Time‐resolved integrated digital image correlation

This paper discusses a method that provides the direct identification of constitutive model parameters by intimately integrating the finite element method (FEM) with digital image correlation (DIC), namely, directly connecting the experimentally obtained images for all time increments to the unknown material parameters. The problem is formulated as a single minimization problem that incorporates all the experimental data. It allows for precise specification of the unknowns, which can be, but are not limited to, the unknown material properties. The tight integration between FEM and DIC enables for identification while providing necessary regularization of the DIC procedure, making the method robust and noise insensitive. Through this approach, the versatility of the FE method is extended to the experimental realm, enhancing the analyses of existing experiments and opening new experimental opportunities. Copyright © 2015 John Wiley & Sons, Ltd.     

Towards Material Testing 2.0. A review of test design for identification of constitutive parameters from full‐field measurements

Full‐field optical measurements like digital image correlation or the grid method have brought a paradigm shift in the experimental mechanics community. While inverse identification techniques like finite element model updating or the virtual fields method have been the object of significant developments, current test methods, inherited from the age of strain gauges or linear variable displacement transducers, are generally not well adapted to the rich information provided by these new measurement tools. This paper provides a review of the research dealing with the design and optimization of heterogeneous mechanical tests for the identification of material parameters from full‐field measurements, christened here Material Testing 2.0 (MT2.0).     

A fully integrated noise robust strategy for the identification of constitutive laws from digital images

Constitutive parameter identification has been greatly improved by the achievement of full‐field measurements. In this context, noise sensitivity has been shown to be of great importance. It is crucial to incorporate noise sensitivity minimization in the design of robust identification procedures. In this paper, we investigate noise sensitivity reduction techniques for constitutive parameter identification based on Finite Element Model Updating. After examining the existing strategies, we propose a single step algorithm based on a mixed optical/mechanical cost function. The key point of this novel procedure is that no boundary conditions are needed. A first example on a real case illustrates the advantages of the proposed methodology in terms of noise sensitivity. A second example shows its capabilities to identify a non‐linear consitutive law. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimised Experimental Characterisation of Polymeric Foam Material Using DIC and the Virtual Fields Method

This article presents a methodology to optimise the design of a realistic mechanical test to characterise the material elastic stiffness parameters of an orthotropic PVC foam material in one single test. Two main experimental techniques were used in this study: Digital Image Correlation (DIC) and the Virtual Fields Method (VFM). The actual image recording process was mimicked by numerically generating a series of deformed synthetic images. Subsequent to this, the entire measurement and data processing procedure was simulated by processing the synthetic images using DIC and VFM algorithms. This procedure was used to estimate the uncertainty of the measurements (systematic and random errors) by including the most significant parameters of actual experiments, e.g. the geometric test configuration, the parameters of the DIC process and the noise. By using these parameters as design variables and by defining different error functions as object functions, an optimisation study was performed to minimise the uncertainty of the material parameter identification and to select the optimal test parameters. The confidence intervals of the identified parameters were predicted based on systematic and random errors obtained from the simulations. The simulated experimental results have shown that averaging multiple images can lead to a significant reduction of the random error. An experimental determination of the elastic coefficient of a PVC foam material was conducted using the optimised test parameters obtained from the numerical study. The identified stiffness values matched well with data from previous tests, but even more interesting was the fact that the experimental uncertainty intervals matched reasonably well with the predictions of the simulations, which is a highly original result and probably the main outcome of the present paper.     

Investigation of the Uncertainty of DIC Under Heterogeneous Strain States with Numerical Tests

Abstract: In this research, numerical 2D digital image correlation (DIC) tests are carried out to assess the uncertainty of DIC under heterogeneous strain states. DIC is implemented to measure the deformation of the numerically deformed images with respect to the undeformed counterparts, which are taken from the real tensile specimens. The tensile specimens are made of three materials, that is, steel DC06, steel DX54D+Z and aluminium alloy Al6016 and cut into three different geometries, namely one standard design and two complex designs. The specimens are all painted manually with random speckle patterns. The original images are deformed by imposed displacement fields, which are obtained by simulating uni‐axial tensile tests of the specimens with finite element analysis (FEA). In this way, the errors sourcing from the hardware of the image system are excluded. According to the geometries of the specimens, homogeneous and heterogeneous strain states are achieved by FEA. The optimum mesh sizes of the models are identified to minimise theirs influence on the imposed fields. The impacts of subset sizes, step sizes and strain window sizes are studied for an optimum correlation. Finally, the influence of the strain state is investigated. It is found that the DIC accuracy and precision decrease under highly heterogeneous strain states.     

