Identification Of Elastic Properties Research Articles

Identification of elastic properties of interphase and interface in graphene-polymer nanocomposites by atomistic simulations

This article tackles the problem of identification of elastic continuum model by atomistic simulations for graphene polymer nanocomposite. The Atomistic Local IdentificAtion of Stiffness method, so-called ALIAS method, is developed to estimate the local stiffness tensor at all points of polymer graphene laminate nanocomposite. Results suggest that the graphene can be modeled at continuum scale by a general imperfect interface with zero thickness. Moreover, the identification procedure reveals the existence of interphase on either side of the graphene with a thickness of 1 nm, which is one and a half times stiffer than the polymer bulk matrix. The identified continuum model is used to study the effective elastic properties of nanocomposites with sandwich microstructure. This study at continuum scale reveals a softening effect due the very low stiffness of slip along graphene plane. The softening due to the interfaces is preponderant in relation to the interphase stiffening. Finally, the continuum model also suggests that the wrinkling of graphene increases the stiffness of nanocomposites.

Identification of Elastic Properties of Composites by Inversion of Ultrasonic Guided Wave Data

Given the inherent manufacturing variabilities and potential for in-service damage of composite parts, the identification of the elastic properties of composites is important to ensuring the safety and the proper performance of the part. The primary objective of this manuscript is to determine, nondestructively, the elastic properties of composite parts, whether as in-situ components that are part of a larger system, or as laboratory coupons. The proposed technique is based on multimode and dispersive ultrasonic guided waves propagating along a single direction, and the inversion of their phase velocity dispersion curves. The inversion procedure utilizes an efficient Semi-Analytical Finite Element method to solve the forward problem, and a Simulated Annealing algorithm as the optimization tool. The method is particularly well-suited for the characterization of composite laminates. In particular, the manuscript presents experimental evidence of the effectiveness of this technique, that was suggested earlier in a solely numerical work previously conducted by the authors. The test results show that reasonable accuracy can be obtained in the identification of four in-plane and three out-of-plane engineering constants of a quasi-isotropic laminate and a highly anisotropic laminate utilizing the single wave propagation direction. Non-obvious sensitivities of certain wave modes to particular constants are explained on the basis of stress coupling phenomena that are revealed by the SAFE wave propagation models. The study gives experimental evidence of the suitability of ultrasonic guided wave inversion schemes to identify the engineering constants of laminated composites, with the potential to properly characterize parts in-situ, because of the insensitivity of guided waves to boundary conditions located outside of the transmitter–receiver path.

Robust Multiscale Identification of Apparent Elastic Properties at Mesoscale for Random Heterogeneous Materials with Multiscale Field Measurements.

The aim of this work is to efficiently and robustly solve the statistical inverse problem related to the identification of the elastic properties at both macroscopic and mesoscopic scales of heterogeneous anisotropic materials with a complex microstructure that usually cannot be properly described in terms of their mechanical constituents at microscale. Within the context of linear elasticity theory, the apparent elasticity tensor field at a given mesoscale is modeled by a prior non-Gaussian tensor-valued random field. A general methodology using multiscale displacement field measurements simultaneously made at both macroscale and mesoscale has been recently proposed for the identification the hyperparameters of such a prior stochastic model by solving a multiscale statistical inverse problem using a stochastic computational model and some information from displacement fields at both macroscale and mesoscale. This paper contributes to the improvement of the computational efficiency, accuracy and robustness of such a method by introducing (i) a mesoscopic numerical indicator related to the spatial correlation length(s) of kinematic fields, allowing the time-consuming global optimization algorithm (genetic algorithm) used in a previous work to be replaced with a more efficient algorithm and (ii) an ad hoc stochastic representation of the hyperparameters involved in the prior stochastic model in order to enhance both the robustness and the precision of the statistical inverse identification method. Finally, the proposed improved method is first validated on in silico materials within the framework of 2D plane stress and 3D linear elasticity (using multiscale simulated data obtained through numerical computations) and then exemplified on a real heterogeneous biological material (beef cortical bone) within the framework of 2D plane stress linear elasticity (using multiscale experimental data obtained through mechanical testing monitored by digital image correlation).

