Orthotropic Material Properties Research Articles

A comparative study of using static and ultrasonic material testing methods to determine the anisotropic material properties of wood

This paper presents a comparative study using static and ultrasonic testing for the determination of the full set of orthotropic material properties of wood. In the literature, material properties are typically only available in the longitudinal direction, and most international standards do not provide details on the testing of the other two secondary directions (radial and tangential). This work provides a comprehensive study and discussions on the determination of all twelve orthotropic material properties of two hardwood species using static testing and an alternative testing approach based on ultrasonic waves. Recommendations are given on the execution of the tests and the interpretation and calibration of the results.

Optimization of bone scaffold structures using experimental and numerical data

Optimization of bone scaffold structures is performed on the basis of homogenized orthotropic elastic properties of trabecular bone tissue and three-scale numerical model. The orthotropic effective material properties are calculated using a finite element method numerical model of bone microstructure with numerical homogenization algorithm and serve as a template of surgically removed bone tissue. The evolutionary algorithm is used to optimize patient-specific, periodic structure of the bone scaffold, possessing parameters similar to the removed bone and so allowing the bone tissue to heal and rebuild faster. The proposed methodology can be used to design bone scaffolds manufactured from biodegradable biopolymers using fused deposition modeling methods.

Elasticity-based free vibration of anisotropic thin-walled beams

The free-vibration of anisotropic open and closed thin-walled beams is studied using approximate solutions to the three-dimensional equations of motion of a linear elastic solid. The three displacement components are approximated using grouped polynomials over both the cross-section coordinates and independent polynomial or trigonometric functions over the axial coordinate of several beams with representative boundary conditions. This method is applied to several sections with varying degrees of anisotropy and shape with both isotropic and orthotropic material properties. Results are compared with those computing using beam or shell theories, and several new results are presented for these geometries.

FINITE ELEMENT MODELING OF THE HUMAN COCHLEA USING FLUID–STRUCTURE INTERACTION METHOD

In this paper, a 3D finite element (FE) model of human cochlea is developed. This passive model includes the structure of oval window, round window, basilar membrane (BM) and cochlear duct which is filled with fluid. Orthotropic material property of the BM is varying along its length. The fluid–structure interaction (FSI) method is used to compute the responses in the cochlea. In particular, the viscous fluid element is adopted for the first time in the cochlear FE model, so that the effects of shear viscosity in the fluid are considered. Results on the cochlear impedance, BM response and intracochlear pressure are obtained. The intracochlear pressure includes the scala vestibule and scala tympani pressure are extracted and used to calculate the transfer functions from equivalent ear canal pressures to scala pressures. The reasonable agreements between the model results and the experimental data in the literature prove the validity of the cochlear model for simulating sound transmission in the cochlea. Moreover, this model predicted the transfer function from equivalent ear canal pressures to scala pressures which is the input to the cochlear partition.

Combined effects of heterogeneity and non-linearity on the critical time parameters of orthotropic conical shells

The work is devoted to the non-linear dynamic stability of heterogeneous orthotropic truncated conical shells subjected to the combined static and time-dependent axial loads. The basic equations are derived using the finite deflection theory with von Karman–Donnell-type of kinematic non-linearity and reduced to a non-linear differential equation with the time variable coefficient using the superposition principle and Galerkin method. The resulting equation is solved numerically using Runge–Kutta method for variety of an axial loading speed, heterogeneity of features, orthotropic material properties and conical shell characteristics to obtain the non-linear critical time parameters. Finally, the influences of the axial loading speed, non-linearity, heterogeneity and orthotropy on the dimensionless critical time parameters are discussed in detail.

Geometry generation challenges for modelling and analysis of micro-structured materials

Engineers evaluating the performance of a component at the design stage will typically convert Computer Aided Design (CAD) geometry into a Finite Element model, and run a Finite Element Analysis (FEA) to determine deformations and stress levels as a result of applied loads or displacements. The analysis results would then be interpreted by comparing them with the required duty of the component. For metallic components, homogeneous and isotropic material properties are generally assumed - "macro-scale" modelling. For components to be manufactured from composite materials, models may represent heterogeneity at the ply level, and orthotropic material properties applied with appropriate directionality. This ply-level modelling is often termed "meso-scale" modelling. Engineering interpretation of failure in materials is often based on empirical understanding of experimental data. This approach is generally robust: safety critical components would always be subject to validation by means of a suitable programme of testing. The aspect that is missing is the opportunity to improve understanding of the material performance by investigating the material performance at the "micro-scale". This paper describes computational algorithms for generating random geometries exhibiting similar characteristics to those seen at the "micro-scale" in real materials, and the use of these to predict the influence of the "micro-scale" structure on the "macro-scale" material performance.