模型缩聚-模型修正迭代方法的研究

模型修正中通常需要解决自由度匹配问题,模型缩聚是解决这一问题的一种方法。当有限元建模误差较大时,模型缩聚的近似会大大降低模型修正的精度。针对这一问题,提出了模型缩聚-模型修正迭代方法,消除模型缩聚带来的误差。文中应用IRS缩聚和基于频响函数的模型修正方法对提出的迭代方法进行了具体讨论。通过板梁混合结构的数值模拟实验,比较了现有修正方法和迭代修正方法的修正精度。结果表明提出的迭代方法有效提高了修正精度,使修正后的模型频率和物理参数更逼近真实值。同时该方法具有较高的迭代收敛效率,符合实际工程应用的要求。     

Evaluating the use of digital image correlation for strain measurement in historic tapestries using representative deformation fields

An analysis technique to assess the viability of digital image correlation (DIC) in tracking the full‐field strains across the surface of hanging historic tapestries is presented. Measurement uncertainty related to the use of the inherent tapestry image in tracking displacements is investigated through use of “synthetic” deformation fields. The latter are generated by mapping the details of a given tapestry image into finite element analyses. The combination of self‐weight loading, material non‐linearity, and image specific heterogeneity (related to slit stitching, damage, and patch‐restorations) serve to generate a bespoke deformation field complex enough to assess the reliability of DIC measurements. Accuracy is evaluated by comparing measured results with the original known deformations. The technique demonstrates that the optimum imaging settings and the choice of subset size for DIC analysis are strongly influenced by the tapestry image and the goal of the measurement, they are found using a compromise between conflicting objectives: minimising measurement error while maximising resolution.     

Model updating of a rotating machine using the self-adaptive differential evolution algorithm

Despite the good accuracy of finite element (FE) models to represent the dynamic behaviour of mechanical systems, practical applications show significant discrepancies between analytical predictions and experimental results, which are mostly due to uncertainties on the geometry configuration, imprecise material parameters and vague boundary conditions. Thereby, different approaches have been proposed to solve the inverse problems associated with the updating of FE models. Among them, the techniques based on minimization processes have shown to be some of the most promising ones. In this paper, a self-adaptive heuristic optimization method, namely the self-adaptive differential evolution (SADE), is evaluated. Differently from the canonical differential evolution (DE) algorithm, the SADE strategy is able to update dynamically the required parameters such as population size, crossover parameter and perturbation rate. This is done by considering a defined convergence rate on the evolution process of the algorithm in order to reduce the number of evaluations of the objective function. For illustration purposes, the SADE strategy is applied to the solution of typical mathematical functions. Additionally, the strategy is equally used to update the FE model of a rotating machine composed by a horizontal flexible shaft, two rigid discs and two unsymmetrical bearings. For comparison purposes, the canonical DE is also used. The results indicate that the SADE algorithm is a recommended technique for dealing with this kind of inverse problem.     

广义逆特征值方法在动力模型修正中的应用

本文针对土木工程中理论计算的要求和特点,基于逆特征值理论给出了一种适合有限元动力模型修正的广义逆特征值方法,该方法在给出修正解的表达式基础上,要求修正解满足动力模型的力学特征,且仅需要少量试验数据,是一种简单、实用的有限元模型修正方法。     

A Dissipation Gap Method for full‐field measurement‐based identification of elasto‐plastic material parameters

