Orthotropic Behavior Research Articles

Designing of Thin Composite Panels with the Post-Buckling Behavior Considering Rigid Support and Loading with Shear Flows

Geometrically non-linear problem of orthotropic thin rectangular panel post-buckling behavior with shear is solved. Deflection function takes all-boundary rigid support conditions into account. Based on derived solution method of smooth panels design which can be used for aircraft structures rib and spar webs optimal parameters is suggested.

Stochastic simulation of top load test on poly(ethylene terephthalate) bottles: An experimental study on dispersion of elastic properties

AbstractDuring the stretch blowing molding process, the elongation of macromolecular chains modifies the final mechanical properties of poly(ethylene terephthalate) (PET) bottle. Especially Young's modulus can be multiplied by two or more in the longitudinal direction and more than three times in the circumferential direction in the cylindrical region of the blown bottle and leads to orthotropic elastic properties. Using digital image correlation, we performed an identification process using two global tests. First, the virtual field method on a specific plane specimen with a hole, allows the identification of the Poisson's ratio. Second, the modulus is measured using a 3D digital image correlation from bottles under internal pressure. The shear modulus is then identified from the heterogeneous tension tests in the first step. Since all the induced mechanical properties exhibit dispersions, a probabilistic description of the orthotropic behavior law is managed and a stochastic simulation of the top load test is performed in order to define a confidence region for the bottle performance. The results of the simulation are validated by experimental measurements of top load tests performed on PET bottles.

Experimentally-validated orthotropic elastic model for Wire-and-Arc Additively Manufactured stainless steel

Abstract Wire-and-Arc Additively Manufactured (WAAM) alloys are characterized by specific mechanical properties which can largely differ from the conventionally-manufactured alloys. In detail, the printing process results in a peculiar microstructure, characterized by preferential crystallographic orientation with reference to the printing direction, that leads to an anisotropic mechanical behavior of the printed part. Previous experimental tests on WAAM-produced stainless steel plates showed in particular a strong anisotropic elastic behavior. Based on the above, the present work formulates a specific anisotropic elastic model for a WAAM-processed austenitic stainless steel, considering an orthogonally anisotropic (or orthotropic) constitutive law and a procedure to calibrate the elastic parameters based on the experimental results. In detail, the procedure is applied to calibrate the numerical values of the elastic parameters of a specific WAAM 304L austenitic stainless steel. For this aim, specific investigations on both the mechanical and microstructural features were carried out. Experimental tensile tests were performed on specimens with different orientations with reference to the printing direction. In detail, Young’s modulus and Poisson’s ratios were evaluated for samples oriented along three different orientations with regard to the printing deposition layers: longitudinally (L), transversally (T) and diagonally (D) to them. Digital Image Correlation (DIC) optical measuring system was used to acquire the full strain fields during the test. Microstructural analysis was also carried out to study the inherent microstructure, characterized by a distinctive grain growth direction, and to assess the preferred crystallographic orientations of specimens extracted along the three considered directions. The experimental results are used to calibrate the orthotropic elastic model. From the calibrated model additional material properties in terms of Young’s and shear modulus for any printing direction are derived. The resulting values exhibit very large variations with the printing angle, with ratios between minimum to maximum values around 2 for the Young’s modulus and 3.5 for the shear modulus. This marked orthotropic behavior could open unexplored design possibilities based on deformability issues. Additionally, the calibrated orthotropic model can also be used for future experimental explorations of the mechanical properties of WAAM alloys and for stiffness-based structural design optimizations.

Rate-dependent viscoplastic modeling and experimental validation of woven glass/epoxy composite materials

The rate-dependent behavior of woven fabric (WF) composite with material nonlinearity and 3D geometrical nonuniformity are predicted using a proposed micro-meso-scale (MMS) model. The viscoelastic fiber and viscoplastic matrix are combined to obtain the properties of viscoplastic composite tows. Applying geometrical properties of WF and considering different local position and orientation of tows, the orthotropic viscoplastic behavior of WF composite is obtained. A progressive damage model is developed to consider damage modes in the composite tows. The stresses are redistributed over the intact regions according to the occurrence of the specific damage modes. Experimental rate-dependent tests are carried out on the epoxy matrix and unidirectional composite to measure the model constants. The rate dependency of the mechanical properties and nonlinearity of the stress-strain curves of the WF composite are then predicted and compared to additional experimental tests on the WF composite.