Determination of material properties for short fibre reinforced C/C-SiC

Determining the mechanical properties of short fibre reinforced CMC using standard sized coupons has always been a challenge due to a high statistical scattering of the measured values. Although the random orientation of short fibres results in a quasi-isotropic material behavior of 2D-structures with a sufficiently large volume, the small volume typical for test coupons usually results in a non-isotropic fibre orientation in the tested volume. This paper describes a method for manufacturing unidirectional oriented short fibre reinforced CMC materials and presents material properties of UD-C/C-SiC. After verifying the fibre orientation of the CMC using micro-computed tomography, coupons were extracted to determine the orthotropic material properties. These orthotropic material properties were then used to predict the properties of C/C-SiC with randomly distributed short fibres. To validate the method, micro-computed tomography is used to quantitatively determine the fibre orientation within coupons extracted from randomly distributed short fibre C/C-SiC. After mechanical three-point-bending tests, the measured stiffness and bending strength is compared with the predicted properties. Finally, the data are used to devise a method suited for reducing the inherent large spread of material properties associated with the measurement of CMC materials with randomly distributed short fibres.

Methodology of experimental investigation of viscoelastic properties of orthotropic material

The paper considers the techniques for the conducting of an experimental investigation of viscoelastic properties of an orthotropic material. The solved problem of stretching and shearing of a thin viscoelastic plate by constant loads enabled an analytical determination of relaxation kernels. The developed method of a fitting of experimental data gained at different time and temperature points allowed a determination of elastic properties and a relaxation kernel of an orthotropic material with viscoelastic properties, whose the degree of anisotropy is determined by the degree of anisotropy of the elastic properties, using the method of least squares. The described methodology will be used for the estimation of the mechanical properties of thin composite structures.

The effects of wood variability on the free vibration of an acoustic guitar top plate.

A finite element model of a bare top plate with braces and a bridge plate was created using orthotropic material properties. The natural variation of the wood properties including dependence on moisture content was also determined. The simulated modes were then compared to experimentally obtained modes from top plate prototypes. Uncertainty analysis was also performed to determine the statistical bound of natural variability between wood samples. The natural frequencies of the model fall within the computed error bound. These results reinforce the importance of obtaining accurate material properties for acoustic guitar modeling.

Prediction of matrix-to-cell stress transfer in heart valve tissues.

Non-linear and anisotropic heart valve leaflet tissue mechanics manifest principally from the stratification, orientation, and inhomogeneity of their collagenous microstructures. Disturbance of the native collagen fiber network has clear consequences for valve and leaflet tissue mechanics and presumably, by virtue of their intimate embedment, on the valvular interstitial cell stress-strain state and concomitant phenotype. In the current study, a set of virtual biaxial stretch experiments were conducted on porcine pulmonary valve leaflet tissue photomicrographs via an image-based finite element approach. Stress distribution evolution during diastolic valve closure was predicted at both the tissue and cellular levels. Orthotropic material properties consistent with distinct stages of diastolic loading were applied. Virtual experiments predicted tissue- and cellular-level stress fields, providing insight into how matrix-to-cell stress transfer may be influenced by the inhomogeneous collagen fiber architecture, tissue anisotropic material properties, and the cellular distribution within the leaflet tissue. To the best of the authors' knowledge, this is the first study reporting on the evolution of stress fields at both the tissue and cellular levels in valvular tissue and thus contributes toward refining our collective understanding of valvular tissue micromechanics while providing a computational tool enabling the further study of valvular cell-matrix interactions.

NUMERICAL ANALYSIS OF A PROJECTILE PENETRATION INTO THE HUMAN HEAD VIA MESHLESS METHOD

In recent years, physicists, engineers and medical scientists have tried to demonstrate the biomechanics of gunshot wounds with numerical methods and experimental observations. Currently, the finite element method (FEM) is the most widely used numerical method among the studies related to ballistic wound injuries. However, when the FEM is used for the penetration analysis, the path of the projectile in the skull is subjected to extremely large deformations which will introduce errors due to distortion of elements. To overcome this error, the meshfree technique was established to simulate the gunshot wound as a preliminary study in which the skull was modeled by smoothed particle hydrodynamics (SPH) and the projectile was modeled by nondeformable rigid elements. In order to simulate a realistic penetration phenomenon, orthotropic material properties were defined for different regions (forehead, zygomatic and mandible) with material principal axis along the surface of the bones. Human response to the ballistics impacts were determined in terms of force occurring along the pathway of the bullet in the skull, residual velocity of the projectile and penetration depth. The obtained results were compared with the data reported in literature. As a result, mechanical behavior of the head under ballistic impacts simulated by the SPH, compared well with the results determined by the data given in literature, which indicates the applicability of the SPH method as a powerful technique in simulating different gunshot wound mechanisms.

