A micromechanical iterative approach for the behavior of polydispersed composites

In this paper, an iterative homogenization method is proposed in order to predict the behavior of polydispersed materials. Various families of heterogeneities according to their geometrical or mechanical properties are progressively introduced into a volume of matrix. At each step, the behavior of intermediate medium is obtained by any analytical homogenization method and is used as matrix of the following step. All homogenization methods, like dilute strain or stress approximations, Hashin’s bounds, three phases method, Mori–Tanaka’s approach or for example the N-layered inclusions method lead to the same effective behavior for the polydispersed material after convergence of the iterative process. Moreover, this convergence is obtained even for significant fractions of heterogeneities and for highly contrasted or polydispersed materials. This method is applied to various composites and validated by comparison with other modellings and experimental results.     

Strength homogenization of matrix-inclusion composites using the linear comparison composite approach

A homogenization procedure to estimate the macroscopic strength of nonlinear matrix-inclusion composites with different strength characteristics of the matrix and inclusions, respectively, is presented in this paper. The strength up-scaling is formulated within the framework of the yield design theory and the linear comparison composite (LCC) approach, introduced by Ponte Castaneda (2002) and extended to frictional models by Ortega et al. (2011), which estimates the macroscopic strength of composite materials in terms of an optimally chosen linear thermo–elastic comparison composite with a similar underlying microstructure. In the paper various combinations for the underlying material behavior for the individual phases of the composite are considered: The matrix phase can be a quasi frictional material characterized either by a Drucker–Prager-type (hyperbolic) or an elliptical strength criterion, which predicts a strength limit also in hydrostatic compression, while the inclusion phase either may represent empty pores, pore voids filled with a pore fluid, rigid inclusions, or solid inclusions, whose strength characteristics also maybe described by a Drucker–Prager-type or an elliptical strength criterion. For generating the homogenized strength criterion efficiently in such general cases of matrix-inclusion composites, a novel algorithm is proposed in the paper. The validation of the proposed strength homogenization procedure for selected combinations of strength characteristics of the matrix material and the inclusions is conducted by comparisons with experimental results and alternative existing strength homogenization models.     

A multi-phase micromechanical model for unsaturated concrete repaired using the electrochemical deposition method

Most concrete structures repaired using the electrochemical deposition method (EDM) are not fully saturated in reality. To theoretically illustrate the deposition healing process by micromechanics and quantitatively describe the effective properties of unsaturated concrete during the EDM healing process, a multi-phase multi-level micromechanical framework is proposed based on the microstructure of unsaturated concrete and the EDM’s healing mechanism. In the proposed model, the volume fractions of water and deposition products, the water effect (including further hydration and viscosity in pores) and the shapes of pores in the concrete are comprehensively considered. Moreover, multi-level homogenization procedures are employed to predict the effective properties of unsaturated concrete repaired using the EDM. For the first-level homogenization of this model, a modified function is presented to correct the Mori–Tanaka (M–T) method, which is used to predict the effective properties of equivalent inclusions composed of deposition products and water. To demonstrate the feasibility of the proposed micromechanical model, predictions obtained via the proposed multi-phase micromechanical model are compared with the experimental data, including results from extreme states during the EDM healing process. Finally, the influences of equivalent aspect ratios and deposition product properties on the healing effectiveness of EDM are discussed based on the proposed micromechanical model.     

A micromechanical model based on hypersingular integro-differential equations for analyzing micro-crazed interfaces between dissimilar elastic materials

The current work models a weak(soft) interface between two elastic materials as containing a periodic array of micro-crazes. The boundary conditions on the interfacial micro-crazes are formulated in terms of a system of hypersingular integro-differential equations with unknown functions given by the displacement jumps across opposite faces of the micro-crazes. Once the displacement jumps are obtained by approximately solving the integro-differential equations, the effective stiffness of the micr...     

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.     

