Showing papers on "Orthotropic material published in 1998"

Composite Materials: Mechanical Behavior and Structural Analysis

Abstract: Preface.- Translators Preface.- Part I: Composite Materials. Basic Features of Composite Materials. The Constituents of a Composite Material. Molding processes and Architecture of Composite Materials.- Part II: Basic Concepts of the Mechanical Behavior of Materials. Mathematical Basics. Stresses. Strains. The Elastic Behavior of Materials. The Mechanics of Deformable Solids.- Part III: Mechanical Behavior of Composite Materials. Elastic Behavior of Unidirectional Composite Materials. Elastic Behavior of an Orthotropic Composite. Off-Axis Behavior of Composite Materials. Fracture Mechanisms and Damage of Composite Materials.- Part IV: Modeling the Mechanical Behavior of Laminates and Sandwich Plates. Basics of Laminate Theory. Classical Laminate Theory. Effect of the Stacking Sequence. Mat and Cloth Reinforced Materials. Governing Equations and Energy Formulation of Classical Laminate Theory. Including Transverse Shear Deformation in Laminate Theory. Theory of Sandwich Plates.- Part V: Analysis of the Mechanical Behavior of Composite Material Structures. Cylindrical bending. Bending of Laminate and Sandwich Beams. Bending of Orthotropic Laminate Plates. Bending of Plates.

Continuum model for masonry: parameter estimation and validation

Abstract: A novel yield criterion that includes different strengths along each material axis is presented. The criterion includes two different fracture energies in tension and two different fracture energies in compression. The ability of the model to represent the inelastic behavior of orthotropic materials is shown, and a set of experimental tests to characterize the constitutive behavior of masonry is proposed. The capability of the model to reproduce the strength behavior of different masonry types is demonstrated through a comparison with available experimental data in masonry panels subjected to uniform biaxial loading conditions. Finally, the model is validated against experimental results on masonry shear walls and good agreement is found. A clear understanding of the behavior of masonry shear walls, and the nonlinear phenomena involved in its collapse, is presented with the help of a detailed comparison between numerical and experimental results.

Evaluation of Layerwise Mixed Theories for Laminated Plates Analysis

Abstract: The evaluation of mixed layerwise theories to calculate the in-plane and out-of-plane responses of thick plates in two-dimensional modeling of multilayered structures is made. The employed models, which were proposed by the author in earlier works, a priori fulfill the continuity of transverse shear and normal stress components at the interface between two adjacent layers. A Reissner's mixed variational equation is used to derive the governing equations, in terms of introduced stress and displacement variables. The interface continuity conditions are imposed by writing the governing equations at a multilayered level. The related standard displacement formulations are also discussed for comparison purpose. Closed-form solutions are presented for plates made of orthotropic lamina and bent by harmonic distribution of transverse pressure. Symmetrically and unsymmetrically laminated, as well as sandwich, plates have been investigated. A comparison with a three-dimensional-elasticity analysis shows that present mixed layerwise models furnish a better description of the in-plane and out-of-plane response of thick plates with respect to existing layerwise and equivalent single-layer theories. In particular, the proposed models describe, with excellent accuracy, the transverse shear and normal stress fields. Unlike available current models, these fields are herein determined a priori without requiring implementation of any postprocessing procedures. The distribution of the transverse displacement and transverse normal stress in the plate thickness direction are also shown for most of the problems.

The anisotropic Hooke's Law for cancellous bone and wood

Abstract: A method of data analysis for a set of elastic constant measurements is applied to data bases for wood and cancellous bone. For these materials the identification of the type of elastic symmetry is complicated by the variable composition of the material. The data analysis method permits the identification of the type of elastic symmetry to be accomplished independent of the examination of the variable composition. This method of analysis may be applied to any set of elastic constant measurements, but is illustrated here by application to hardwoods and softwoods, and to an extraordinary data base of cancellous bone elastic constants. The solid volume fraction or bulk density is the compositional variable for the elastic constants of these natural materials. The final results are the solid volume fraction dependent orthotropic Hooke's law for cancellous bone and a bulk density dependent one for hardwoods and softwoods.