Study of Elastic Behavior of Polylactic Acid with Yanchama Fibers Composite Simulated as Elastic Orthotropic Material

ABSTRACT A new biocomposite material based on polylactic acid (PLA) with meshes of Yanchama fibers is introduced. This bio-based composite was fabricated by compression molding and film-staking process. This new biocomposite material was tested by tensile tests in different directions and was numerically simulated. The composite was simulated as an elastic orthotropic material. The nine constants of elastic orthotropic behavior are calculated from modules of Young measured experimentally. The experiment results and simulations are the same. The results show that the mechanical behavior of the PLA-Yanchama composite under different load solicitudes can be predicted if it is simulated as an orthotropic elastic material.

Reducing the risk of rostral bending failure in Curculio Linnaeus, 1758

With over 300 species worldwide, the genus Curculio Linnaeus, 1758 is a widespread, morphologically diverse lineage of weevils that mainly parasitize nuts. Females use the rostrum, an elongate cuticular extension of the head, to excavate oviposition sites. This process causes extreme bending and deformation of the rostrum, without apparent harm to the structure. The cuticle of the rostral apex exhibits substantial modifications to its composite structure that enhance the elasticity and resiliency of this structure. Here we develop finite element models of the head and rostrum for three Curculio species representing disparate North American clades and rostral morphotypes. The models were subjected to varying apical loads and to prescribed dislocation of the head capsule, with and without representing the cuticular modifications of the rostral apex. We found that the altered layer thicknesses and macrofiber orientation angles of the rostral apex fully explain the observed elasticity of the rostrum. These modifications have a synergistic effect that greatly enhances the flexibility of the rostral apex. Consequently, the cuticle composite profile of the rostral apex substantially mitigates the risk of fracture in dorso-apical flexion. Removing the cuticular modifications, in turn, causes a negative margin of safety for rostral bending, implying strong risk of catastrophic structural failure. The occipital sulci were identified as an important source of biomechanical constraint upon the elasticity of the rostrum, and exhibit the greatest risk of failure within this structure. The apical cuticle profile greatly reduced the maximum stresses and strain energy accumulated in the rostrum, thereby resulting in a positive margin of safety and reducing the risk of fracture. Our findings imply that the primary selective pressure influencing the evolution of the rostral cuticle was most likely negative selection of structural failure caused by bending. Statement of significanceWeevils are among the most diverse and evolutionarily successful animal lineages on Earth. Their success is driven in part by a structure called the rostrum, which gives weevil heads a characteristic “snout-like” appearance. Nut weevils in the genus Curculio use the rostrum to drill holes into developing fruits and nuts, into which they deposit their eggs. During oviposition this exceedingly slender structure is bent into a straightened configuration – in some species up to 90∘ – but does not suffer any damage during this process. Using finite element models of the rostra of three morphologically distinct species, we show that the Curculio rostrum is only able to withstand repeated, extreme bending because of modifications to the composite structure of the cuticle in the rostral apex. These modifications were shown previously to enhance the intrinsic toughness of the cuticle; in this study, we demonstrate that modification of the rostral cuticle also results in more evenly distributed bending stresses, further reducing the risk of fracture. This is the first time that the laminate profile, orthotropic behavior, and functional gradation of the cuticle have been incorporated into a three-dimensional finite element model of an insect cuticular structure. Our models highlight the significance of biomechanical constraint – i.e., avoidance of catastrophic structural failure – on the evolution of insect morphology.