Modeling anisotropic Reynolds-stress dissipation in particle- or droplet-laden flows

Particles or droplets dispersed in turbulent flows at sufficiently high volume loadings lead to modifications of turbulence characteristics. More specifically, in a detailed experimental investigation by Poelma and coworkers, where the particle phase moves with a non-zero mean velocity relative to the fluid phase, it was found that anisotropic Reynolds-stress dissipation is induced. Recently, we have proposed a model that can account for this effect in RANS-based and PDF method simulations. In our previous work, however, no simulation results of the RANS model formulation were presented. In the present work, a new compact tensorial RANS formulation is presented and the new formulation is validated against the experimental data of Poelma and coworkers.     

振动轮式硅微陀螺仪检测轴的闭环特性

研究了振动轮式硅微陀螺仪敏感结构的谐振特性,重点进行了检测轴的闭环控制系统分析和测试。通过对不同气压条件下检测轴谐振特性的研究及驱动轴和检测轴谐振频率匹配的试验,分析了静电力反馈控制系统中的变刚度问题,进行了硅微陀螺仪检测轴的闭环控制系统设计,给出了检测轴闭环控制系统的原理框图和传递函数,同时分析了闭环条件下驱动轴回路和检测轴回路各部分的相位关系以及正交分量的消除方法。试验结果表明闲环控制提高了硅微陀螺仪的精度指标。     

Modeling the anisotropic finite-deformation viscoelastic behavior of soft fiber-reinforced composites

This paper presents constitutive models for the anisotropic, finite-deformation viscoelastic behavior of soft fiber-reinforced composites. An essential assumption of the models is that both the fiber reinforcements and matrix can exhibit distinct time-dependent behavior. As such, the constitutive formulation attributes a different viscous stretch measure and free energy density to the matrix and fiber phases. Separate flow rules are specified for the matrix and the individual fiber families. The flow rules for the fiber families then are combined to give an anisotropic flow rule for the fiber phase. This is in contrast to many current inelastic models for soft fiber-reinforced composites which specify evolution equations directly at the composite level. The approach presented here allows key model parameters of the composite to be related to the properties of the matrix and fiber constituents and to the fiber arrangement. An efficient algorithm is developed for the implementation of the constitutive models in a finite-element framework, and examples are presented examining the effects of the viscoelastic behavior of the matrix and fiber phases on the time-dependent response of the composite.     

Modeling the viscoplastic micromechanical response of two-phase materials using Fast Fourier Transforms

A viscoplastic approach using the Fast Fourier Transform (FFT) method for obtaining local mechanical response is utilized to study microstructure-property relationships in composite materials. Specifically, three-dimensional, two-phase digital materials containing isotropically coarsened particles surrounded by a matrix phase, generated through a Kinetic Monte Carlo Potts model for Ostwald ripening, are used as instantiations in order to calculate the stress and strain-rate fields under uniaxial tension. The effects of the morphology of the matrix phase, the volume fraction and the contiguity of particles, and the polycrystallinity of matrix phase, on the stress and strain-rate fields under uniaxial tension are examined. It is found that the first moments of the stress and strain-rate fields have a different dependence on the particle volume fraction and the particle contiguity from their second moments. The average stresses and average strain-rates of both phases and of the overall composite have rather simple relationships with the particle volume fraction whereas their standard deviations vary strongly, especially when the particle volume fraction is high, and the contiguity of particles has a noticeable effect on the mechanical response. It is also found that the shape of stress distribution in the BCC hard particle phase evolves as the volume fraction of particles in the composite varies, such that it agrees with the stress field in the BCC polycrystal as the volume of particles approaches unity. Finally, it is observed that the stress and strain-rate fields in the microstructures with a polycrystalline matrix are less sensitive to changes in volume fraction and contiguity of particles.     

