Orthotropic Elastic Properties Research Articles

Multiscale modelling and characterisation of fused filament fabricated neat and graphene nanoplatelet reinforced G-polymers

AbstractIn this study, the fused filament fabrication of novel biodegradable G-polymer is investigated, including also filaments reinforced by graphene nanoplatelets. A combined framework of computational multiscale modelling and experimental studies is applied to characterise and model the mechanical behaviour of composite and nanocomposite materials, fabricated using a 3D-printer by depositing G-polymer filaments in +45$$^\circ$$ ∘ and $$-45^\circ$$ - 45 ∘ angles. The investigation is performed on both hot-extruded single filaments and 3D-printed specimens. Experimental results of hot-extruded single filaments are utilized on the microscale to extract the macroscale constitutive models. At the microscale level, representative volume elements with different percentages of penetration are analyzed to compute the effective orthotropic elastic material properties. A comprehensive comparison study is conducted using different micromechanical models, multiscale simulation outputs, and the mechanical properties resulting from experiments. The accuracy of the results obtained from the homogenization technique is validated against realistic finite element microstructural models and experimental measurements. The results demonstrate that computational homogenization, when coupled with accurate property characterisation, serves as a reliable tool for predicting the elastic response of 3D-printed parts. Furthermore, the proposed framework reduces the need for extensive experimental replication and lowers manufacturing costs.

A fast and efficient pseudo-direct identification method for orthotropic elastic properties of multi-layered composite plates

New types of laminated composites are continuously being developed to meet various requirements involved in engineering applications. Before mass production of these new composite materials can take place, it is necessary to identify their elastic properties. Although current identification methods based on vibration tests and optimization algorithms are highly accurate, their high computation cost is a drawback. To address this issue, this paper proposes a new method to identify orthotropic elastic properties of multi-layered composite plates. The proposed method is based on the Modal Stability Procedure, using the experimental vibration frequencies and corresponding numerical mode shapes of structures. It converges after only two or three iterations without requiring an optimization algorithm. Therefore, the computational cost of the proposed method is significantly lower than that of optimization-based methods. The effectiveness and robustness of this method are demonstrated through three examples with different material, stacking sequences, and geometries including curved plate.

Effect of the Hole Diameter in Mechanical Properties of Wood: Experimental and Numerical Approaches

Introducing openings or holes into wooden structures is a common practice for providing utility services. However, this practice leads to stress concentration, resulting in a reduction in stiffness and load-carrying capacity. Therefore, understanding the effects of holes on beam properties is important for design considerations. This study investigates the mechanical behavior of a wooden beam made from juvenile Pinus elliottii containing open cylindrical holes with three different diameters: 4, 8, and 12 mm. The mechanical properties were evaluated for compression parallel to the fibers, quasi-static bending, and tension perpendicular to the fibers. Numerical simulations were conducted using a finite element (FE) model, considering the orthotropic elastic properties determined from experimental tests and elastic ratios reported in the literature. The experimental results indicated that the influence of hole diameter was not significant on the compressive properties; however, longitudinal crack failures began to form for holes with diameters of 8–12 mm. Regardless of hole size, the compressive and bending characteristics revealed that hole location did not affect the stiffness, strength, or damage mechanisms.

The influence of layer height in the orthotropic elastic properties of PLA material obtained by additive processes

Polylactic acid (PLA) is a biodegradable thermoplastic polyester used extensively in 3D printing, that can be obtained from renewable resources with low production costs and low carbon emissions. The extrusion temperature of PLA is lower, and its tensile strength and elastic modulus are higher than that of other common polymeric thermoplastic materials.To assess the structural integrity of parts obtained by additive manufacturing, especially in more complex geometries, the finite element method is extensively used, being necessary, for this purpose, to characterize the constitutive model of the material. From the printer manufacturing parameters, one of the most affecting the elastic and strength properties is the layer height.The layer-by-layer slicing sequence of additive manufacturing processes can introduce anisotropy into the materials, whereby, in most applications, materials obtained by these processes are considered orthotropic. The mechanical characterization of anisotropic materials through classical tests is not always the most suitable for this purpose, given the economic aspects, the time required, precision requirements and, sometimes, the technological difficulties of the tests. The ASTM E1876-21 standard presents a method for determining the dynamic elastic properties of materials by impulse excitation of vibration, at room temperature.In this article, the influence of the layer height in the dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio obtained by impulse excitation of vibration (ASTM E1876-21 standard), of Tough PLA is analyzed.