Riveted joints in composites, a practical tool to estimate stresses around the rivet hole

Riveted joints have different failure mechanisms, some associated to the failure of the rivet itself, and others associated to the materials to be joined. The failures associated to the material are mainly due to the stress concentrations at the rivet holes. In joints with metallic (ductile) materials, these stress concentrations might not play a relevant role in the failure initiation, but with unidirectional composite (brittle) materials, they do control the failure. Both the orthotropic behavior of joined materials and the non-linear contact conditions between the rivet and the hole, make that the problem does not have a general solution. In the present work, several finite element analyses have been carried out for basic load cases, different materials, and orientations of the fiber. Furthermore, a two-steps least squares adjustment has been performed to obtain a polynomial expression of the stress distributions for all cases. As a result, a tool is provided, allowing the users to easily estimate the stress distribution (σrr, σθθ) along the hole contour, and σxy along the tangential lines to the hole circumference. Such stress ditribution can be used for failure predictions. All input and output data are available to readers, by means of a spreadsheet, to estimate mentioned stress distributions.

A robust multisurface return-mapping algorithm and its implementation in Abaqus

The simulation of complex material failure processes requires a precise differentiation of the involved failure mechanisms like fracture or plasticity. This is commonly achieved by using a so-called multisurface failure criterion, where each failure surface is related to a certain failure mechanism. In the case of plasticity, failure surfaces define the elastic domain of the material and any stress state outside of this domain is considered non-admissible and must be returned to the boundary of the elastic domain. So-called return-mapping algorithms are often used and well-studied methods for finding such valid stress states. However, their implementation in numerical simulation tools is often not robust and efficient enough for complex problems that involve sophisticated multisurface definitions. In this work, we present a multisurface return-mapping algorithm and its implementation in the finite element software Abaqus. We found that with additional and enhanced iterative solver methods, the classic Newton-Raphson-based implementation of the algorithm can be improved in order to find solutions to otherwise not returnable stress states. The added computational burden is minimal, as more stress states can be returned without reducing the size of the load increments. The paper focuses on the implementation aspects of such problems and offers the reader a thorough guide and the source code for an Abaqus implementation. We applied the algorithm to simulate the highly orthotropic behavior of wood, allowing us to predict plastic failure of various wooden structures and components.

A loading assisted diffuse wave inspection of delamination in a unidirectional composite

Delamination localization and characterization are critical for the structure integrity of fiber reinforced polymer composites with various fiber distributions and geometries. Different to direct wave based methods, the diffuse wave inspection is promising for rapid structure interrogation with only a few ultrasonic transducers required. The angle dependant diffusivity and dissipation are first measured in a unidirectional composite plate manufactured from hot press. Both coefficients represent an orthotropic behavior and can be predicted through rotation matrix calculation. 27% signal energy variation is found between the 0.1 mm thick delamination zone and the intact zone. The measurement along the fiber direction gives the best signal-to-noise ratio among all directions. No coefficient difference exists under amplitude normalization. A compressive loading is then applied to have different acoustic responses from different zones. Based on the acoustoelastic effect, the decorrelation coefficient variation is negligible in the intact zone with the strain of 10−3. Similar to the clapping effect, the loading triggered decorrelation coefficient variation becomes important as the transducer pairs approach the delamination zone. This has also been validated by the energy variation method. In addition, when the loading is centered in the delamination zone, the decorrelation coefficient variation area that can be captured by the diffuse wave is 45 × 210 mm2. Based on the Locadiff imaging method, the delamination geometry is finally characterized through Bayesian inference together with the numerical defect sensitivity kernel and the decorrelation coefficients. According to this loading-delamination-diffuse wave interaction analysis, the loading unveiled delamination geometry is found to center at [146,138] mm with an area of 3.5 × 10−4 ~ 11 × 10−4 m2 compared to the ground truth of [145,150] mm and 5.2 × 10−4 m2 respectively. It is promising for early-stage defect inspection in advanced composite structures.