Modelling the three-dimensional elastic constants of parallel-fibred and lamellar bone

Abstract: The complex hierarchical structure of lamellar bone makes understanding structure–mechanical function relations, very difficult. We approach the problem by first using the relatively simple structure of parallel-fibred bone to construct a mathematical model for calculating Young's moduli in three-dimensions. Parallel-fibred bone is composed essentially of arrays of mineralized collagen fibrils, which are also the basic structural motif of the individual lamellae of lamellar bone. Parallel-fibred bone structure has orthotropic symmetry. As the sizes and shapes of crystals in bone are not well known, the model is also used to compare the cases of platelet-, ribbon- and sheet-reinforced composites. The far more complicated rotated plywood structure of lamellar bone results in the loss of the orthotropic symmetry of individual lamellae. The mathematical model used circumvents this problem by sub-dividing the lamellar unit into a thin lamella, thick lamella, transition zone between them, and the recently observed “back-flip” lamella. Each of these is regarded as having orthotropic symmetry. After the calculation of their Young's moduli they are rotated in space in accordance with the rotated plywood model, and then the segments are combined to present the overall modulus values in three-dimensions. The calculated trends compare well with the trends in microhardness values measured for circumferential lamellar bone. Microhardness values are, as yet, the only measurements available for direct comparison. Although the model is not directly applicable to osteonal bone, which is composed of many hollow cylinders of lamellar bone, the range of calculated modulus values and the trends observed for off-axis calculations, compare well with measured values. © 1998 Chapman & Hall

Plastic anisotropy of sheet metals determined by simple shear tests

Abstract: The possibilities offered by the simple shear test to analyze the in-plane plastic anisotropy of metals are described In particular, orthotropic materials (rolled sheets) are concerned because symmetry arguments help to determine the origin of the anisotropy (eg, textural or structural sources) Both initial and induced anisotropies are discussed and illustrated with relevant examples

Stress-Induced Seismic Anisotropy Revisited

Abstract: This summary contains formulas (***) which can not be displayed on the screenA general principle outlined by P. Curie (1894) regarding the influence of symmetry in physical phenomena states, in modern language, that the symmetry group of the causes is a sub-group of the symmetry group of the effects. For instance, regarding stress-induced seismic anisotropy, the most complex symmetry exhibited by an initially isotropic medium when tri-axially stressed is orthorhombic, or orthotropic, symmetry characterized by three symmetry planes mutually perpendicular (Nur, 1971). In other respects, Schwartz et al. (1994) demonstrated that two very different rock models, namely a cracked model and a weakly consolidated granular model, always lead to elliptical anisotropy when uniaxially stressed. The addressed questions are : Is this result true for any rock model? and more generally : Do initially isotropic rock form a well-defined sub-set of orthorhombic media when triaxially stressed?Under the hypothesis of 3rd order nonlinear isotropic hyperelasticity (i. e. , no hysteresis and existence of an elastic energy function developed to the 3rd order in the strain components) it is demonstrated that the qP-wave stress-induced anisotropy is always ellipsoidal, for any strength of anisotropy. For instance point sources generate ellipsoidal qP-wave fronts. This result is general and absolutely independent of the rock model, that is to say independent of the causes of nonlinearity, as far as the initial assumptions are verified. This constitutes the main result of this paper. Thurston (1965) pointed out that an initially isotropic elastic medium, when non-isotropically pre-stressed, is never strictly equivalent to an unstressed anisotropic crystal. For instance the components of the stressed elastic tensor lack the familiar symmetry with respect to indices permutation. This would prohibit Voigt's notation of contracted indices. However if the magnitude of the components of the stress deviator is small compared to the wave moduli, which is always verified in practical situations of seismic exploration, the perfect equivalence is re-established. Under this condition, the 9 elastic stiffnesses C'ij (in contracted notation) of an initially isotropic solid, when triaxially stressed, are always linked by 3 ellipticity conditions in the coordinate planes associated with the eigen directions of the static pre-stress, namely :(***)Thus only 6 of the 9 elastic stiffnesses of the orthorhombic stressed solid are independent (Nikitin and Chesnokov, 1981), and are simple functions of the eigen stresses, and of the 2 linear (2nd order) and the 3 nonlinear (3rd order) elastic constants of the unstressed isotropic solid. Furthermore, given the state of pre-stress, the strength of the stress-induced P- or S-wave anisotropy and S-wave birefringence (but not the magnitude of the wave moduli themselves) are determined by only 2 intrinsic parameters of the medium, one for the P-wave and one for the S-waves. Isotropic elastic media, when triaxially stressed, constitute a special sub-set of orthorhombic media, here called ellipsoidal media , verifying the above conditions. Ellipsoidal anisotropy is the natural generalization of elliptical anisotropy. Ellipsoidal anisotropy is to orthorhombic symmetry what elliptical anisotropy is to transversely isotropic (TI) symmetry. Elliptical anisotropy is a special case of ellipsoidal anisotropy restricted to TI media. In other words, ellipsoidal anisotropy degenerates in elliptical anisotropy in TI media. In ellipsoidal media the qP-wave slowness surface is always an ellipsoid. The S-wave slowness surfaces are not ellipsoidal, except in the degenerate elliptical case, and have to be considered as a single double-valued self-intersecting sheet (Helbig, 1994). The intersections of these latter surfaces with the coordinate planes are either ellipses, for the S-vave polarized out of the coordinate planes, or circles, for the qS-wave polarized in the coordinate planes. The nearly exhaustive collection of experimental data on seismic anisotropy in rocks (considered as transverse isotropic) by Thomsen (1986) show that elliptical anisotropy is more an exception than a rule. Since stress-induced anisotropy is essentially elliptical when restricted to transversely isotropic media, as a consequence this work clearly shows that stress can be practically excluded as a unique direct cause of elastic anisotropy in rocks.

