3D Heterogeneous Stiffness Reconstruction Using MRI and the Virtual Fields Method

The first extension of the virtual fields method to the reconstruction of heterogeneous stiffness properties from 3D bulk full-field displacement data is presented in this paper. Data are provided by Magnetic Resonance Imaging (MRI). Two main issues are addressed: 1. the identification of the stiffness ratio between two different media in a heterogeneous solid; 2. the reconstruction of stiffness heterogeneities buried in a heterogeneous solid. The approach is based on a finite element discretization of the equilibrium equations. It is tested on experimental full-field data obtained on a phantom with the stimulated echo MRI technique. The phantom is made of a stiff spherical inclusion buried within a lower modulus material. Preliminary independent tests showed that the material of the inclusion was four times stiffer than the surrounding material. This ratio value is correctly identified by our approach directly on the phantom with the MRI data. Moreover, the modulus distribution is promisingly reconstructed across the whole investigated volume. However, the resulting modulus distribution is highly variable. This is explained by the fact that the approach relies on a second order differentiation of the data, which tends to amplify noise. Noise is significantly reduced by using appropriate filtering algorithms.     

Identification of orthotropic elastic constants using the Eigenfunction Virtual Fields Method

The Virtual Fields Method (VFM – Pierron and Grediac, 2012), an inverse method based on the principle of virtual work (PVW), is being increasingly used to estimate mechanical properties of materials from full-field deformations obtained from techniques such as Digital Image Correlation, moiré and speckle interferometry and grid methods. By making specific choices for virtual fields (VFs) in PVW, one obtains a system of algebraic equations, which is then solved for the unknown material constants. Recently, a new variant of VFM, known as the Eigenfunction Virtual Fields Method (EVFM) has been proposed (Subramanian, 2013). In EVFM, principal components of the measured (i.e. true) strain fields are used to systematically generate VFs. We extend EVFM to orthotropic elastic materials in this work, and estimate the relevant material parameters from full-field strain data generated from a finite-element model of an unnotched Iosipescu test. Varying levels of Gaussian white noise are added to the synthetic strain data to evaluate the sensitivity of EVFM to input noise. It is observed that for low to moderate noise, the material properties estimated by the proposed method are relatively insensitive to noise. However, when noise levels are high, the proposed method yields large variance in some of the computed properties when compared to the state-of-the-art optimized piecewise continuous VFM (Toussaint et al., 2006; Pierron and Grediac, 2012). Some of the large variance in properties estimated from noisy data using EVFM is traced to the sensitivity of the third dominant eigenfunction and modifications to the proposed method to address this issue are suggested.     

On a boundary condition used in Virtual Fields methods

The Virtual Fields Method (VFM) and the Eigenfunction Virtual Fields Method (EVFM) are inverse techniques for estimating constitutive properties from full-field experimental data. In these, a set of virtual fields is used in the Principle of Virtual Work (PVW) to yield a system of algebraic equations for the unknown material parameters. In a typical experiment, one does not know the distribution of tractions over the external surface of the specimen, but the total force is generally measured. In order to still enable evaluation of the external virtual work integral that appears in PVW, in all the work to date on Virtual Fields methods, the virtual displacements are restricted to be uniform over the portion of the exterior surface where tractions are prescribed so that the external virtual work is simply the inner product of the known total force vector and the uniform value of the chosen virtual displacement vector. In this work, we show that this constraint can be relaxed to obtain a more flexible version of EVFM. The proposed modification is used to obtain orthotropic elastic constants from a simulated unnotched Iosipescu test, and is shown to yield tighter estimates than previously obtained wherein the boundary virtual displacements were constrained to be uniform. This approach, which is novel to Virtual Fields methods, allows us to include domains in the interior of the specimen and therefore, results in an EVFM formulation capable of dealing with material heterogeneity, missing data and discontinuities in specimen geometry.     