Using enriched data such as displacement fields obtained from digital image correlation is a pathway to the local identification of material parameters. Up to now, most of the identification techniques for nonlinear models are based on Finite Element Updating Methods. This article explains how an appropriate use of the Dissipation Gap Method can help in this context and be an interesting alternative to these classical techniques. The Dissipation Gap Methods rely on the concept of error in dissipation that has been used mainly for the verification of finite element simulations. We provide here an original application of these founding developments to the identification of material parameters for nonlinear behaviors. The proposed technique and especially the main technical keypoint of building the admissible fields are described in detail. The approach is then illustrated through the identification of heterogeneous isotropic elasto‐plastic properties. The basic numerical features highlighted through these simple examples demonstrate this approach to be a promising tool for nonlinear identification.Copyright © 2012 John Wiley & Sons, Ltd.     

Modelling Strategies for Property Identification Based on Full‐Field Surface Displacement Data

Abstract: The use of full‐field displacement measurements in mechanical testing provides detailed response information that can be used, in conjunction with modelling and optimisation, for precise material property identification. One limitation of this technique is that the collection of response data and the sectioning of a specimen to reveal the material microstructure are both destructive tests and mutually exclusive, as the displacement measurement occurs only on the exposed surface. Therefore, modelling of an experiment to interpret a full‐field experiment requires assumptions about the structure of the material below the visible surface. This study evaluates the effects of several possible modelling assumptions on the errors in model‐predicted response and on the resulting material property estimates. A 3‐D microstructural model, for which the subsurface grain geometry and orientations are known, provides the basis for comparison of several common modelling assumptions based on the grain geometry and orientations on the visible surface of a specimen.     

实测模态和结构模型同步修正的结构损伤识别方法

在基于灵敏度分析的有限元模型修正方法基础上,提出一种对实测模态和结构模型同步修正的结构损伤识别方法。即利用有损结构模态与测量噪声在时频域内的差异,以结构有限元模型为基准,对实测模态差进行小波去噪处理,再利用修正后的模态构造目标函数,进行有限元模型修正,经过迭代计算最终可识别结构的损伤。数值算例表明该方法可有效降低噪声的影响,提高损伤识别的精度。     

数字图像相关方法辅助的IM7/8552碳纤维/环氧树脂复合材料单向带层合板沿厚度方向非线性本构参数识别

提出了采用数字图像相关(DIC)方法和有限元模型修正(FEMU)技术相结合,通过短梁剪切(SBS)试验获得碳纤维增强环氧树脂(IM7/8552)正交各向异性复合材料单向带层合板沿厚度方向压缩本构关系参数的试验方法.该方法根据假设材料初始本构,采用3D有限元模型(FEM)计算获得主平面压头下方沿厚度方向的应力和应变分布,...     

Damage identification in three-dimensional structures using single-objective evolutionary algorithms and finite element model updating: evaluation and comparison

This study presents a methodology which integrates single-objective evolutionary algorithms (EAs) and finite element (FE) model updating for damage inference in three-dimensional (3D) structures. First, original well-known EAs, namely the genetic algorithm, differential evolution (DE) and particle swarm optimization (PSO), are combined with FE model updating for detecting damage in a 3D four-storey modular structure and their performances are compared. Next, to obtain more accurate results, hybrid Lévy flights–DE and hybrid artificial bee colony–PSO are developed for enhancing damage identification. With each method, the objective function composed of modal strain energy and mode shape residuals, taken from the FE model of the intact structure and the simulated damage responses, is initially created. Then, the performance of each algorithm combined with FE model updating for damage detection is assessed in terms of three characteristics: consistency, computational cost and accuracy, and the best performing algorithm is recommended.     