Structural Analysis of the ITER Thermal Shield for Final Design Verification

The structural integrity of the ITER thermal shield (TS) has been verified by structural analysis. In this paper, the analysis process methodology and demonstration of the structural integrity for the TS are described. The analysis is performed for the TS global models and detailed models, such as supports and joints. TS joints in the shell model are modeled using orthotropic material properties. To verify the structural reliability for the TS, plastic collapse, buckling, ratcheting, and fatigue are assessed in accordance with ASME Section VIII, Div. 2.

Analysis of TF Insert Coil

The United States ITER Project Office (USIPO) is responsible for the design of the oroidal Field (TF) insert coil, which will allow validation of the performance of significant lengths of the conductors to be used in the full scale TF coils in relevant conditions of field, current density and mechanical strain. The Japan Atomic Energy Agency (JAEA) will build the TF insert which will be tested at the central solenoid model coil (CSMC) test facility at JAEA, Naka, Japan. Three dimensional mathematical model of TF insert was created based on the initial design geometry data, and included the following features: orthotropic material properties of superconductor material and insulation; external magnetic field from CSMC, temperature dependent properties of the materials; precompression and plastic deformation in lap joint. Major geometrical characteristics of the design were preserved including cable jacket and insulation shape, mandrel outline, and support clamps and spacers. The model is capable of performing coupled structural, thermal, and electromagnetic analysis using ANSYS. Numerical simulations were performed for room temperature conditions; cool down to 4 K, and the operating regime with 68 kA current at 11.8 Tesla background field. Numerical simulations led to the final design of the coil producing the required strain levels on the cable, while simultaneously satisfying the ITER magnet structural design criteria.

A novel approach to estimate trabecular bone anisotropy from stress tensors.

Continuum finite element (FE) models of bones and bone-implant configurations are usually based on clinical CT scans. In virtually all of these models, material properties assigned to the bone elements are chosen as isotropic. It has been shown, however, that cancellous bone can be highly anisotropic and that its elastic behavior is best described as orthotropic. Material models have been proposed to derive the orthotropic elastic constants from measurements of density and a fabric tensor. The use of such relationships in FE models derived from CT scans, however, is hampered by the fact that the measurement of such a fabric tensor is not possible from clinical CT images since the resolution of such images is not good enough to resolve the trabecular micro-architecture. In this study, we explore an alternative approach that is based on the paradigm that bone adapts its micro-architecture to the loading conditions, hence that fabric and stress tensors should be aligned and correlated. With this approach, the eigenvectors and eigenvalues of the element continuum-level stress tensor are used as an estimate of the element fabric tensor, from which the orthotropic material properties then are derived. Using an iterative procedure, element orthotropic material properties and fabric tensors are updated until a converged situation is reached. The goals of this study were to investigate the feasibility and accuracy of such an iterative approach to derive orthotropic material properties for a human proximal femur and to investigate whether models derived in this way can provide more accurate results than isotropic models. Results were compared to those obtained from models of the same femurs for which the fabric was measured from micro-CT scans. It was found that the iterative approach could well estimate the orientation of the fabric principal directions. When comparing the stress/damage values in the models with material properties based on estimated and measured fabric tensors, the differences were not significant, suggesting that the material properties based on the estimated fabric tensor well reflected those based on the measured fabric tensor. Errors were less than those obtained when using isotropic models. It is concluded that this novel approach can provide a reasonable estimate of anisotropic material properties of cancellous bone. We expect that this approach can lead to more accurate results in particular for models used to study implants, which are usually anchored in highly anisotropic cancellous bone regions.