Numerical simulation of thermo-mechanical fatigue properties for particulate reinforced composites

In this paper, a two dimensional Voronoi cell element, formulated with creep, thermal and plastic strain, is applied for the numerical simulation of thermo-mechanical fatigue behavior for particulate reinforced composites. The relation between mechanical fatigue phases and thermal fatigue phases influences the thermo-mechanical fatigue behavior and cyclic creep damage. The topological features of micro-structure in particulate reinforced composites, such as the orientation, depth-width ratio, distribution and volume fraction of inclusions, have a great influence on thermo-mechanical behavior. Some related conclusions are obtained by examples of numerical simulation.The project supported by the Special Funds for the National Major Fundamental Research Projects (2004CB619304), the National Natural Science Foundation of China (10276020 and 50371042), the Key Grant Project of Chinese Ministry of Education (0306)     

Identification of Elasto-Plastic Constitutive Parameters from Statically Undetermined Tests Using the Virtual Fields Method

This paper presents an experimental validation of the use of the virtual fields method to identify the elasto-plastic behaviour of an iron specimen from full-field measurements with the grid method and a simple heterogeneous test configuration. The experimental procedure is carefully detailed since it is of primary importance to obtain good identification results. In particular, the use of two back-to-back cameras has proved essential to eliminate out-of-plane effects. Then, the procedure for extracting the elastic parameters and the parameters of a Voce’s hardening model using the virtual fields method is presented. The results are very convincing and encouraging for future developments using more complex test geometries leading to fully multi-axial stress states. It is a first step towards the development of such inverse procedures as an alternative to difficult and costly methods involving homogeneous tests using multi-axial testing machines.     

Mechanical properties of lattice grid composites

An equivalent continuum method only considering the stretching deformation of struts was used to study the in-plane stiffness and strength of planar lattice grid com- posite materials. The initial yield equations of lattices were deduced. Initial yield surfaces were depicted separately in different 3D and 2D stress spaces. The failure envelope is a polyhedron in 3D spaces and a polygon in 2D spaces. Each plane or line of the failure envelope is corresponding to the yield or buckling of a typical bar row. For lattices with more than three bar rows, subsequent yield of the other bar row after initial yield made the lattice achieve greater limit strength. The importance of the buckling strength of the grids was strengthened while the grids were relative sparse. The integration model of the method was used to study the nonlinear mechanical properties of strain hardening grids. It was shown that the integration equation could accurately model the complete stress-strain curves of the grids within small deformations.     

A study on validity of using average fiber aspect ratio for mechanical properties of aligned short fiber composites with different fiber aspect ratios

A closed-form solution using the actual distribution of the fiber aspect ratio is proposed for predicting the stiffness of aligned short fiber composite. The present model is the simplified form of Takao and Taya’s model and the extended version of Taya and Chou’s model, where Eshelby’s equivalent inclusion method modified for finite fiber volume fraction is employed. The validity of using average fiber aspect ratio for predicting the composite stiffness is justified in terms of the scatter of fiber aspect ratio, fiber volume fraction, and constituents‘ Young’s modulus ratio, comparing with the results by the present model. The guideline for selection of either the actual distribution or the average fiber aspect ratio is presented for the better prediction of the composite stiffness.     

On the identification of non-linear mechanical systems using orthogonal functions

Real world mechanical systems present non-linear behavior and in many cases simple linearization in modeling the system would not lead to satisfactory results. Coulomb damping and cubic stiffness are typical examples of system parameters currently used in non-linear models of mechanical systems. This paper uses orthogonal functions to represent input and output signals. These functions are easily integrated by using a so-called operational matrix of integration. Consequently, it is possible to transform the non-linear differential equations of motion into algebraic equations. After mathematical manipulation the unknown linear and non-linear parameters are determined. Numerical simulations, involving single and two degree-of-freedom mechanical systems, confirm the efficiency of the above methodology.     

纺织结构复合材料冲击拉伸研究进展

纺织结构复合材料是以纺织结构作为增强体的一类复合材料, 其在一系列实际应用时往往要承受着高速冲击拉伸、冲击压缩等冲击载荷(冲击加载) 的作用. 因为纺织结构的整体性能, 纺织结构复合材料具有优异的抗冲击、抗分层与高损伤容限性能. 研究复合材料的冲击性能对于纺织结构复合材料的设计与应用具有指导作用. 本文详细介绍了纺织结构复合材料的发展, 纺织结构的种类及纺织结构复合材料的冲击拉伸性能实验与有限元分析研究情况, 同时也分析了纺织结构复合材料冲击拉伸破坏下的破坏机理研究进展, 并对纺织结构复合材料冲击拉伸性能研究的发展进行了展望.     

