Isotropic Material Properties Research Articles

THE EFFECTS OF INTRA-ABDOMINAL PRESSURE ON THE STABILITY AND UNLOADING OF THE SPINE

In spite of earlier experimental and modeling studies, the relative role of the intra-abdominal pressure (IAP) in spine mechanics has remained controversial. This study employs simple analytical and finite element (FE) models of the spine and its surrounding structures to investigate the contribution of IAP to spinal loading and stability. The analytical model includes the abdominal cavity surrounded by muscles, lumbar spine, rib cage and pelvic ring. The intra-abdominal cavity and its surrounding muscles are represented by a thin deformable cylindrical membrane. Muscle activation levels are simulated by changing the Young's modulus of the membrane in the direction of muscle fibers, yielding IAP values recorded under the partial Valsalva maneuver. In the FE model, the abdominal cavity is cylindrical and filled with a nearly incompressible fluid. The surrounding muscles are modeled as membrane elements with transverse isotropic material properties simulating their fiber orientation. Results indicate a good qualitative agreement between the analytical and FE models. Larger external force and/or higher levels of muscle activation generate higher IAP thereby increasing spinal stiffness. These effects are more pronounced for activation of muscles with more horizontally directed fibers, e.g., transverse abdominis (TA). The capacity of the abdominal muscles to indirectly unload and stabilize the spine by generating IAP depends mostly on their fiber orientation, and secondarily on their cross-section area.

Analysis of functionally graded plates by meshless method: A purely analytical formulation

Functionally graded plates under static and dynamic loads are investigated by the local integral equation method (LIEM) in this paper. Plate bending problem is described by the Reissner moderate thick plate theory. The governing equations for the functionally graded material with respect to the neutral plane are presented in the Laplace transform domain and therefore the in-plane and bending problems are uncoupled. Both isotropic and orthotropic material properties are considered. The local integral equation method is developed with the locally supported radial basis function (RBF) interpolation. As the closed forms of the local boundary integrals are obtained, there are no domain or boundary integrals to be calculated numerically in this approach. The solutions of the nodal values for the entire plate are obtained by solving a set of linear algebraic equation system with certain boundary conditions. Details of numerical procedures are presented and the accuracy and convergence characteristics of the method are examined. Several examples are presented for the functionally graded plates under static and dynamic loads and the accuracy for proposed method has been observed compared with 3D analytical solutions.

J025024 X線CT画像に基づく骨組織の異方性情報抽出と個体別有限要素解析

There are many studies of patient-specific stress analyses of musculoskeletal systems based on x-ray CT images. However, conventional finite element models reported in these researches were composed of the elements which have isotropic material properties in spite of the anisotropy of anatomical bony tissue. It means that more accurate analysis of bone requires a huge amount of tiny elements to represent material anisotropy of bone. This study aims to generate a small FE model of bone with anisotropic material properties in order to perform more reliable stress analyses with a personal computer. This paper proposes quantification algorithm of material anisotropy of bone based on micro-focused CT images. A stress analyses were performed and it reveals the consideration of bone anisotropy is important for patient-specific analysis of bone tissue.

Modelling and Simulation of SAW Sensor Using FEM

Abstract The paper deals with modelling and simulation of surface acoustic waves sensor using finite element method. SAW sensor is made from piezoelectric GaN layer and SiC substrate. In the modelling, FEM code ANSYS is used, where modal and transient piezoelectric analysis are performed. Only plane behavior of the SAW device with transversally isotropic material properties are considered. Modal analysis is used to determined eigenmode and eigenfrequency of the system and the frequency is used as input in transient analysis as frequency of excitation. In transient analysis with harmonic loading wave propagation on the surface of piezoelectric layer as well as wave propagation into the substrate is investigated.

Mechanical Bending Simulation of Thin Stainless Steel by Using Isotropic and Orthotropic Properties

The most important factors in hard disk drive suspension manufacturing is the suspension preload, so call “gram load”. The suspensions were generally made from cold rolled stainless steel (SUS304). The suspensions were formed by mechanical forming and gram load was adjusted by mechanical bending until reached a specification. The material properties in mechanical bending simulation of thin stainless steel were usually as isotropic for simple calculation. But the properties of thin stainless steel should be defined as orthotropic materials. Therefore, this work aimed to study gram load results of using isotropic and orthotropic properties. The thin stainless sheet was cut and test for mechanical properties in rolling and transverse directions. The properties of the thin sheet were applied to simulation model. It was found that orthotropic material properties shows a good agreement with the experimental results more than using isotropic material properties. Therefore, the results of this work could be used to explain and predict the mechanical response on the suspension manufacturing.

