A constitutive model for fibrous tissues considering collagen fiber crimp

A micromechanically based constitutive model for fibrous tissues is presented. The model considers the randomly crimped morphology of individual collagen fibers, a morphology typically seen in photomicrographs of tissue samples. It describes the relationship between the fiber endpoints and its arc-length in terms of a measurable quantity, which can be estimated from image data. The collective mechanical behavior of collagen fibers is presented in terms of an explicit expression for the strain-energy function, where a fiber-specific random variable is approximated by a Beta distribution. The model-related stress and elasticity tensors are provided. Two representative numerical examples are analyzed with the aim of demonstrating the peculiar mechanism of the constitutive model and quantifying the effect of parameter changes on the mechanical response. In particular, a fibrous tissue, assumed to be (nearly) incompressible, is subject to a uniaxial extension along the fiber direction, and, separately, to pure shear. It is shown that the fiber crimp model can reproduce several of the expected characteristics of fibrous tissues.     

An empirical constitutive equation of integral type for viscoelastic liquids

A 5-constant constitutive equation is proposed. The analytical form for the relaxation modulus as a function of flow conditions was chosen based on experimental data for stress-relaxation in solid polymers. The resulting formulae for the material functions in simple and oscillatory shear flow fulfil the empirical Cox-Merz rule as well as other phenomenological relations formulated by Coleman and Markowitz. The theoretical results are compared with experimental data obtained by Han for various polymer melts. Good agreement between theory and experiment is found.     

A dynamic damage constitutive model for a rock mass with non-persistent joints under uniaxial compression

Most problems faced by the practicing rock mass engineering involve the evaluation of rock mass dynamic strength and deformability. As part of a rock mass, the mesoscopic flaws such as the microcracks and the macroscopic ones such as the joints both inherently affect the rock mass dynamic strength and deformational behavior. Nearly none of the existing models can handle the co-effect of these two kinds of flaws on the rock mass dynamic mechanical behavior. This study focusses on the rock mass with multi-sets of non-persistent joints and establishes a mathematical model accounting for the anisotropy in dynamic strength and deformability induced by the joints. Accordingly, an approach incorporating the existing models or methods to enable perfect simulation of the dynamic stress-strain relationship of a rock mass is proposed, in which the joint geometrical parameters such as the joint length and dip angle, the strength ones such as the joint internal friction and the deformational ones such as the joint normal and shear stiffness can all be taken into account. In order to investigate the validity of the proposed model, a series of calculation examples have been made and the results fits very well with the theoretical ones.     

Generic strength model for dry jointed rock masses

A new nonlinear thermo-mechanical model for heavily jointed rock masses is presented. The model describes poroelasticity, shear-enhanced compaction and brittle–ductile transition in dry porous rocks. The key input parameters of the model, such as elastic moduli, tensile and compressive strength are expressed as functions of the reference porosity of the rock. These functions are based on empirical data for limestones and sandstones and assume that the medium is isotropic. The effect of joints is modeled by scaling down the key model parameters. The scaling rules are found with the help of explicit numerical modeling of randomly jointed media.     

A viscoelastic constitutive model of rubber under small oscillatory load superimposed on large static deformation considering the Payne effect

The viscoelastic behavior of carbon-black-filled rubber under small oscillatory loads superimposed on large static deformation is dealt with. In this class of problems, as the strain amplitudes of the load increase, the dynamic stiffness decreases, and this phenomenon is known as the Payne effect. Besides the effects of the static deformation and the frequencies of the superimposed dynamic load, the Payne effect is considered in this study. Influence factors are introduced in this model in order to consider the influence of static predeformation, the dynamic-strain-dependent properties, and frequency-dependent properties. For simplicity, separation of the three dominant variables, frequency, prestatic deformation, and dynamic amplitude of strain, is assumed. The Kraus model is used for describing the Payne effect. Dynamic tension tests are executed to obtain the model parameters and also for the verification of the proposed model. The suggested constitutive equation shows reasonable agreement with test data.     