Identification of elastic properties utilizing non-destructive vibrational evaluation methods with emphasis on definition of objective functions: a review

Defining a suitable objective function is important as it affects the solution search process and the solution quality. In vibrational material identification, a number of objective functions have been employed since the last decades. It is the intent of the present study to provide a comprehensive review of the previous and current trends of non-destructive vibrational material identification with emphasis on the definition of objective function. Prior to defining an objective function, several aspects should be given utmost attention, including selection of responses, design variables and goals. Along with the critical review of past research, potential areas that could be worth for future investigation are as well explicated.

On the identification of the elastic properties of composites by ultrasonic guided waves and optimization algorithm

This paper examines the potential of ultrasonic guided waves to identify the elastic properties of fiber-reinforced composite laminates widely used in light-weight structures. Due to variability in manufacturing processes, complexities involved in the constituent materials, or degradation in service, a non-destructive tool for the characterization of the composite’s properties can be extremely useful. A common assumption is the necessity for multiple wave propagation directions to fully characterize the properties. This paper examines the potential for property characterization by a single wave propagation direction. It proposes a property inversion scheme based on matching phase velocity dispersion curves of relevant guided modes by means of a Simulated Annealing optimization algorithm and a Semi-Analytical Finite Element method to solve the forward problem. Proof-of-principle numerical studies are presented to demonstrate the potential of each selected wave mode to provide identification of several properties, including the lamina elastic constants and the laminate effective constants. It is shown that the complex stress and strain profiles generated by the waves, aided by the anisotropy of the composite, create interesting “coupling” effects that ultimately enable accurate identification of several elastic properties away from the wave propagation direction.

Inverse Identification of Elastic Properties of Constituents of Discontinuously Reinforced Composites.

This paper is devoted to determination of elastic properties of composite constituents by using an inverse identification procedure. The aim of the developed identification procedure is to compute the elastic constants of individual material phases on the basis of known properties of composite materials. The inverse problem of identification has been solved by combining an evolutionary algorithm with a micromechanical model. The paper also focuses on selection of a suitable micromechanical model for optimization which should ensure a compromise between accuracy and complexity. Two different cases have been studied: composite reinforced with short cylindrical fibers and composite reinforced with cubic particles. Moreover, Monte Carlo simulations have been carried out to expose a difference in outcome of identification which may occur when uncertain input data is considered. Obtained results show that identification is successful only when properties of composite materials with at least two different volume fractions of the reinforcement are known.

Experimental and numerical investigation of the damping of flax–epoxy composite plates

In this paper, the vibration behaviour and damping performances of Flax Fiber Reinforced Epoxy (FFRE) are investigated. Static tests using FFRE composite beams are carried out leading to the identification of elastic properties of each layer. Then, three FFRE composite plates are elaborated and used in experimental vibration tests to identify their eigenfrequencies and their modal damping. In numerical part, a constant complex representation of the stiffness is assumed and the loss factors are supposed constants and identified from the first experimental vibration mode. The homogenization technique and the finite element method are applied to describe their damped dynamic behaviour. The resolution of the resulting non-linear problem is carried out using the Asymptotic Numerical Method (ANM). Experimental results show that the modal damping is greater when the flax fibers are oriented at 90°. Comparing numerical and experimental results, the proposed finite element modelling enables to estimate the damped eigenfrequencies with high accuracy. However, the predicted modal loss factors are over-estimated compared to experimental ones. It is concluded that the present modelling should be improved considering the frequency dependence of damping.