PP/CF增强珊瑚砂水泥基复合材料冲击压缩力学性能研究

在人工海水制备珊瑚砂水泥基复合材料中混杂加入碳纤维和聚丙烯纤维,得到4种不同纤维掺量的碳-聚丙烯混杂纤维增强珊瑚砂水泥基复合材料。采用直径100 mm的分离式Hopkinson压杆,对材料进行5种应变率下的冲击压缩试验,采用LS-DYNA进行相应的冲击压缩数值模拟。结果表明：(1) 试验应变率临界值为200 s⁻¹,当试验应变率大于200 s⁻¹时,混杂碳纤维和聚丙烯纤维所形成的纤维网络对试块的增韧效果加强;(2) 碳-聚丙烯混杂纤维增强珊瑚砂水泥基复合材料峰值应力具有明显的应变率效应,且动态增强因子对应变率的敏感程度较高;(3) 使用珊瑚砂细骨料导致试块内微裂纹和微空洞等缺陷较多,在珊瑚砂水泥基复合材料内混杂掺加碳纤维和聚丙烯纤维后,试块冲击抗压强度的提升有限,但珊瑚砂水泥基复合材料的抗冲击韧性显著提升;(4) 通过试验数据和参数调试确定了HJC模型的参数,试块峰值应力的模拟结果与试验结果的误差在5.97 %以内。

     

Using two scaling exponents to describe the mechanical properties of swollen elastomers

We study the ability of two scaling exponents to describe the mechanical properties of swollen elastomers. Swelling effects on the Young's modulus and osmotic pressure of swollen elastomers at equilibrium swelling are investigated using literature data and the Flory–Rehner free energy function. An extended model is developed by introducing two scaling exponents into elastic strain energy functions that are separated into deviatoric and volumetric components. This extended model satisfactorily reproduces the two different swelling effects, and also predicts swelling-induced rupture. The predicted tendency readily explains experimental observations well, i.e., swelling-induced rupture occurs when small extensions are applied in good solvents, and elucidates the mechanism of swelling-induced rupture of elastomers.     

Effect of crystalline grain structures on the mechanical properties of twinning-induced plasticity steel

In order to improve the mechanical properties of twinning-induced plasticity steel, the grain morphology was tailored by different solidification technologies combined with deformation and heat treatment processing routes. Three typical grain morphologies, i.e., equiaxed, columnar as well as equiaxed/columnar grains were formed, and their mechanical behaviors were comparatively studied. Among the three materials, the equiaxed grain material exhibited the highest strength but the lowest plasticity. Depending on the grain size, the smaller the grain size, the higher the strength, but the lower the elongation. The columnar grain material possessed the most excellent plasticity but the weakest strength.These properties presented a non-monotonic dependence on the dendrite spacing, and the moderate spacing resulted in the optimum combination of strength and plasticity. The equiaxed/columnar grain coexisted material showed interesting properties, i.e., the strength and plasticity were just between those of single grain-shaped materials. The three materials also presented different strain hardening behaviors particularly in the uniform deformation stage. The equiaxed grain material showed a constant strain hardening rate, while the columnar grain and equiaxed/columnar grain materials showed a progressively increasing rate with increasing the true strain.     

On the experimental determination of some mechanical properties of porcine periodontal ligament

This work analyzes some aspects of the experimental determination of the mechanical properties of the periodontal ligament (PDL). The necessity of extracting small samples, with a geometry as regular as possible, from a complex biological structure, makes it quite difficult both to establish a correct testing protocol and to obtain reliable results, for instance usable by bioengineers to develop constitutive models. Here, by means of more than 250 experiments performed on small samples of porcine PDL, we try both to provide some statistically significant information, and to clarify some issues related to the testing protocols. Some basic mechanical parameters for the PDL (Young’s modulus, shear modulus, failure stress and strain for tension, compression, and shear tests) are measured, and a relevant statistical analysis is provided. The influence of some experimental parameters (sample conservation procedure, testing modalities), is also studied; on the basis of our results, we can conclude that (i) if conservation is needed, a cooling at −80° is sufficient to guarantee statistically significant results, (ii) it is important to perform at least the compression tests keeping the samples immersed in pressurized fluid, and (iii) preconditioning cycles are necessary only for studying the initial (toe) region of the stress–strain curves. It is also observed that, with these types of samples, some special care is required when computing stresses and strains from force and displacement measurements. In order to illustrate this aspect, some non-linear Finite Element analyses are performed, aimed at evaluating the influence of the sample geometry on the stress and strain calculation. Finally, the issue of fiber damage due to the cutting procedures is briefly discussed.     