A numerical study of the shape stability of sawn timber subjected to moisture variation: Part 1: Theory

Abstract: A three-dimensional theory for the numerical simulation of deformations and stresses in wood during moisture variation is described. The constitutive model employed, assumes the total strain rate to be the sum of the elastic strain rate, the moisture-induced strain rate and the mechano-sorption strain rate. Wood is assumed to be an orthotropic material with large differences between the longitudinal, radial and tangential directions in the properties found. The influence of the growth rings, the spiral grain and the conical shape of the log on the orthotropic directions in the wood is taken account of in the model. A finite element formulation is used to describe the deformation process and the stress development during drying.

Adhesively-bonded repairs to fibre-composite materials II. Finite element modelling

Abstract: Part I described the static performance (i.e. the performance under a monotonic rate of loading) of carbon-fibre reinforced-plastic (CFRP) composites which had been repaired by adhesively bonding and co-curing, a second section of CFRP prepreg to the original parent material. The mechanical behaviour of these repair joints, as well as of the adhesive and CFRP forming the joint, were determined both in the unaged condition and after ageing. The hot/wet ageing of the repair joints and materials was simulated by immersing the joints and materials in water at 50°C. In Part II, the mechanical properties of the adhesive and the CFRP have been used in conjunction with a finite element analysis (FEA) to determine failure criteria which would predict the experimentally observed failure paths and strength of the adhesively-bonded repair joints. Two material models were used for the adhesive: a linear elastic and linear elastic–plastic. Two models were also used for the composite. In the first model, the composite was assumed to be a homogeneous orthotropic material with smeared properties. In the second, it was modelled as a combination of individual plies of various orthotropic/anisotropic properties, depending upon the fibre orientation angle. Three possible types of failure for the repair joints were analysed in order to predict the expected failure paths and failure loads. The general agreement between the experimental observations, and predictions of the failure path and loads was found to be good.

Optimal orientation of orthotropic materials using an energy based method

Abstract: In this paper, an energy based method is proposed to determine the optimal orientation of orthotropic materials under static loading. Instead of assuming that the strain or stress fields are fixed with respect to orientational variables, the dependency of strain and stress fields on material orientation is explored by introducing an energy factor in the inclusion model. From the derivations, the strain based method and the stress based method can be recovered and their limitations are discussed. Numerical examples from these methods are presented and compared.

