Identification Of Elastic Constants Research Articles

Material characterization of laminated composite materials using a three-point-bending technique

A three-point-bending technique is presented for identifying the elastic constants of laminated composite materials . In the proposed technique, three strains in the axial, lateral, and 45° directions on the bottom surface at the mid-span of a symmetric angle-ply beam subjected to three-point-bending testing are measured for elastic constants identification. The narrow beam theory together with the trial elastic constants is used to predict the theoretical strains of the beam. The theoretical and experimental strains of the beams are then used in a stochastic optimization method to identify the elastic constants of the beam. The accuracy and applications of the proposed technique are demonstrated by means of a number of examples on the elastic constants identification of graphite/epoxy (Gr/ep) or glass/epoxy (Gl/ep) laminated composite materials. The effects of specimen aspect ratio and thickness on the accuracy of the proposed method are investigated.

Elastic Constants Identification of Composite Materials Using Single Angle-Ply Laminate

A method is presented for identification of elastic constants for composite materials using three measured strains of a single angle-ply laminate subjected to tensile testing. In the proposed method, the trial material constants of the angle-ply laminate are used to predict the corresponding strains in the laminate. An error function is established to measure the difference between the experimental and theoretical predictions of the strains. The identification of material constants is then formulated as a constrained minimization problem in which the material constants are determined to make the error function a global minimum. The accuracy and capability of the proposed method are demonstrated by means of a number of examples of the identification of material constants of angle-ply laminates with different lay-ups. Experimental data obtained from static tensile tests of several angle-ply laminates are used to identify the material constants of the laminates. The excellent results obtained in the experimental investigation have validated the applicability of the proposed method.

Estimation of elastic constants of thick laminated plates within a Bayesian framework

Abstract This paper compares two estimators for the dynamic identification of elastic constants of thick laminated composite plates. The plate’s response is modeled by finite elements based on Reddy’s third-order theory. The elastic constants are estimated within a Bayesian framework, using two estimators available in the literature. The estimators differ in the way they account for a priori information on the elastic constants to be identified. The resultant estimation procedures are critically examined and compared by paying special attention to the influence of a priori information on the final estimates. A unified interpretation of the two estimators is given and a modified strategy is proposed in order to improve reliability and convergence of the estimation process. Identification results for various case studies are presented.

Elastic constants identification of symmetric angle-ply laminates via a two-level optimization approach

A two-level optimization method for elastic constants identification of symmetric angle-ply laminates is presented. Measured axial and lateral strains of two symmetric angle-ply laminates with different fiber angles are used in the proposed method to identify four elastic constants of the composite laminates. In the first-level optimization process, the theoretically and experimentally predicted axial and lateral strains of a [(45°/−45°)2]s laminate are used to construct the error function which is a measure of the differences between the experimental and theoretical predictions of the axial and lateral strains. The identification of the material constants is then formulated as a constrained minimization problem in which the best estimates of the shear modulus and Poisson’s ratio of the laminate are determined by making the error function a global minimum. The problem of this level of optimization is then solved using a multi-start global minimization algorithm. In the second-level optimization process, the shear modulus and Poisson’s ratio determined in the previous level of optimization are kept constant while the Young’s moduli of the second angle-ply laminate with fiber angles other than 45° are identified using the same minimization technique that has been used in the previous level. The accuracy of the proposed method are studied by means of a number of numerical examples on the material constants identification of symmetric angle-ply laminates made of different composite materials. Finally, static tensile tests of [(45°/−45°)2]s and [(30°/−30°)2]s laminates made of Gr/ep composite material are performed to measure the strains of the laminates. The experimental data are then used to identify the elastic constants of the laminates. The excellent results obtained in the experimental investigation have demonstrated the feasibility and applications of the proposed method.

Adaptive Finite Element Methods for the Identification of Elastic Constants

In this paper, the elastic constants of a material are recovered from measured displacements where the model is the equilibrium equations for the orthotropic case. The finite element method is used for the discretization of the state equation and the Gauss---Newton method is used to solve the nonlinear least squares problem attained from the parameter estimation problem. A posteriori error estimators are derived and used to improve the accuracy by an appropriate mesh refinement. A numerical experiment is presented to show the applicability of the approach.

Identification of elastic constants for orthotropic materials from a structural test

In this paper, a new methodology for identifying numerous elastic parameters of any orthotropic material from a single structural test is presented. The state of stress in the tested structure (sample with non-uniform stress field) is admittedly complex and different points in it follow widely different stress paths. However, it has recently been shown that data of displacements at several points on the sample can be used to train a neural network embedded in a finite element code. The constitutive matrix resulting from the trained neural network based constitutive model (NNCM) is compared with the conventional constitutive matrix for an orthotropic material to determine the nine independent elastic constants. In order to demonstrate the methodology, test configuration of a panel of anisotropic material having a circular cavity at its centre and undergoing incremental vertical loads is adopted. Data of monitored displacements at several points needed to validate the methodology are obtained from a three-dimensional elastic finite element analysis assuming a set of orthotropic elastic constants for the material of the model. The elastic constants inferred from the trained NNCM are compared to those used for generating the load-deformation data. A very good agreement is noted.

Elastic Constants Identification of Shear Deformable Laminated Composite Plates

A constrained minimization method is presented for the identification of elastic constants of shear deformable laminated composite plates. Strains and/or displacements obtained from static testing of laminated composite plates are used in the proposed method to identify the elastic constants of the plates. In the identification process, the trial elastic constants of a laminated composite plate are used in a finite-element analysis to predict the strains and displacements of the plate. An error function is established to measure the differences between the experimental and theoretical predictions of strains and/or displacements. A constrained minimization technique is used to minimize the error function and update the trial elastic constants. The best estimates of the elastic constants of the plate are then determined by subsequently reducing the size of the feasible region of the elastic constants and making the error function a global minimum. The accuracy and applications of the proposed method are demonstrated by means of a number of examples. A sensitivity analysis is also performed to study the effects of variations of experimental data on the accuracy of the identified elastic constants.