Design and Optimization of Soft Magnetic Composite Machines With Finite Element Methods

In this paper, a synthesis of design methodologies for electromagnetic devices made with soft magnetic composite (SMC) material is presented. To realize efficient and low-cost SMC devices, it is necessary to benefit from interesting isotropic SMC material properties such as 3-D flux circulation path. In this case, the best approach is to carry out a topological structure research and perform a global optimization using physical models. However, the iterative optimization process can be computationally intensive and some compromises should be found between accuracy and computation time. One way is to use coarse models with important simplifying hypotheses but the optimal solution is often not valid. In this case, one can perform a limited number of finite element (FE) simulations to compute some correction coefficients and improve optimization convergence to a valid optimal solution. Another way is to perform the device optimization by using directly FE models with low mesh density and several simplifications of the device geometry. Such design approaches are illustrated by three concrete realizations with SMC material.

Eddy-Current Simulations Using an Independent Impedance Method in Anisotropic Biological Tissues

A widely applied method for simulating the induced eddy currents in biological tissues is the impedance method (IM). This method has recently been extended to the independent impedance method (IIM), which identifies and solves a linear system of independent equations, resulting in acceleration of computations. Both IM and IIM assume isotropic material properties, even though some tissues have directionally dependent characteristics. Therefore, we formulate IIM toward space-dependent anisotropic material properties. In this paper, the method is applied to the simulation of transcranial magnetic stimulation (TMS) for both isotropic and anisotropic spherical head models. The numerical results show that anisotropy has a nonnegligible effect on the induced currents, yielding maximum differences of about 40% in the skull and 19% in gray matter. The method is validated by comparing the results with finite element method (FEM) solutions. This study leads to a more realistic numerical modeling of the eddy currents due to the incorporation of anisotropy.

Elastic and plastic properties of powder materials: a continuum model

A continuum model based on the physical hypotheses of the discrete contact model is developed to describe the elastic and plastic properties of isotropic powder materials, taking into account the inhomogeneous deformation of the solid phase. The localization of elastic and plastic deformation is described by hypothesizing that deformable and nondeformable volumes form in the solid phase and that the resistance to deformation is associated only with the deformable volume. An analytical dependence of the deformable volume on the density of powder material is provided. The proposed model ensures high-accuracy fit to the experimental compaction curves at the stages of interparticle slip and plastic deformation of particles. At the beginning of plastic deformation, a particle is regarded as a cast one already plastically deformed and hardened to the level of the effective yield strength of the solid phase. The particle is further hardened as a cold-worked cast material is. Good agreement is reached between calculated and experimental data on the elastic moduli and plastic compaction of powders during isostatic pressing and deposition in a high-pressure chamber.

Simultaneous Estimation of Electrical and Thermal Properties of Isotropic Material from the Tone-Burst Eddy Current Thermography (TBET) Time–Temperature Data

In this paper, an inversion method is proposed to determine simultaneously the electrical and the thermal properties of a given isotropic material from the time-temperature data obtained from tone-burst eddy current thermography (TBET). A multiphysics forward model for computing the surface temperature data was used in a genetic algorithm (GA) based inversion technique to determine the material properties such as electrical conductivity (σ), thermal conductivity ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> ), density (ρ), and specific heat ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cp</i> ) simultaneously. Different trials were carried out initially with simulated temperature data (with and without noise) and then validated with experiments.

Patient-Specific Finite-Element Analyses of the Proximal Femur with Orthotropic Material Properties Validated by Experiments

Patient-specific high order finite-element (FE) models of human femurs based on quantitative computer tomography (QCT) with inhomogeneous orthotropic and isotropic material properties are addressed. The point-wise orthotropic properties are determined by a micromechanics (MM) based approach in conjunction with experimental observations at the osteon level, and two methods for determining the material trajectories are proposed (along organs outer surface, or along principal strains). QCT scans on four fresh-frozen human femurs were performed and high-order FE models were generated with either inhomogeneous MM-based orthotropic or empirically determined isotropic properties. In vitro experiments were conducted on the femurs by applying a simple stance position load on their head, recording strains on femurs' surface and head's displacements. After verifying the FE linear elastic analyses that mimic the experimental setting for numerical accuracy, we compared the FE results to the experimental observations to identify the influence of material properties on models' predictions. The strains and displacements computed by FE models having MM-based inhomogeneous orthotropic properties match the FE-results having empirically based isotropic properties well, and both are in close agreement with the experimental results. When only the strains in the femoral neck are being compared a more pronounced difference is noticed between the isotropic and orthotropic FE result. These results lay the foundation for applying more realistic inhomogeneous orthotropic material properties in FEA of femurs.