Orthotropic Behaviour of Magnesium AZ31 Sheet during Strain Localization

It is known that metallic materials are characterized by anisotropy of their mechanical properties, with this being attributed to the conditions during the manufacturing process. For sheet metals, this anisotropy occurs symmetrically to the three orthogonal axes of the rolling, transverse and normal direction. This characteristic is referred to as orthotropic behaviour and manifests itself, for example, in earing during cupping tests. Therefore, orthotropic yield criteria are highly relevant for the numerical simulation of sheet metal forming processes. The Lankford coefficient, also known as the r-value, is a good experimental measure for characterizing orthotropic ductile behaviour of sheets, and can easily aid in parameter identification for yield criteria such as the Hill approaches. In the present investigations, Lankford coefficients were determined as a function of local strain in uniaxial tensile tests through high-resolution digital image correlation. The sample direction was varied between 0°, 45° and 90° to the rolling direction and the test temperature varied from RT to 350 °C at three different strain rates (0.01-1 s-1). By means of a novel backward analysis, the measuring range for the Lankford coefficients was positioned exactly in the necking area. An increase in temperatures showed a decrease in the initial Lankford coefficient. The results showed non-constant Lankford coefficients and commence the course of a natural exponential function depending on the local strain. Regardless of strain rate, the results revealed that the Lankford coefficients (r-values) at 150 °C, 250 °C and 350 °C approaches a steady-state of r = 1.14 with strains greater than 50 %.

Orthotropic Viscoelastic Properties of Chinese Fir Wood Saturated with Water in Frozen and Non-frozen States

Abstract In order to better understand the differences in orthotropic viscoelastic properties of Chinese fir (Cunninghamia lanceolata) in frozen and non-frozen states, the storage modulus (E′) and loss modulus (E″) of the longitudinal, radial, and tangential specimens were investigated under water-saturated conditions with temperatures ranging from −120°C (or 30°C) to 280°C. Results revealed that the order of magnitude in E′ for each orientation was consistent for temperatures below 0°C, while the anisotropy in E′ was reduced due to the enhancement effect of ice. Frequency-dependent γ-relaxation was observed at approximately −96°C for all orthotropic directions. A sharp discontinuity in E′ occurred at approximately 0°C for each specimen, together with the corresponding sharp peak in the E″ spectrum. Furthermore, the frozen free water had an effect on the orthotropic viscoelastic behavior in the water-saturated specimens within the range of −120°C to 280°C. Specimens with a frozen history leveled off at the initial temperature ramping phase for each orientation, while a frozen history reduced the decline in stiffness of the wood specimens. Similar to the variations in E′, the dramatic loss of water increased the complexity of the E″ values. The loss of free water also had a pronounced effect on the viscoelastic properties during the temperature ramping process. Thus, in the wood industry, it necessary to consider the variations in the orthotropic viscoelastic performance of specimens under water-saturated conditions during the water loss process.

Laboratory and numerical experimentation for masonry in compression

In this paper, the initial part of a laboratory and numerical experimental campaign dedicated to historical masonry is described. One leaf masonry panels with regular texture are built in order to simulate a historical material characterised by strong resisting elements and weak mortar joints. Laboratory tests are first dedicated to masonry components and then to the behaviour in compression of masonry panels, which is applied both orthogonal and parallel to bed joints, in order to highlight the orthotropic behaviour of the material. First of all, the mechanical parameters of masonry constituents are calibrated and then a heterogeneous finite element model is introduced and calibrated for reproducing the orthotropic behaviour of masonry, together with the initial elastic response and the initial nonlinear behaviour due to the first level of damage.

Mechanical response of porcine hind leg muscles under dynamic tensile loading

A modified split Hopkinson tension bar (SHTB) apparatus was used to investigate the dynamic tensile mechanical response of porcine muscles. A hollow aluminum alloy transmission bar and a semiconductor strain gauge were used to enhance the weak signal from porcine muscles. A ring-shaped copper pulse shaper was used to achieve stress equilibrium and constant approximate strain rates in the specimens. The thin muscle specimen, fixed by 3D-printed clamps, was warped around the bar ends to minimize the radial inertial effect during tensile loading. The quasi-static tests at strain rates of 0.1 s∧-1 were also conducted on a universal material testing machine to investigate the strain rate dependence. The true stress-strain curves of porcine muscle tissues along the fiber direction were determined at approximate strain rates of 800 s∧-1, 2000 s∧-1, and 3000 s∧-1. The experimental results show that the porcine muscle exhibits nonlinear, rate-sensitive, and orthotropic behavior. The Mooney–Rivlin model with two material constants was sufficient to represent the tensile response of porcine muscles at each strain rate. The rate-dependent Fields–Backofen model can describe the high strain rate response of the porcine muscles.