Exploring the relationship between critical state and particle shape for granular materials

The relationship between critical state and particle shape corresponds to the most fundamental aspect of the mechanics of granular materials. This paper presents an investigation into this relationship through macro-scale and micro-scale laboratory experiments in conjunction with interpretation and analysis in the framework of critical state soil mechanics. Spherical glass beads and crushed angular glass beads of different percentages were mixed with a uniform quartz sand (Fujian sand) to create a sequence of mixtures with varying particle shape. On the micro-scale, particle shape was accurately measured using a laser scanning technique, and was characterized by aspect ratio, sphericity and convexity; a new shape index, taken as the average of the three shape measures and referred to as overall regularity, was proposed to provide a collective characterization of particle shape. On the macro-scale, both undrained and drained triaxial tests were carried out to provide evidence that varying particle shape can alter the overall response as well as the critical states in both stress space and volumetric compression space. The mixtures of Fujian sand and spherical glass beads were found to be markedly more susceptible to liquefaction than the mixtures of Fujian sand and crushed angular glass beads. The change in liquefaction susceptibility was shown to be consistent with the change in the position of the critical state locus (CSL) in the compression space, manifested by a decrease in the intercept and gradient of the CSL due to the presence of spherical glass beads. Quantitative relationships have been established between each of the critical state parameters and each of the shape parameters, thereby providing a way to construct macro-scale constitutive models with intrinsic micro-scale properties built in.     

An elementary molecular-statistical basis for the Mooney and Rivlin-Saunders theories of rubber elasticity

By relaxing the assumption that the end-to-end vectors of molecules transform as macroscopic material line elements, we arrive at a generalization of the molecular-statistical theory of rubber elasticity. This generalization includes as special cases continuum-mechanical theories proposed by Mooney and by Rivlin and Saunders as improvements upon the classical neo-Hookean theory.     

基于TCK模型的非贯通节理岩体动态损伤本构模型

提出在岩体动态损伤本构模型中应同时考虑宏、细观缺陷;基于能量原理和断裂力学理论推导得出了同时考虑节理几何及力学特征的宏观损伤变量(张量)的计算公式;基于综合考虑宏、细观缺陷的复合损伤变量(张量)及完整岩石动态损伤Taylor-Chen-Kuszmaul(TCK)模型,建立了相应的单轴压缩下节理岩体动态损伤本构模型;利用该模型讨论了节理内摩擦角及节理长度对岩体动态力学特性的影响规律。研究表明,试件动态峰值强度随着节理内摩擦角的增大而增大,随着节理长度的增加而减小。     

An elastoplastic damage model for metal matrix composites considering progressive imperfect interface under transverse loading

An elastoplastic damage model considering progressive imperfect interface is proposed to predict the effective elastoplastic behavior and multi-level damage progression in fiber-reinforced metal matrix composites (FRMMCs) under transverse loading. The modified Eshelby’s tensor for a cylindrical inclusion with slightly weakened interface is adopted to model fibers having mild or severe imperfect interfaces [Lee, H.K., Pyo, S.H., 2009. A 3D-damage model for fiber-reinforced brittle composites with microcracks and imperfect interfaces. J. Eng. Mech. ASCE. doi:10.1061/(ASCE)EM.1943-7889.0000039]. An elastoplastic model is derived micromechanically on the basis of the ensemble-volume averaging procedure and the first-order effects of eigenstrains. A multi-level damage model [Lee, H.K., Pyo, S.H., 2008a. Multi-level modeling of effective elastic behavior and progressive weakened interface in particulate composites. Compos. Sci. Technol. 68, 387–397] in accordance with the Weibull’s probabilistic function is then incorporated into the elastoplastic multi-level damage model to describe the sequential, progressive imperfect interface in the composites. Numerical examples corresponding to uniaxial and biaxial transverse tensile loadings are solved to illustrate the potential of the proposed micromechanical framework. A series of parametric analysis are carried out to investigate the influence of model parameters on the progression of imperfect interface in the composites. Furthermore, a comparison between the present prediction and experimental data in the literature is made to assess the capability of the proposed micromechanical framework.     

Investigation of scale effect for the computation of turbulent flow around a circular cylinder

In order to investigate the scale effect of turbulent flow around a circular cylinder, two similarity numbers （criteria） based on turbulent kinetic and dissipation rates associ- ated with the fluctuation characteristics of turbulence wake are deduced by analyzing the Reynolds averaged NavierStokes equations （RANS）. The RNG k-s models and finite volume method are used to solve the governing equations and the second-order implicit time and upwind space discretization algorithms are used to discrete the governing equations. A numerical computation of flow parameters around a two-dimensional circular cylinder with Reynolds numbers ranging from 102 to l07 is accomplished and the result indicates that the fluctuation of turbulence flow along the center line in the wake of circular cylinder can never be changed with increasing Reynolds numbers when Re ≥ 3 × 10^6. This conclusion is useful for controlling the scale of numerical calculations and for applying model test data to engineering practice.     