A vibration-based identification of elastic properties of stitched sandwich panels

Stitched sandwich becomes popular in structural application owing to its better performance in the transverse direction with respect to classical sandwich structure and relatively low-cost additional stitching process. The identification of its elastic properties is essential for offering a tailored structure for specific applications. A non-destructive identification method based on vibration test is proposed to obtain these parameters. The number of parameters is firstly reduced by a sensibility analysis. The retained parameters are identified by minimizing the cost function which indicates the gap between measured frequencies from vibration test and calculated frequencies from a finite element model. This method is applied to a stitched sandwich panel and its elastic properties are successfully identified.

Identification of elastic properties in the belief function framework

Handling the uncertainty of information sources is a key issue in parameter identification. In this work, we address this issue using the theory of belief functions. First, measurement information is described through likelihood-based belief functions, and prior information is represented by an arbitrary belief function. Second, both belief functions are combined by Dempster's rule using point-cloud representation of focal sets and Monte Carlo simulation. Lastly, to summarize the combined belief function, we propose to find the minimal-area region in the parameter space, whose belief and plausibility values exceed given thresholds. As compared to Bayesian inference, this approach is more flexible, as it allows us to specify weak prior information. Experimental results show that it is also more robust than Bayesian inference to unreliable prior information.

A displacement field approach based on FEM-ANN and experiments for identification of elastic properties of composites

An inverse approach combining numerical and experimental results with full-field displacement measurements will allow the identification of all the in-plane elastic properties from experimental tests. Instead of the use of a non-destructive technique, an alternative hybrid approach is proposed to obtain the field displacement. The experimental displacement field was replaced by the nodal displacement values numerically determined using the finite element method (FEM). The use of a surrogate model based on artificial neural network (ANN) enables to establish the relationship between the elastic properties and the displacement field avoiding the exhaustive calculations based on FEM. The Uniform Design Method is used to select the input values for ANN learning procedure. The optimal estimation of the model parameters is performed by minimizing an error functional defined as the difference between the experimental measurements and the simulated output results from ANN approximation model. Two examples were chosen to validate the proposed approach. The first one uses the off-axis tensile test in order to calibrate the numerical method eight-harness satin weave glass fiber reinforced phenolic composite. The second example is a hinged cross-ply laminated plate supporting a vertical load. The numerical results show strong agreement with the experimental values.

Identification of elastic properties of individual material phases by cou-pling of micromechanical model and evolutionary algorithm

The paper is devoted to an inverse problem of identification of individual material phases properties in dependence of known effective properties. In order to solve the identification problem, combining evolutionary algorithm with Mori-Tanaka method is proposed. In particular, the study focuses on a three-phase composite and takes experimental results from literature as an input data to analysis. The original contribution of this paper is a new identification strategy involving a resultant error that represents the uncertain character of both experimental data and model predictions. The new approach is demonstrated by performing several analyses with various assumptions. DOI: http://dx.doi.org/10.5755/j01.mech.22.5.16313

Identification of elastic properties of human patellae using micro-finite element analysis

Current homogenized finite element (hFE) models of the patella lack a validated material law and mostly overlook trabecular anisotropy. The objective of this study was to identify the elastic constants of patellar trabecular bone. Using μCT scans of 20 fresh-frozen cadaveric patellae, we virtually extracted 200 trabecular cubes (5.3mm side length). Bone volume fraction and fabric tensor were measured. The elastic constants were identified from six independent load cases using micro finite element (μFE) analyses. Both anisotropic and isotropic material laws were considered. The elastic constants were validated by comparing stiffness, strain and stress between hFE and μFE predictions of 18 patellar sections and six load cases. The hFE section models were built from μCT (anisotropic law) and CT (isotropic law) scans. The homogenized anisotropic model induced less error (13±5%) in the global stiffness prediction than the isotropic one (18±6%), and less error in the prediction of local apparent strain, stress, and strain energy, compared to the isotropic one. This validated hFE model could be used for future applications, either with the anisotropic constants, or with the isotropic ones when the trabecular fabric is unavailable.