Frequency-dependent orthotropic damping properties of Nomex honeycomb composites

In this paper, the orthotropic damping behavior and mechanism of Nomex honeycomb composites are investigated. The needed specimen sizes for the measurement of the frequency-dependent transverse shear moduli (TSM) and fundamental damping coefficients of the honeycomb cores were analyzed at first. Then, the effects of cell side length and beam orientation on the orthotropic damping properties were explored. The results reveal that relatively high TSM (GLT) and damping values (ηWT) can be obtained by decreasing the cell side length without adding any additional weight. The analytical results of the damping mechanism indicate that the difference in the damping contributions of the interfacial phase to the honeycomb core in different directions leads to the orthotropic damping behavior of the honeycomb core. This study is helpful to guide the TSM measurement and structure design of honeycomb composites.

A uniquely defined multiplicative elasto-plasticity model with orthotropic yield function and plastic spin

A rate-independent model for isotropic elastic–orthotropic plastic material behaviour including the plastic spin is presented in this paper. The plastic spin, as introduced by Dafalias, is the spin of the continuum relative to the material substructure. The model is based on a specific multiplicative decomposition of the deformation gradient tensor, which introduces a uniquely defined intermediate configuration as motivated by Casey. We focus our attention on metal sheets in forming processes, in which pre-existing preferred orientations govern the orthotropic plastic behaviour. As a result, we advocate a Hill-type yield criterion enriched by the notion of plastic spin to describe this material behaviour. Our formulation yields three key findings: firstly, the uniquely defined intermediate configuration, namely a plastically stretched intermediate configuration, allows for a neat implementation of the plastic spin; secondly, the algorithmic formulation is straightforward and shows no additional difficulties in the implementation; and thirdly, a good agreement of our numerical model with experimental and numerical results from in-plane sheet forming processes reported in the literature is achieved.

Finite element analysis of fused filament extrusion build part using different build orientation

3D printing has converged the whole manufacturing process in this competitive world of technology. Replacement of subtractive to additive principle introduced trouble-free production of complex shapes with least wastage of material. Fused Filament Extrusion (FFE) is a widely used 3D printing technique. But strength of the 3D printed part was always be the question for critical application. Build orientation is one of the listed parameters of 3D printing process which plays a vital role on the fracture resistance of the 3D printed part. In order to understand the fracture resistance numerically, Finite Element Analysis has been performed on the CT-specimen. In the present work, Acrylonitrile Butadiene Styrene (ABS) material has been considered. The CT-specimen is loaded in the crack opening mode with displacement-controlled loading. Orthotropic behaviour was used for material definition. The value of load and Fracture toughness in terms of J-integral is estimated at the crack initiation. It was observed that the value of J-integral increased considerably with the increase in build orientation from 0 to 90 degrees.

Numerical Prediction of Equivalent Mechanical Properties of Corrugated Paperboard by 3D Finite Element Analysis

This study is to obtain the equivalent (effective) mechanical properties of corrugated paperboard specifically that is widely applied in Korea for packaging of agricultural products. To analyze the equivalent properties of corrugated paperboard, finite element modeling, measurement of the reaction force, and superposition theory for the unit cell were applied. The stress-strain behavior obtained by applying the calculated equivalent mechanical properties to the simplified model of the corrugated paperboard is compared with experimental results. Nine equivalent mechanical properties governing the orthotropic behavior of corrugated paperboard were analyzed through finite element analysis (FEA). The stress-strain behavior of the corrugated paperboard experimentally showed elastic-plastic behavior, although the equivalent mechanical properties applied to the simplified model were elastic properties based on the theoretical approach, so that the finite element analysis results showed linearity. Therefore, when applying the calculated equivalent mechanical properties through FEA, the characteristics of the section where the strain only increases without the increase in the load due to the flute should be taken into consideration.