Mechanics of fish skin: A computational approach for bio-inspired flexible composites

Natural materials and structures are increasingly becoming a source of inspiration for the design novel of engineering systems. In this context, the structure of fish skin, made of an intricate arrangement of flexible plates growing out of the dermis of a majority of fish, can be of particular interest for materials such as protective layers or flexible electronics. To better understand the mechanics of these composite shells, we introduce here a general computational framework that aims at establishing a relationship between their structure and their overall mechanical response. Taking advantage of the periodicity of the scale arrangement, it is shown that a representative periodic cell can be introduced as the basic element to carry out a homogenization procedure based on the Hill-Mendel condition. The proposed procedure is applied to the specific case of the fish skin structure of the Morone saxatilis, using a computational finite element approach. Our numerical study shows that fish skin possesses a highly anisotropic response, with a softer bending stiffness in the longitudinal direction of the fish. This softer response arises from significant scale rotations during bending, which induce a stiffening of the response under large bending curvature. Interestingly, this mechanism can be suppressed or magnified by tuning the rotational stiffness of the scale-dermis attachment but is not activated in the lateral direction. These results are not only valuable to the engineering design of flexible and protective shells, but also have implications on the mechanics of fish swimming.     

三维编织复合材料渐进损伤的非线性模型及强度分析

建立了考虑周期性位移边界条件的细观体胞模型,对三维编织复合材料的渐进损伤过程进行数值模拟。采用Eshelby-Mori—Tanaka方法计算含损伤裂纹的材料的剐度矩阵,并将有限元网格尺寸和单元裂纹尺寸引入损伤演化方程,有效地降低了模拟结果对有限元网格的依赖程度。通过计算得到了材料应力应变的非线性关系和失效时的极限强度,并分析了材料的破坏机理。结果表明,大编织角材料的破坏模式主要是基体失效与纤维横向拉剪破坏,模拟计算结果与文献中的实验值吻合较好。     

Nonlinear progressive damage model for composite laminates used for low-velocity impact

In order to effectively describe the progressively intralaminar and interlam- inar damage for composite laminates, a three dimensional progressive damage model for composite laminates to be used for low-velocity impact is presented. Being applied to three-dimensional （3D） solid elements and cohesive elements, the nonlinear damage model can be used to analyze the dynamic performance of composite structure and its failure be- havior. For the intralaminar damage, as a function of the energy release rate, the damage model in an exponential function can describe progressive development of the damage. For the interlaminar damage, the damage evolution is described by the framework of the continuum mechanics through cohesive elements. Coding the user subroutine VUMAT of the finite element software ABAQUS/Explicit, the model is applied to an example, i.e., carbon fiber reinforced epoxy composite laminates under low-velocity impact. It is shown that the prediction of damage and deformation agrees well with the experimental results.     

含孔复合材料层合板静拉伸三维逐渐损伤分析

针对面内静拉伸纤维增强复合材料含中孔层合板，发展了参数化三维逐渐损伤模型. 该模型 可以模拟含中孔层合板损伤起始、发展及最终结构破坏整个过程，并能较好地预测含中孔层 合板的破坏模式和破坏强度. 采用所发展的模型和有限元三维逐渐损伤分析技术即应力分 析、失效判定准则及损伤过程中材料性能退化等，对其他文献所提供的9种不同类型含中孔层合板进行了损伤扩展分析及强度预测，同时对层合板的损伤基本机理、类型及其相互关联作用进行了探讨，计算结果与文献实验结果非常吻合.     

Negative Poisson's ratios in composites with star-shaped inclusions: a numerical homogenization approach

Summary Materials with specific microstructural characteristics and composite structures are able to exhibit negative Poisson's ratio. This result has been proved for continuum materials by analytical methods in previous works of the first author, among others [1]. Furthermore, it also has been shown to be valid for certain mechanisms involving beams or rigid levers, springs or sliding collars frameworks and, in general, composites with voids having a nonconvex microstructure.Recently microstructures optimally designed by the homogenization approach have been verified. For microstructures composed of beams, it has been postulated that nonconvex shapes with re-entrant corners are responsible for this effect [2]. In this paper, it is numerically shown that mainly the shape of the re-entrant corner of a non-convex, star-shaped, microstructure influences the apparent (phenomenological) Poisson's ratio. The same is valid for continua with voids or for composities with irregular shapes of inclusions, even if the individual constituents are quite usual materials. Elements of the numerical homogenization theory are reviewed and used for the numerical investigation. Accepted for publication 10 September 1996     