Investigation of 3D anisotropic electrical conductivity in TIG welded 5A06 Al alloy using eddy currents

Electrical conductivity undergoes changes in the weld zones of the material. In this study, its anisotropic components along longitudinal, transverse and through-thickness directions have been investigated nondestructively using circular eddy current probe with Hall Effect sensor. The electromagnetic forward model has been solved with material resistivity input profiles corresponding to tensile and compressive residual stresses in a typical welded joint. For reconstruction of 3D anisotropic electrical conductivity, constrained linear least square optimization has been used. Compared with measurements based on calibration with homogeneous specimen or calculated assuming isotropic material properties in forward model, the results indicate that change in conductivity is significantly larger. A quantitative comparison is made between results based on isotropic and anisotropic material models. The conductivity mapping is required for residual stress measurement in components and structures.

Energy Finite Element Analysis Developments for Vibration Analysis of Composite Aircraft Structures

The Energy Finite Element Analysis (EFEA) has been utilized successfully for modeling complex structural-acoustic systems with isotropic structural material properties. In this paper, a formulation for modeling structures made out of composite materials is presented. An approach based on spectral finite element analysis is utilized first for developing the equivalent material properties for the composite material. These equivalent properties are employed in the EFEA governing differential equations for representing the composite materials and deriving the element level matrices. The power transmission characteristics at connections between members made out of non-isotropic composite material are considered for deriving suitable power transmission coefficients at junctions of interconnected members. These coefficients are utilized for computing the joint matrix that is needed to assemble the global system of EFEA equations. The global system of EFEA equations is solved numerically and the vibration levels within the entire system can be computed. The new EFEA formulation for modeling composite laminate structures is validated through comparison to test data collected from a representative composite aircraft fuselage that is made out of a composite outer shell and composite frames and stiffeners. NASA Langley constructed the composite cylinder and conducted the test measurements utilized in this work.

The mechanical properties of a transverse isotropic voided material

The mechanical properties of a transverse isotropic honeycomb porous material were investigated by the experiment and the finite element method. The relative density dependence of the macroscopic elastoplastic constants along the in-plane and out of plane directions (e.g., Young’s modulus, Poisson’s ratio, yielding stress, etc.) was systematically studied. Good agreement between the experimental and numerical results was observed. In addition, the three dimensional numerical results were compared with simplified foam models and self-consistent estimates, showing the necessity to improve available models for foams in order to achieve a better predictive capability. At the same time, the elastic–plastic failure mechanism was discussed in detail.

Model for Transversely Isotropic Materials Based on Distinct Lattice Spring Model (DLSM)

A two-phase DLSM model is proposed to model transverse isotropic materials, in which the layer structure of the anisotropic materials is explicitly represented. Equations are derived to obtain elastic parameters of the two phase model from the elastic modules in parallel to the bedding planes and that in normal direction of the bedding planes. Then, the mechanical properties of the two-phase DLSM model are studied and compared with experimental observations. Results indicate that the mechanical properties of transverse isotropic materials can be well represented by the proposed model. Following this, the model is applied to study the influence of the weakness layers (bedding planes) on the anisotropic deformation and Damaged Zone (DZ) evolution of underground disposal galleries in transverse isotropic medium. Finally, some conclusions are presented.

Structure, morphology and mechanical properties of Rhectophyllum camerunense (RC) plant fiber. Part II: Computational homogenization of the anisotropic elastic properties

In part I of this paper, we used statistics to derive some parameters (actual area of the cross-section, polar moment of inertia) and Voronoi partitioning techniques to reconstruct the section of a plant fiber. The reconstructed geometry is used here to perform bottom-up predictive simulations of the anisotropic elastic properties of the fiber taking into account the underlying physics at the finer scales (thicknesses of the cell wall layers, microfibril angle). For this purpose, three load cases are considered and the overall response of the fiber is computed numerically at each material point by a detailed modeling of the microstructure at the point under consideration. The predicted longitudinal modulus is in good agreement with experimental results. Moreover, computational homogenization allow us to access to the overall elastic properties of the transverse isotropic material, which is very hard to do by direct measurement due to the minute cross-section of the fiber.

The impact of bone and suture material properties on mandibular function in Alligator mississippiensis: testing theoretical phenotypes with finite element analysis