Modified constitutive relation error: An identification framework dealing with the reliability of information

This paper proposes an identification strategy based on the principles of the Modified Constitutive Relation Error (M-CRE). The basic idea is to construct mechanical fields and material parameters that are a trade-off between all the available information but with no further hypothesis. The paper focuses on the identification of elastic properties from DIC (Digital Image Correlation) data in statics and the dealing of various kinds of boundary conditions (unknown or known) is especially discussed. We study our methodology on numerical examples in both homogeneous and heterogeneous isotropic elasticity, but a target application is the orthotopic behavior of aeronautic composites.

A dynamic analysis approach for identifying the elastic properties of unstitched and stitched composite plates

The identification of elastic properties from the dynamic behavior of structure has long been an alternative method to mechanical test. This method can avoid the variability of properties due to extraction of the specimen and achieve better homogenization by involving the whole structure. The mode classification is proposed and integrated in the identification process in this paper and helps to reduce the calculation time.Firstly, the measured frequencies are provided by vibration test while the calculated frequencies are provided by a finite element model with discrete Kirchhoff plate element. Then a mode classification process is conducted to accelerate the identification. Every constant is identified by minimizing the difference between the calculated and the measured frequencies of the group that it dominates. This method has been applied to two types of composite plate: unstitched plate and dispersedly stitched plate which presents both macro and meso heterogeneity. The limited dimension along the width direction of the stitch makes the modulus inaccessible by mechanical test and thus this dynamic method turns to be indispensable.

Plasma-sprayed coatings: Identification of plastic properties using macro-indentation and an inverse Levenberg–Marquardt method

Plasma-sprayed coatings are widely used for thermal protection and wear stability of structural components. These coatings feature an anisotropic porous structure as a result of the thermal spraying process. Although current literature provides methods for the identification of elastic properties of these materials, to our knowledge little research is dedicated to describing their plastic behavior, especially when these coatings are subjected to macro-scale contacts encountered in industrial applications. In this work we present a novel inverse method for the identification of plastic properties of thick plasma-sprayed coatings by means of macro-indentation and finite element simulations coupled to a Levenberg–Marquardt optimization. This optimization aims to fit numerically generated residual indentation profiles to the experimentally obtained ones. For the description of the coatings’ plastic behavior we made use of the Gurson–Tvergaard plasticity criterion coupled to a linear isotropic work hardening of the matrix. This criterion is appropriate for ductile porous solids as it takes into account the hydrostatic pressure, and it is readily implementable in commercial finite element software. The constitutive parameters to be identified include the yield strength σy0 and the work hardening coefficient K of the solid matrix as well as two dimensionless fitting parameters q1 and q2 and the void fraction f. For the given plasma-sprayed coating we could show that the proposed method is capable of identifying these parameters after as little as three iterations where σy0=1624MPa, K=33,340MPa, q1=3.29, q2=4.60 and f=4.2%.

Interfacial fracture of thin elastic layers due to cyclic load

Fracture of thin surface layers, which are harder or softer than the substrate material, is considered for the case of cyclic sliding contact. The study is based on modeling of multiple and single contact of two-layered elastic half-space, identification of elastic properties of the surface layers from indentation results, theoretical and experimental study of relatively hard coatings delamination due to contact fatigue, which arises at the level of asperities. The parameters of damage accumulation law at the coating-substrate interface for two component oxide coating are estimated. The properties of relatively soft coatings, which arises during friction of aluminium alloys because of soft faze extrusion are obtained from indentation data.

A Hertzian Integrated Contact Model of the Total Knee Replacement Implant for the Estimation of Joint Contact Forces

The prediction of lower limb muscle and contact forces may provide useful knowledge to assist the clinicians in the diagnosis as well as in the development of appropriate treatment for musculoskeletal disorders. Research studies have commonly estimated joint contact forces using model-based muscle force estimation due to the lack of a reliable contact model and material properties. The objective of this present study was to develop a Hertzian integrated contact model. Then, in vivo elastic properties of the Total Knee Replacement (TKR) implant were identified using in vivo contact forces leading to providing reliable material properties for modeling purposes. First, a patient specific rigid musculoskeletal model was built. Second, a STL-based implant model was designed to compute the contact area evolutions during gait motions. Finally, a Hertzian integrated contact model was defined for the in vivo identification of elastic properties (Young’s modulus and Poisson coefficient) of the instrumented TKR implant. Our study showed a potential use of a new approach to predict the contact forces without knowledge of muscle forces. Thus, the outcomes may lead to accurate and reliable prediction of human joint contact forces for new case study.