An investigation of intelligent tires using multiscale modeling of cord-rubber composites

A computational model based on the multiscale progressive failure analysis is employed to provide the theoretical predictions for damage development in the cord-rubber composites in tires. Vulcanized rubber, reinforcing belts, and carcass used in tire structures cause the anisotropic behavior under different loading conditions. Steel reinforcement layers made of steel wires combined with rubber complicate the macro-scale finite element modeling of tires. This paper presents a new three-dimensional model of the cord-rubber composite used in tires in order to predict the different types of damage including matrix cracking, delamination, and fiber failure based on the micro-scale analysis. Additionally, intelligent tires have the potential to be widely used to enhance the safety of road transportation systems, and this paper provides an estimation of the effects of void volume fraction, fiber volume fraction, and stacking sequence of the cord-rubber composites on the acceleration profile of the tire measured at the inner-liner.     

Modeling of impact on concrete plates by use of the microplane approach

A numerical approach to model 3D impact scenarios on concrete structures is presented and validated by experimental investigations. Special focus is given to dynamic contact modeling of an impactor loading a concrete plate at very high velocity. In this context, the main aspect is the elimination of non-physical oscillations of the kinematic fields by using an updated Newmark integration scheme. Two Lagrangian multipliers are used for this update which successfully reduces the unphysical oscillations of the above mentioned fields. In a further step, the material behavior of concrete is described by the microplane model introducing a new rate-dependent non-local damage formulation. Using the equivalent strain as a non-local field, the method is able to model, in an adequate manner so that the crack pattern in concrete is represented by the damage evolution in case of transient problems. The accuracy is validated and proved by the help of benchmark simulations as well as the observed phenomena to experimental investigations.     

Modeling of anisotropic softening phenomena: Application to soft biological tissues

A thermodynamically consistent dissipative model is proposed to describe softening phenomena in anisotropic materials. The model is based on a generalized polyconvex anisotropic strain energy function represented by a series. Anisotropic softening is considered by evolution of internal variables governing the anisotropic properties of the material. Accordingly, evolution equations are formulated and anisotropic conditions for the onset of softening are defined. In numerical examples, the model is applied to simulate the preconditioning behavior of soft biological tissues subjected to cyclic loading experiments. The results suggest that the general characteristics of preconditioning with different upper load limits are well captured including hysteresis and residual deformations. A model for the Mullins effect is obtained as a special case and shows very good agreement with experimental data on mouse skin.     

Hysteresis in magnetic shape memory composites: Modeling and simulation

Magnetic shape memory alloys are characterized by the coupling between the reorientation of structural variants and the rearrangement of magnetic domains. This permits to control the shape change via an external magnetic field, at least in single crystals. Composite materials with single-crystalline particles embedded in a softer matrix have been proposed as a way to overcome the blocking of the reorientation at grain boundaries.We investigate hysteresis phenomena for small NiMnGa single crystals embedded in a polymer matrix for slowly varying magnetic fields. The evolution of the microstructure is studied within the rate-independent variational framework proposed by Mielke and Theil (1999). The underlying variational model incorporates linearized elasticity, micromagnetism, stray field and a dissipation term proportional to the volume swept by the twin boundary. The time discretization is based on an incremental minimization of the sum of energy and dissipation. A backtracking approach is employed to approximately ensure the global minimality condition.We illustrate and discuss the influence of the particle geometry (volume fraction, shape, arrangement) and the polymer elastic parameters on the observed hysteresis and compare with recent experimental results.