The functional effects of bone and suture stiffness were considered here using finite element models representing three different theoretical phenotypes of an Alligator mississippiensis mandible. The models were loaded using force estimates derived from muscle architecture in dissected specimens, constrained at the 18th and 19th teeth in the upper jaw and 19th tooth of the lower jaw, as well as at the quadrate-articular joint. Stiffness was varied systematically in each theoretical phenotype. The three theoretical phenotypes included: (i) linear elastic isotropic bone of varying stiffness and no sutures; (ii) linear elastic orthotropic bone of varying stiffness with no sutures; and (iii) linear elastic isotropic bone of a constant stiffness with varying suture stiffness. Variation in the isotropic material properties of bone primarily resulted in changes in the magnitude of principal strain. By comparison, variation in the orthotropic material properties of bone and isotropic material properties of sutures resulted in: a greater number of bricks becoming either more compressive or more tensile, changing between being either dominantly compressive or tensile, and having larger changes in the orientation of maximum principal strain. These data indicate that variation in these model properties resulted in changes to the strain regime of the model, highlighting the importance of using biologically verified material properties when modeling vertebrate bones. When bones were compared within each set, the response of each to changing material properties varied. In two of the 12 bones in the mandible, varied material properties within sutures resulted in a decrease in the magnitude of principal strain in bricks adjacent to the bone/suture interface and decreases in stored elastic energy. The varied response of the mandibular bones to changes in suture stiffness highlights the importance of defining the appropriate functional unit when addressing relationships of performance and morphology.

Strain in the ostrich mandible during simulated pecking and validation of specimen-specific finite element models

Finite element (FE) analysis is becoming a frequently used tool for exploring the craniofacial biomechanics of extant and extinct vertebrates. Crucial to the application of the FE analysis is the knowledge of how well FE results replicate reality. Here I present a study investigating how accurately FE models can predict experimentally derived strain in the mandible of the ostrich Struthio camelus, when both the model and the jaw are subject to identical conditions in an in-vitro loading environment. Three isolated ostrich mandibles were loaded hydraulically at the beak tip with forces similar to those measured during force transducer pecking experiments. Strains were recorded at four gauge sites at the dorsal and ventral dentary, and medial and lateral surangular. Specimen-specific FE models were created from computed tomography scans of each ostrich and loaded in an identical fashion as in the in-vitro test. The results show that the strain magnitudes, orientation, patterns and maximum : minimum principal strain ratios are predicted very closely at the dentary gauge sites, even though the FE models have isotropic and homogeneous material properties and solid internal geometry. Although the strain magnitudes are predicted at the postdentary sites, the strain orientations and ratios are inaccurate. This mismatch between the dentary and postdentary predictions may be due to the presence of intramandibular sutures or the greater amount of cancellous bone present in the postdentary region of the mandible and requires further study. This study highlights the predictive potential of even simple FE models for studies in extant and extinct vertebrates, but also emphasizes the importance of geometry and sutures. It raises the question of whether different parameters are of lesser or greater importance to FE validation for different taxonomic groups.

Mechanics of cranial sutures using the finite element method

To investigate how cranial suture morphology and the arrangement of sutural collagen fibres respond to compressive and tensile loads, an idealised bone–suture–bone complex was analysed using a two-dimensional finite element model. Three suture morphologies were simulated with an increasing interdigitation index (I.I.): butt-ended, moderate interdigitated, and complex interdigitated. The collagen matrix within all sutures was modelled as an isotropic material, and as an orthotropic material in the interdigitated sutures with fibre alignment as reported in studies of miniature pigs. Static uniform compressive or tensile loading was applied to the complex. In interdigitated sutures with isotropic material properties, the orientation of the maximum (tensile) principal stresses within the suture matched the collagen fibre orientation observed in compressed and tensed sutures of miniature pigs. This suggests that randomly arranged sutural collagen fibres could optimise to an orientation most appropriate to withstand the predominant type of loading. A compression-resistant fibre arrangement imparted the highest suture strain energy relative to the isotropic and tension-resistant arrangements, indicating that this configuration maximises energy storage. A comparison across the different suture morphologies indicated that bone strain energy generally decreased with a decrease in I.I., irrespective of the sutural fibre arrangement. However, high bone stress at the interdigitation apices shifted to the limbs of the suture with an increase in I.I. These combined findings highlight the importance of suture morphology and anisotropy as properties having a significant influence on sutural mechanics.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

Axisymmetric interaction of a rigid disc with a transversely isotropic half‐space

AbstractA theoretical formulation is presented for the determination of the interaction of a vertically loaded disc embedded in a transversely isotropic half‐space. By means of a complete representation using a displacement potential, it is shown that the governing equations of motion for this class of problems can be uncoupled into a fourth‐order partial differential equation. With the aid of Hankel transforms, a relaxed treatment of the mixed‐boundary value problem is formulated as dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. In addition to furnishing a unified view of existing solutions for zero and infinite embedments, the present treatment reveals a severe boundary‐layer phenomenon, which is apt to be of interest to this class of problems in general. The present solutions are analytically in exact agreement with the existing solutions for a half‐space with isotropic material properties. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are included for cases of different degrees of the material anisotropy and compared with existing solutions. Further numerical examples are also presented to elucidate the influence of the degree of the material anisotropy on the response. Copyright © 2009 John Wiley &amp; Sons, Ltd.