Application of genetic algorithms for the identification of elastic constants of composite materials from dynamic tests

This work has been placed within the framework of the identification of stiffness properties of composite materials from dynamic tests. More precisely, the used approach has been inserted in the general context of model updating. The genetic algorithms method has been used as a complementary technique allowing a first estimation of the elastic coefficients. In other words, the initial finite element model is estimated. The refinement of solutions can thus be made by a classical updating method, such as the sensitivity method. The procedure allows the simultaneous estimation of several properties from a single test. Properties of extension, bending, twisting and transverse shear effects can be identified. Results obtained by numerical simulation show the efficiency and robustness of the genetic algorithms. Copyright © 1999 John Wiley & Sons, Ltd.

Application of genetic algorithms for the identification of elastic constants of composite materials from dynamic tests

This work has been placed within the framework of the identification of stiffness properties of composite materials from dynamic tests. More precisely, the used approach has been inserted in the general context of model updating. The genetic algorithms method has been used as a complementary technique allowing a first estimation of the elastic coefficients. In other words, the initial finite element model is estimated. The refinement of solutions can thus be made by a classical updating method, such as the sensitivity method. The procedure allows the simultaneous estimation of several properties from a single test. Properties of extension, bending, twisting and transverse shear effects can be identified. Results obtained by numerical simulation show the efficiency and robustness of the genetic algorithms. Copyright © 1999 John Wiley & Sons, Ltd.

Application of model updating techniques in dynamics for the identification of elastic constants of composite materials

This work consists of the identification of the stiffness properties of composite materials from dynamic tests. Unknown coefficients are identified by a technique of model updating. The formulation used (modal approach) is based on the minimization of the eigensolution residuals (sensitivity method). This technique allows the simultaneous identification of several properties from a single test. Stiffness properties of extension, bending, twisting and transverse shear have been identified. A discussion of the different identification approaches of elastic constants of composite materials from dynamic tests has been presented. Important points of the model updating in dynamics have been addressed: generalized mass errors, placement of sensors and approximate reanalysis of eigensolutions. Results obtained by numerical simulations show the efficiency of the proposed methodology.

Experimental Procedure and Results for the Identification of Elastic Constants of Thick Orthotropic Plates

Ability to determine six independent material parameters of thick orthotropic plates by a non-destructive numerical/experimental method is demonstrated. The parameters, which are the four in-plane elastic constants and the two transverse shear moduli, are deduced simultaneously from natural frequencies of the completely free plate by a nonlinear least squares approach. The main new contribution of the present paper is the consideration of higher mode natural frequencies of thick plates linked with an accurate numerical model based on a higher-order shear deformation theory for the theoretical predictions. This has enabled both transverse shear moduli to be estimated along with the in-plane parameters. Focus is here on the experimental technique and the application of the method in real tests. High quality frequency measurements are performed by the impulse technique employing a non-contacting microphone combined with advanced curve fitting of the frequency response function. The first 12 to 15 natural frequencies are typically considered. The different sources of errors associated with the method are discussed. The method is illustrated by evaluating the six elastic constants of an aluminium plate and of two different unidirectional composite plates. For the composites, close agreement is found between in-plane and out-of-plane shear moduli in the planes parallel to the fibres, confirming transverse isotropy.

Numerical method to recover the elastic constants from ultrasound group velocities

This paper proposes a numerical method for the identification of elastic constants. The method is based on a least-squares fit from the ultrasonic wave group velocities, as a function of the propagation direction in the principal planes. This algorithm is deduced from considerations on the Cagniard-de Hoop contour, associated with the fact that the wave arrival times correspond to discontinuities on the waveform. Two polynomials, in terms of group velocities, are then obtained. These two polynomials are linked by the phase slowness component on the surface. The method to recover the elastic constants is applied to simulated group velocities corresponding to a real composite material.

Identification of elastic constants of alloys with sheet and fibre textures based on resonance measurements and finite element analysis

This paper presents a method for identifying the elastic constants of alloys of cubic crystal structure with sheet and fibre textures. It is based on conventional resonance measurements and finite element (FE) analysis. It includes a non-linear optimizer, an FE program for solving eigenvalue equations in which the exact stress-strain constitutive law for orthorhombic or hexagonal symmetry is considered, and a frequency assignment algorithm based on the orthogonality of natural modes. The identification strategy consists in the adjustment of the elastic constants in an optimization procedure by minimizing the differences between calculated and measured natural frequencies of several specimens. The determination of the elastic single-crystal constants from textured material measurements is also discussed. The results of four practical applications to Ni-based alloys demonstrate the efficiency and the economy of this method.

Study of stratified rock masses by means of large-scale tests with an hydraulic pressure chamber : Oberti, G; Goffi, L; Rossi, P P Proc 5th Congress of the International Society for Rock Mechanics, Melbourne, 10–15 April 1983V1, PA133–A141. Publ Rotterdam: A. A. Balkema, 1983

The identification of elastic constants of stratified rock through large-scale in-situ tests with an hydraulic pressure chamber is discussed. Above all the anisotropy parameters of a stratified mass have been stated as a function of moduli and thicknesses of the layers. The influence of the stratification is analysed with reference to the equivalent crystalline anisotropy. Experimental measures performed by a special technique in a stratified rock mass consisting of alternating layers of sandstone and marl have been analysed and interpreted in comparison with the results of the theoretical approach. Finally the most recent development of ismes testing technique is illustrated and discussed. The number of the covering abstract of the congress is TRIS no. 385148. (TRRL)