Metamodeling and robust minimization approach for the identification of elastic properties of composites by vibration method

This paper describes a method for determination of elastic parameters (elastic moduli and Poisson's ratio) of orthotropic composite plate‐type structural elements using the results of natural frequency measurements. The identification of parameter values is provided by minimization of weighted squared difference (discrepancy) between physically measured frequencies and natural frequencies calculated by Finite Element Method. The metamodels for the frequency dependence on the elastic parameters and other geometrical and physical parameters of test specimens, including parameters with uncertainty (“noisy constants”) are built using experimental designs optimized according to the Mean Squared Error space filling criterion and third‐order polynomial approximations. The minimum of weighted squared difference between measured and calculated frequencies is found using the multistart random search method. The expressions for standard deviations of identified parameters depending on deviations of “noisy constants” are derived using linearized metamodels. The expressions for identification errors allow the statement of the identification task as a robust minimization problem by simultaneous minimization of the discrepancy function and standard deviations of the identified values by varying the values of unknown elastic parameters and weighting coefficients for different frequencies. The partial scaling of natural frequencies is used for the reduction of the uncertainty impact on the identification error. This allows reducing the identification error of elastic moduli about two times and Poisson's ratio about 20 times in comparison with the results obtained by using dimensioned frequencies.

Simultaneous identification of elastic properties, thickness, and diameter of arteries excited with ultrasound radiation force

The elastic and geometric properties of arteries have been long recognized as important predictors of cardiovascular disease. This work presents a robust technique for the noninvasive characterization of anisotropic elastic properties as well as thickness and diameter in arterial vessels. In our approach, guided waves are excited along arteries using the radiation force of ultrasound. Group velocity is used as the quantity of interest to reconstruct elastic and geometric features of the vessels. One of the main contributions of this work is a systematic approach based on sparse-grid collocation interpolation to construct surrogate models of arteries. These surrogate models are in turn used with direct-search optimization techniques to produce fast and accurate estimates of elastic properties, diameter, and thickness. One of the attractive features of the proposed approach is that once a surrogate model is built, it can be used for near real-time identification across many different types of arteries. We demonstrate the feasibility of the method using simulated and in vitro laboratory experiments on a silicon rubber tube and a porcine carotid artery. Our results show that using our proposed method, we can reliably identify the longitudinal modulus, thickness, and diameter of arteries. The circumferential modulus was found to have little influence in the group velocity, which renders the former quantity unidentifiable using the current experimental setting. Future work will consider the measurement of circumferential waves with the objective of improving the identifiability of the circumferential modulus.

Multiscale Displacement Field Measurement Using Digital Image Correlation: Application to the Identification of Elastic Properties

As any Digital Image Correlation (DIC) method, Finite-Element (FE) based DIC methods lead to uncertainties which are related to the spatial resolution (in pixel/element). To overcome the tricky and well-known compromise between spatial resolution and uncertainty, a multiscale approach to FE-DIC is proposed. Additional nearfield images are used to improve locally the resolution of the measurement for a given measurement mesh. An automatic and accurate estimation of the nearfield/farfield transformation is obtained by a dedicated DIC based method, in order to bridge precisely the measurement performed at both scales. This multiscale measurement is then associated to a multiscale Finite Element Model Updating (FEMU) identification technique. After being validated on synthetic test cases, the method is applied to a tensile test carried out on an open-hole specimen made of glass/epoxy laminate. The four in-plane orthotropic elastic parameters are identified at different levels of loading. Results show that the multiscale approach greatly improves the uncertainty of both the measured displacements and the identified material parameters.