Identification of the Elastic Properties of Isotropic and Orthotropic Thin-Plate Materials with the Pulsed Ultrasonic Polar Scan

Already in the early 1980’s, it has been conjectured that the pulsed ultrasonic polar scan (P-UPS) provides a unique fingerprint of the underlying mechanical elasticity tensor at the insonified material spot. Until now, that premise has not been thoroughly investigated, nor validated, despite the opportunities this would create for NDT and materials science in general. In this paper, we report on the first-ever implementation of an inverse modeling technique on the basis of a genetic optimization scheme in order to extract quantitative information from a P-UPS. We validate the optimization approach for synthetic data, and apply it to experimentally obtained polar scans for annealed aluminum, cold rolled DC-06 steel as well as for carbon fiber reinforced plastics. The investigated samples are plate-like and do not require specific preparation. The inverted material characteristics show good agreement with literature, micro-mechanical models as well as with results obtained through conventional testing procedures.

Performance of a cured-in-place pressure pipe liner passing through a pipe section without structural integrity

The performance of a cured-in-place pipe (CIPP) liner as it spans a section of host pipe that has lost its structural integrity is examined through finite element analyses. Orthotropic and nonlinear analyses are used to examine 3D effects. The 3D analysis is compared to an earlier axisymmetric model. The effects of friction between the liner and the old pipe as well as the orthotropic material properties of the liner are investigated. Failure pressures and unconfined hoop displacements are calculated using failure criteria from ASTM F2207-06 and it is concluded that the liner response is dominated by uniaxial rather than multiaxial strength properties. Lastly, it is recommended that the maximum stress criterion be used over the interactive stress criterion for this loading condition.

The combined influences of heterogeneity and elastic foundations on the nonlinear vibration of orthotropic truncated conical shells

The aim of the present paper is to study the nonlinear vibration of heterogeneous orthotropic truncated conical shells resting on the Winkler–Pasternak elastic foundations. The formulation is based on the Donnell shell theory, exponential-law distribution of orthotropic material properties and von Karman geometric nonlinearity. The basic equations are reduced to a time dependent geometrical nonlinear differential equation and solved using homotopy perturbation method (HPM). Finally, the influences of elastic foundations, heterogeneity, material orthotropy and shell characteristics on the nonlinear vibration of the truncated conical shell are studied.

画像相関法による変位分布の測定値を用いた一方向CFRPの弾性係数の同定

Identification of in-plane and through-thickness material properties of a unidirectional carbon fiber reinforced plastics (CFRP) plate from displacement fields is performed using a virtual fields method. The displacement fields are obtained through the measurement using digital image correlation. In order to obtain appropriate identification results, the measured displacements are reasonably smoothed and the optimized virtual displacement fields are determined for minimizing the influence of the measurement errors. The material properties are determined by applying this method to the displacement fields obtained for the beam specimen under three-point bending. Results show that the orthotropic material properties can be identified from the measured displacement fields. As the orthotropic material properties are obtained from measured displacement distributions, this method is expected to be applied to various materials.

Adaptive multi-scale modeling of high velocity impact on composite panels

A computationally efficient adaptive multi-scale methodology for modeling composites under high rates of loading is proposed. The physically based model relies on micromechanical properties of the constituents only. The adaptive algorithm switches between two different constitutive laws. Initially, the material response is calculated based on effective linear-elastic, orthotropic material properties at the ply scale which are calculated using the rule of mixtures. A modified Hashin–Rotem criterion is then used to identify the switch to a more accurate micromechanical analysis based on the generalized method of cells (GMC). The methodology is verified by simulating tensile tests on laminates with different stacking sequences. Finally the model validated against experimental data for high-velocity impact on quasi-isotropic composite targets taken from the literature in order to illustrate the efficiency and accuracy of the proposed methodology.

Characterization of the Orthotropic Elastic Constants of a Micronic Woven Wire Mesh via Digital Image Correlation

Woven structures are steadily emerging as excellent reinforcing components in dual-phase composite materials subjected to multiaxial loads, thermal shock, and aggressive reactants in the environment. Metallic woven wire mesh materials in particular display good ductility and relatively high specific strength and specific resilience. While use of this class of materials is rapidly expanding, a significant gap in property characterization remains. This research classifies the homogenized, orthotropic material properties of a representative twill dutch woven wire mesh through the use of in-plane uniaxial tensile experiments incorporating a Digital Image Correlation (DIC) strain measurement technique. Values for elastic modulus and Poisson’s ratio are calculated from the experimental data, and shear modulus values are identified by means of constitutive modeling. This approach establishes a reproducible method for characterizing the in-plane elastic response of micronic metallic woven materials via macro-scale uniaxial tensile tests, and shows that a homogenous orthotropic constitutive model may be employed to describe the macro-scale elasticity of this class of materials with reasonable accuracy.