A macroscopic multi-mechanism based constitutive model for the thermo-mechanical cyclic degeneration of shape memory effect of NiTi shape memory alloy

A macroscopic based multi-mechanism constitutive model is constructed in the framework of irreversible thermodynamics to describe the degeneration of shape memory effect occurring in the thermo-mechanical cyclic deformation of NiTi shape memory alloys(SMAs). Three phases,austenite A, twinned martensite Mtand detwinned martensite M~d, as well as the phase transitions occurring between each pair of phases( A → M~t, M~t→ A, A → M~d,M~d→ A, and M~t→ M~d) are considered in the proposed model. Meanwhile, two kinds of inelastic deformation mechanisms, martensite transformation-induced plasticity and reorientation-induced plasticity, are used to explain the degeneration of shape memory effects of NiTi SMAs. The evolution equations of internal variables are proposed by attributing the degeneration of shape memory effect to the interaction between the three phases(A, M~t, and M~d) and plastic deformation. Finally, the capability of the proposed model is verified by comparing the predictions with the experimental results of NiTi SMAs. It is shown that the degeneration of shape memory effect and its dependence on the loading level can be reasonably described by the proposed model.     

A fractional non-linear creep model for coal considering damage effect and experimental validation

Accurate prediction of coal׳s creep behavior is of great significance to coalbed methane extraction. In this study, taking into account the visco-elastic–plastic characteristics and the damage effect, a fractional non-linear model is proposed to describe the creep behavior of coal. The constitutive and creep equations of the proposed fractional non-linear model are derived via the Boltzmann superposition principle and discrete inverse Laplace transform. Furthermore, uniaxial creep tests under different axial stress conditions were carried out to validate the proposed model. It is found that the present model can describe the experimental data from creep tests with better accuracy than classical models. Particularly, the present model can predict the accelerating creep deformation of coal which classical models fail to reproduce. Finally, the parametric sensitivity analysis is performed to investigate the effects of model parameters on the creep strain. It is verified that the introduction of fractional parameters and damage factor in the present model is essential to accurate prediction of the full creep stage of coal.     

一种冲击波作用下结构毁伤算法研究

针对爆炸冲击波与建筑物结构相互作用过程,分析了冲击波与结构碎块作用机理,发展了一种能够模拟建筑物结构破坏及冲击波传播过程的计算模型和方法。采用建筑物结构工程毁伤载荷作为判据,处理结构在冲击波作用下的破坏问题;利用流固耦合界面算法处理结构运动引起的泄压效应,利用“虚拟网格通气技术”处理结构碎块对冲击波的阻碍作用,模拟了冲击波作用下典型建筑物的毁伤过程及冲击波传播过程。结果表明,该模型在模拟冲击波与结构的作用过程中,压力计算结果与非结构动网格模拟结果符合较好;在典型建筑物毁伤过程的数值模拟中,计算得到的建筑物毁伤效果和冲击波超压分布与建筑物物理毁伤特点符合。

     

Tension–compression asymmetry of phosphor bronze for electronic parts and its effect on bending behavior

In-plane tension and compression experiments on copper alloy sheets (phosphor bronze) and 6000 series aluminum alloy sheets (AA6016-T4) were conducted using a specially designed testing apparatus. The apparatus is equipped with comb-type dies so that stress–strain curves of a sheet specimen subjected to tension followed by compression, and vice versa, can be measured without buckling of the specimen, as well as those for monotonic tension and compression. A difference was observed in the flow stresses between tension and compression for the as-received copper alloy, but not for the aluminum alloy. Moreover, stress reversal tests, such as tension followed by compression and compression followed by tension, were carried out in order to measure the Bauschinger effect. In the second part of the experiment, bending moment–curvature diagrams were measured for the as-received and pre-stretched specimens. The bending moment–curvature diagrams were compared with those calculated using the stress–strain curves obtained from the tension–compression tests, and were in good agreement with those calculated with the tension–compression asymmetry and the Bauschinger effect correctly reproduced.