Nonlinear finite - element analysis of rc shear panels and walls

Abstract: In the assessment of existing reinforced concrete structures, finite-element analysis plays an important role, particularly in regard to the evaluation of critical regions, regions with special detailing, or regions of stress concentration. A popular class of concrete model uses an orthotropic constitutive relation in which the directions of orthotropy are the principal direction of total strain. Since these directions change during the load-displacement response, such an approach is known as a rotating crack model. The models proposed to date differ in the description of the biaxial failure envelope, the uniaxial equivalent stress-strain relation, Poisson ratio, and the tension-compression behavior. This paper describes the implementation of an orthotropic concrete constitutive model in the finite-element analysis of reinforced concrete members. The emphasis of the paper is on the evaluation of the effect of orthotropic model parameters on the monotonic load-displacement relation of shear panels and walls under different stress states. The ability of the orthotropic concrete material model to assess failure mode, ultimate strength, and load-deformation behavior of this type of structural element is evaluated by correlation studies with available experimental data.

A continuum model of layered rock masses with non-associative joint plasticity

Abstract: Layered rock masses can be modelled either as standard, orthotropic continua if the layer bending can be neglected or as Cosserat continua if the influence of layer bending is essential. This paper presents a finite element smeared joint model based on the Cosserat theory. The layers are assumed to be elastic with equal thickness and equal mechanical properties. All the cosserat parameters are expressed through the elastic properties of layers, layer thickness and joint stiffness. Plastic-slip as well as tensile-opening of layer interface (joint) are accounted for in a manner similar to the conventional non-associative plasticity theory. As an application, the behaviour of an excavation in a layered rock mass is examined. The displacement and stress fields given by smeared joint models based on the Cosserat continuum and the conventional anisotropic continuum approaches are compared with those obtained from the discrete joint model. The conventional anisotropic continuum model is found to break-down completely when the effective shear modulus in the direction parallel to layering is low in comparison to the shear modulus of the intact layer, whereas the Cosserat model is found to be capable of accurately reproducing complex load–deflection patterns irrespective of the differences in shear moduli. © 1998 John Wiley & Sons, Ltd.

A T-shaped specimen for the direct characterization of orthotropic materials

Abstract: This paper deals with the definition of a new test specimen geometry for the direct measurement of the four in-plane stiffness components of orthotropic materials. The technique is based on a suitable use of the principle of virtual work. The choice and application of four different types of virtual kinematic fields leads to a system of equations that links the our stiffness components to the global force applied and geometry parameters. A numerical simulation based on finite lement modelling is used to validate the approach. The stability of the process is also demonstrated.

Elastodynamic Solution for the Thermal Shock Stresses in an Orthotropic Thick Cylindrical Shell

Abstract: An elastodynamic solution for the thermal shock stresses in an orthotropic thick cylindrical shell is presented. The solution is achieved by the proper usage of integral transforms such as the finite Hankel transform and the Laplace transform. No restrictive assumptions on the shell thickness are placed. Results are presented for the well,formed wave propagation phenomenon of elastic stresses through the thickness of an orthotropic thick cylindrical shell. Thermal shock stresses become of significant magnitude due to stress wave propagation which is initiated at the boundaries by sudden thermal loading.

A finite element based method to determine the properties of planar soft tissue.

Abstract: A finite element based method to determine the incremental elastic material properties of planar membranes was developed and evaluated. The method is applicable to tissues that exhibit inhomogeneity, geometric and material nonlinearity, and anisotropy. Markers are placed on the tissue to form a four-node quadrilateral element. The specimen is loaded to an initial reference state, then three incremental loading sets are applied and the nodal displacements recorded. One of these loadings must include shear. These data are used to solve an over-determined system of equations for the tangent stiffness matrix. The method was first verified using analytical data. Next, data obtained from a latex rubber sheet were used to evaluate experimental procedures. Finally, experiments conducted on preconditioned rat skin revealed nonlinear orthotropic behavior. The vector norm comparing the applied and calculated nodal force vectors was used to evaluate the accuracy of the solutions.