Modeling and numerical simulation of the dynamic behavior of magneto-electro-elastic multilayer plates based on a Winkler-Pasternak elastic foundation

This work presents the effect of the elastic foundation and the viscoelastic interface on the dynamic behavior of laminated magneto-electro-elastic rectangular plates with simply supported boundary conditions using the state space method in Laplace domain. The Kelvin-Voigt model is used to take into accounted the viscoelastic interface effects in this domain. The final solution is transferred to the time domain by the Fourier inversion method. The dynamic responses of 3D displacements, stresses, and electric and magnetic displacements are analyzed with respect to the thickness direction and the orthotropic behavior under harmonic stress. A variant of the numerical tests shown the effect of the Winkler-Pasternak elastic foundation on a magneto-electro-elastic rectangular plates dynamic behavior and may contribute to optimize the design and the manufacturing of these materials.

Characterization of mechanical performance of Pinus radiata wood impregnated with octadecane as phase change material

This article presents the mechanical responses of Pinus radiata wood that was impregnated with octadecane to obtain a shape-stabilized phase change material (PCM). PCMs are used as heat storage materials to reduce the temperature peaks and displace the thermal loads in an enclosed space. It is important to study the effect of PCMs on the mechanical properties of wood, since these composite materials are intended to be used as a structural materials in low-thermal-mass housing, wherein a reduction in mechanical properties can generate structural resistance problems. For this purpose, tensile and compression tests were performed in the three principle directions (longitudinal, radial, and tangential) and bending tests were performed in the longitudinal direction. These mechanical tests were carried out using non-impregnated wood and PCM-impregnated wood, which was fabricated using a double vacuum method consisting of alternately applying a vacuum and atmospheric conditions. Different impregnation yields could be visualized using computerized microtomography, and different mechanical behaviors in the three principle directions were observed; the results showed an orthotropic behavior. However, the longitudinal direction exhibited the highest mechanical resistance. In general, the statistical tests showed that the mechanical performances of the wood samples were not affected by octadecane impregnation.

A basic orthotropic viscoelastic model for composite and wood materials considering available experimental data and time-dependent Poisson’s ratios

Long-term deformation in creep is of significant engineering importance. For anisotropic materials, such as wood, composites and reinforced concrete, creep testing in several axial directions including shear is necessary to obtain a creep model which is able to predict deformation in the basic orthotropic case. Such a full set of experimental data is generally not available, and simplifying assumptions are typically made to conceive a useful 3D model. These assumptions should preferably be made based on the material behaviour and sound engineering arguments. This problem appears to be addressed in many different ways and sometimes the assumptions are not well justified. In the present study, we examine 3D creep of wood and composite materials. Particular emphasis is made on explaining the choices made in developing the model, considering practicality, incomplete material data and the specific behaviour of wood and composites. An orthotropic linear viscoelastic model is implemented as a material model in a commercial FE software. The constitutive equations are derived in the 1D case using a hereditary approach, then later generalized to the 3D formulation. Guidelines are shown how to implement it into the FE software to predict creep of components and structures. Although the model itself is conventional, the effect of considering time-dependent Poisson’s ratios is investigated here, as well an optimization approach when inserting inevitably asymmetric experimental creep data into the model. As far as the authors know, creep of wooden materials have not been defined using this approach before. The model of interest is calibrated against experimental data. Examples using experimental results from solid wood data and a unidirectional fiber composite are demonstrated. The results show that the model is able to capture the orthotropic behaviour adequately. Orthotropy requires symmetry of the creep compliance matrix, which typically is not the case experimentally. It is shown that in rendering the matrix symmetric, one needs to decide which direction is more important. It is also shown that the frequently employed assumption of constant Poisson’s ratios should be made with caution.