Investigations to the effect of heating-rate on the mechanical properties of aluminum alloy LY12

Two classes of experiments were conducted with a Gleeble 1500 thermal–mechanical testing system to investigate the effect of heating-rate and its history on the mechanical behavior of aluminum alloy LY12. In the first class of experiment, specimens were heated at different heating-rates to prescribed temperatures and then stretched until fracture. It was found that the specimen heated with higher heating-rate possesses lower rupture strength. In the second class of experiment, the specimens were preloaded and then heated at different rates until fracture. It was found that the higher the heating-rate was, the lower the failure temperature would be. Metallographical analysis showed that there are more defects in the specimens undergoing higher heating-rate. It was conjectured that higher heating-rate may cause stronger local thermal inconsistency due to the heterogeneous nature of the material. It may then cause local residual microstress fields, which, together with external thermal–mechanical load, may result in the changes in the microstructure of the material, such as recovery, recrystallization, nucleation and growth of microdefects, accounting for the changes in the macroscopic mechanical properties including hardening/softening, damage and failure, etc. A numerical simulation was performed, in which the mechanisms of local thermal inconsistency and the effect of the influencing factors were investigated.     

三维编织复合材料模量的双尺度有限元计算

针对三维编织复合材料的力学性能进行了双尺度有限元(TSA)数值计算,给出了计算模型和算法过程,并将数值结果与文献中的实验数据进行了比较,验证了算法的物理准确性。编织复合材料的力学性能不仅依赖于材料的基本组份,也与细观构造相关。双尺度有限元计算可以数值模拟出三维编织复合材料的整体力学性能,从而为材料的研发提供指导。本文的双尺度有限元三维数值计算方法可以推广到其他增强／孔隙等多相复合材料的数值模拟。     

2D dynamic analysis of cracks and interface cracks in piezoelectric composites using the SBFEM

The dynamic stress and electric displacement intensity factors of impermeable cracks in homogeneous piezoelectric materials and interface cracks in piezoelectric bimaterials are evaluated by extending the scaled boundary finite element method (SBFEM). In this method, a piezoelectric plate is divided into polygons. Each polygon is treated as a scaled boundary finite element subdomain. Only the boundaries of the subdomains need to be discretized with line elements. The dynamic properties of a subdomain are represented by the high order stiffness and mass matrices obtained from a continued fraction solution, which is able to represent the high frequency response with only 3–4 terms per wavelength. The semi-analytical solutions model singular stress and electric displacement fields in the vicinity of crack tips accurately and efficiently. The dynamic stress and electric displacement intensity factors are evaluated directly from the scaled boundary finite element solutions. No asymptotic solution, local mesh refinement or other special treatments around a crack tip are required. Numerical examples are presented to verify the proposed technique with the analytical solutions and the results from the literature. The present results highlight the accuracy, simplicity and efficiency of the proposed technique.     

Numerical analysis of effective elastic properties of geomaterials containing voids using 3D random fields and finite elements

The purpose of the study is to investigate the influence of porosity and void size on effective elastic geotechnical engineering properties with a 3D model of random fields and finite element. The random field theory is used to generate models of geomaterials containing spatially random voids with controlled porosity and void size. A “tied freedom” analysis is developed to evaluate the effective Young’s modulus and Poisson’s ratio in an ideal block material of finite elements. To deliver a mean and standard deviation of the elastic parameters, this approach uses Monte-Carlo simulations and finite elements, where each simulation leads to an effective value of the property under investigation. The results are extended to investigate an influence of representative volume element (RVE). A comparison of the effective elastic stiffness of 2D and 3D models is also discussed.     

Simultaneous identification of stiffness and damping properties of isotropic materials from forced vibrating platesIdentification simultanée de rigidités et d'amortissements de matériaux isotropes à partir de plaques en vibrations forcées

This paper presents a novel methodology for the identification of damping of isotropic plates. It relies on forced inertial excitation of a clamped plate and full-field curvature measurements using a suitable optical technique. Using the Virtual Fields Method, it is shown that the damping parameter is easily related to the curvature field, even on a non-resonant plate. This paper opens a totally new field of investigation for damping identification. To cite this article: A. Giraudeau, F. Pierron, C. R. Mecanique 331 (2003).     

L'identification des propriétés mécaniques de matériaux avec la méthode des champs virtuels,une alternative au recalage par éléments finisIdentification of the mechanical properties of materials with the virtual fields method,an alternative to finite element model updating

A method allowing the identification of parameters that govern constitutive equations of materials is proposed in this Note. These parameters are identified from heterogeneous strain fields. The method is direct so that iterative calculations based on finite element model updating are avoided. To cite this article: M. Grédiac et al., C. R. Mecanique 330 (2002) 107–112.