新的模型修正与模态扩展迭代方法

由于有限元模型与实验模型自由度的不匹配,模型修正中经常需要使用模态扩展技术。利用动态扩充法进行模态扩展进而进行模型修正时,模型修正过程中并没有考虑到使用有限元模型对实验数据进行模态扩展而造成的误差。针对这一问题,提出一种新的迭代方法,在模型修正过程中计及了上述的误差项,并将其以修正项的形式添加到模型修正当中,同时该方法没有限定所使用模型修正的方法,具有一定的通用性。通过Cross-model Cross-mode method(CM-CM)模型修正方法对新的迭代方法进行了详细讨论。算例表明,新的迭代方法较原方法可以极大地提高模型修正的迭代收敛速度。     

去噪正则化模型修正方法在桥梁损伤识别中的应用

以传统基于灵敏度分析的有限元模型修正方法为基础,提出一种结合小波去噪过程的正则化模型修正损伤识别方法.为改进模型修正方法损伤识别效果,一方面利用有损结构模态与模态噪声的波形在时频域内的差异,以结构有限元模型为基准,对实测模态差进行小波去噪处理,并利用修正后的模态构造目标函数;一方面采用正则化方法改善反问题求解的非适定性.由于从输入数据和求解过程两方面同时改善了结构损伤识别反问题的求解,因此可以有效抑制实测模态参数中噪声的影响,正确识别结构损伤.以连续梁桥模型为例的损伤识别数值模拟表明,所提出方法在保持识别算法鲁棒性、抑制噪声的同时,可有效提高桥梁结构损伤的识别精度.     

基于区间分析的不确定性结构动力学模型修正方法

提出了一种基于区间分析的不确定性有限元模型修正方法。在区间参数结构特征值分析理论和确定性有限元模型修正方法基础上,假设不确定性与初始有限元模型误差均较小,采用灵敏度方法推导了待修正参数区间中点值和不确定区间的迭代格式。以三自由度弹簧-质量系统和复合材料板为例,采用拉丁超立方抽样构造仿真试验模态参数样本,开展仿真研究。结果表明,当仿真试验样本能准确反映结构模态参数的区间特性时,方法的收敛精度和效率均较高;修正后计算模态参数能准确反映试验数据的区间特性。所提出方法适用于解决试验样本较少,仅能得到试验模态参数区间的有限元模型修正问题。     

Single‐camera special stereo‐digital image correlation applied for accurate virtual fields method identification

A single‐camera special stereo‐DIC (SS‐DIC) is proposed for accurate virtual fields method (VFM) identification. The single‐camera SS‐DIC allows accurate surface 3D deformation measurements using a single colour camera and a specially designed colour separation device. It not only effectively eliminates the unavoidable out‐of‐plane movement/rotation due to unideal in‐plane loading but also delivers uniformly distributed measurement points that brings great simplicity and convenience for internal virtual work calculation in VFM. In addition, since only a single camera is used for stereovision, the proposed SS‐DIC system requires no complicated synchronisation devices. The effectiveness and practicality of the proposed method are evaluated by heterogeneous deformation experiments of a holed aluminium alloy and 304 stainless steel plate. Combined with a high‐speed colour camera, the proposed method is expected to be a simple and practical method for the calibration of material constitutive model under intermediate and high strain rate conditions using VFM.     

A 3D domain decomposition approach for the identification of spatially varying elastic material parameters

The post‐treatment of (3D) displacement fields for the identification of spatially varying elastic material parameters is a large inverse problem that remains out of reach for massive 3D structures. We explore here the potential of the constitutive compatibility method for tackling such an inverse problem, provided an appropriate domain decomposition technique is introduced. In the method described here, the statically admissible stress field that can be related through the known constitutive symmetry to the kinematic observations is sought through minimization of an objective function, which measures the violation of constitutive compatibility. After this stress reconstruction, the local material parameters are identified with the given kinematic observations using the constitutive equation. Here, we first adapt this method to solve 3D identification problems and then implement it within a domain decomposition framework which allows for reduced computational load when handling larger problems. Copyright © 2015 John Wiley & Sons, Ltd.     

修正结构有限元模型的一种方法

本文讨论了一个寻找结构有限元模型的误差源和对它进行修正的方法.为了减少待修正模型的未知参数数目,将质量、刚度矩阵描述为设计变量的函数.在此基础上,先用少量测得的静位移数据修正刚变矩阵;然后用少数几阶实验的固有频率、固有振型数据修正质量矩阵.为了避免测量旋转自由度的静位移和固有振型分量的困难,还讨论了聚缩模型的修正问题.最后,文中附有算例及结果.