phenomenological time-dependent Ginzburg–Landau–Devonshire model including electrostatic long-range interactions. Calculations are done on cube or rectangle area blocks with periodic boundary conditions, employing the previously proposed method consisting in eliminating the elastic field using Euler's equations and solving the kinetic equations in Fourier space. The authors demonstrate that both strong anisotropy of the Ginzburg gradient interaction and realistic estimation of elastic and electrostatic long-range interactions are crucial for correct domain wall properties of BaTiO₃-type ferroelectrics. Domain architecture obtained from simulations performed with the authors' model parameters for BaTiO₃ is found to be in reasonable agreement with experiment.     

Novel experimentally observed phenomena in soft matter

Soft materials such as colloidal suspensions, polymer solutions and liquid crystals are constituted by mesoscopic entities held together by weak forces. Their mechanical moduli are several orders of magnitude lower than those of atomic solids. The application of small to moderate stresses to these materials results in the disruption of their microstructures. The resulting flow is non-Newtonian and is characterized by features such as shear rate-dependent viscosities and non-zero normal stresses. This article begins with an introduction to some unusual flow properties displayed by soft matter. Experiments that report a spectrum of novel phenomena exhibited by these materials, such as turbulent drag reduction, elastic turbulence, the formation of shear bands and the existence of rheological chaos, flow-induced birefringence and the unusual rheology of soft glassy materials, are reviewed. The focus then shifts to observations of the liquid-like response of granular media that have been subjected to external forces. The article concludes with examples of the patterns that emerge when certain soft materials are vibrated, or when they are displaced with Newtonian fluids of lower viscosities.     

Soft lubrication

We consider some basic principles of fluid-induced lubrication at soft interfaces. In particular, we quantify how a soft substrate changes the geometry of and the forces between surfaces sliding past each other. By considering the model problem of a symmetric nonconforming contact moving tangentially to a thin elastic layer, we determine the normal force in the small and large deflection limit, and show that there is an optimal combination of material and geometric properties which maximizes the normal force. Our results can be generalized to a variety of other geometries which show the same qualitative behavior. Thus, they are relevant in the elastohydrodynamic lubrication of soft elastic and poroelastic gels and shells, and in the context of biolubrication in cartilaginous joints.     

Wave field localization in a prestressed functionally graded layer

Characteristic features of wave field formation caused by a surface source of harmonic vibration in a prestressed functionally graded layer are investigated. It is assumed that the elastic moduli and the density of the material vary with depth according to arbitrary laws. The initial material of the medium is represented by a model hyperelastic material with third-order elastic moduli. The boundary-value problem for a set of Lamè equations is reduced to a set of Cauchy problems with initial conditions, which is solved by the Runge–Kutta–Merson method modified to fit the specific problem under study. Considering shear vibrations of a functionally graded layer as an example, effects of the type of its inhomogeneity, variations in its properties, and nature of its initial stressed state on the displacement distribution in depth are investigated. Special attention is paid to characteristic features of displacement localization in a layer with an interface-type inclusion near critical frequencies. A direct relation between the inhomogeneous layer structure and the type of displacement localization in depth is demonstrated. It is found that the role of initial stresses and variations in material parameters considerably increases in the vicinities of critical frequencies.     

Large-amplitude nonlinear vibrations of a Mooney–Rivlin rectangular membrane

An analysis of the linear and nonlinear vibration response and stability of a pre-stretched hyperelastic rectangular membrane under harmonic lateral pressure and finite initial deformations is presented in this paper. Geometric nonlinearity due to finite deformations and material nonlinearity associated with the hyperelastic constitutive law are taken into account. The membrane is assumed to be made of an isotropic, homogeneous, and incompressible Mooney–Rivlin material. The results for a neo-Hookean material are obtained as a particular case and a comparison of these two constitutive models is carried out. First, the exact solution of the membrane under a biaxial stretch is obtained, being this initial stress state responsible for the membrane stiffness. The equations of motion of the pre-stretched membrane are then derived. From the linearized equations, the natural frequencies and mode shapes of the membrane are analytically obtained for both materials. The natural modes are then used to approximate the nonlinear deformation field using the Galerkin method. A detailed parametric analysis shows the strong influence of the stretching ratios and material parameters on the linear and nonlinear oscillations of the membrane. Frequency–amplitude relations, resonance curves, and bifurcation diagrams, are used to illustrate the nonlinear dynamics of the membrane. The present results are compared favorably with the results evaluated for the same membrane using a nonlinear finite element formulation.     

A Wavelet-Based Processing method for simultaneously determining ultrasonic velocity and material thickness

Methods of measuring ultrasonic wave velocity in an elastic sample require data on the thickness of the sample and/or the distances between the transducers and the sample. The uncertainty of the ultrasonic wave velocity measurements generally depends on that of the data available. Conversely, to determine the thickness of a material, it is necessary to have a priori information about the wave velocity. This problem is particularly hard to solve when measuring the parameters of biological specimens such as bones having a greater acoustical impedance contrast (typically 3-5 MRayl) than that of the surrounding soft tissues (typically 1.5 MRayl). Measurements of this kind cannot easily be performed. But obtaining the thickness of a bone structure and/or the ultrasonic wave velocity is a important problem, for example, in biomechanical field for the calculation of elastic modulus, or in acoustical imaging field to parameterize the images, and to reference the grey or color level set to a physical parameter.The aim of the present study was to develop a method of simultaneously and independently determining the velocity of an ultrasonic wave in an elastic sample and the wave path across the thickness of this sample, using only one acquisition in pure transmission mode. The new method, which we have called the “Wavelet-Based Processing” method, is based on the wavelet decomposition of the signals and on a suitable transmitted incident wave correlated with the experimental device, and the mathematical properties such as orthonormality, of which lend themselves well to the time-scale approach. By following an adapted algorithm, ultrasonic wave velocities in parallelepipedic plates of elastic manufactured material and the apparent thicknesses were both measured using a water tank, a mechanical device and a matched pair of 1 MHz ultrasonic focused transducers having a diameter of 3 mm, a focal length of 150 mm and beam width of 2 × 2 mm at the focus (mean temperature 22°). The results were compared with those obtained with a conventional Pulse-mode method and with the control values, to check their validity. Measurements performed on bovine and human dry cortical bone samples are also presented to assess the limitations of the method when it is applied to elastic biological samples, including those of an equal-wavelength size (≈1.5 mm). The thicknesses and the ultrasonic wave velocities were then measured in this kind of (quasi-) parallelepipedic elastic materials with an mean estimated error ranged from 1% to 3.5% compared to the referenced values.