Determination of the Orthotropic Mechanical Elastic Properties of Gas Diffusion Layers for PEMFCs

One of the most important components of proton exchange membrane fuel cell is the gas diffusion layer (GDL), due to its position between the catalyst layers, where the electrochemical reactions take place, and the bipolar plates supplying the reactant gases. The GDL must have an optimal mechanical stiffness to ensure the transport of the different gases and the water produced by the fuel cell operation. Measuring the mechanical properties of the different GDLs available in the market require the development of specific methodologies due to their orthotropic behavior. This article aims to assess and create a database for selecting GDLs for specific applications and assisting engineers in fuel cell modeling. This study focuses on developing robust characterization methods to assess the different properties of GDLs in different directions: within the plane, along both the machine and transverse directions, and perpendicular to the plane. These tests allow to determine parameters like in-plane tensile and shear moduli, out-of-plane compression and shear moduli, and in-plane Poisson’s ratios. By examining a wide range of commercial specimens, including different types, area weights, hydrophobic treatments, manufacturing processes, and microporous layers, this study aims to provide a comprehensive analysis of the orthotropic mechanical properties of GDLs.

A normalization method of measured elastic properties of glass NCF composites with respect to fiber volume fraction based on periodic microstructure micromechanics

International standards have requested the normalization of fiber-dominated properties in composites with respect to fiber volume fraction. However, the normalization of matrix-dominated properties has not yet been requested because there is no clear model. This partial normalization might deteriorate accuracy in design and analysis. This study developed a systematic approach for normalizing both fiber-dominated and matrix-dominated properties of composites, based on periodic microstructure micromechanics (PMM). To evaluate the accuracy of PMM, this study started from comparing the elastic properties calculated by PMM to those calculated by FEA. Then, the eight measured elastic properties were obtained by testing three different types of glass NCFs/epoxy laminates. Since PMM needs the elastic properties of raw materials, the three unknown properties among them were determined by using the back-calculation procedure developed in this study. After all, the PMM gave us highly accurate properties of the laminates, resulting in a maximum error of less than 1% when comparing the calculated elastic properties with the measured ones. Lastly, the orthotropic elastic properties of the laminates were normalized with respect to fiber volume fraction. This study makes a significant step forward in composite structures by providing a systematic approach for normalizing full elastic properties in composites.

Vibration-based numerical identification of effective orthotropic elastic properties for finite element model of cross-laminated timber panel

The influence of non-gluing of narrow surfaces of boards on all effective orthotropic elastic moduli for shell or solid finite element models of cross-laminated timber (CLT) panels is investigated. This lack of gluing leads to discontinuous layers and severe meshing difficulties. The objective of this study is to create an equivalent homogeneous layer and equivalent material properties in this case. Two finite element (FE) models were built for comparison. The first model, using solid elements, is the reference without gluing the narrow surfaces. The second considers homogeneous layers and equivalent material properties. Thanks to an identification process, all the elastic moduli of the model with homogeneous layers are adjusted to minimize the difference in vibration frequencies between the two models. A method is proposed to significantly speed-up the calculation of first derivatives, which are necessary for the identification process. The process was applied for 36 configurations of CLT panels with different geometrical properties (number of layers, width and thickness of boards) within the practical range. Metamodels are proposed to quickly calculate the effective moduli based on the vibration properties of CLT panels. The Verification and Validation methodology was applied to evaluate the performance of the two simplified FE models using the effective moduli.

Stochastic FE analysis of stress concentrations in curved glulam beams due to the uncertainty of material direction

When curved glulam beams are subjected to bending, tension perpendicular to grain is introduced. In this work, Monte-Carlo analysis is conducted to study the influence of the annual-ring orientation of individual board on stress concentration in the radial direction. A virtual cutting program is developed which simulates the sawing processes of boards and yields a database of sawn boards, each with a characterized material direction with respect to the pith location. Lamellas are randomly selected from the database to construct curved glulam beams in FE models for Monte-Carlo simulation. Parameters including lumber diameter distribution, taper function, orthotropic elastic properties are considered for four common wood genera in Europe: spruce, pine, larch, and beech.Statistical analysis shows that when the annual-ring effect is considered, the average radial stress in the middle height area of the glulam beams can reach up 1.56 times (even higher on the middle width and height area) compared to the common practice, where wood is usually simplified as transverse isotropic material. Such stress concentration, which can trigger early damage of the structure, indicates an underestimation of stress perpendicular to grain in common practice. Moreover, parameter studies show that the stress redistribution depends not only on the mechanical properties of wood species but also on the width of the board layer.

Tailored elastic properties of beam-based lattice unit structures

AbstractIn this paper a structural optimization framework is developed to design three-dimensional periodic lattice unit cells that meets specific mechanical requirements. The work is motivated by the high design freedom of additive manufacturing technologies, which enable complex multiscale lattice structures to be printed. An optimized lattice unit cell delivers desired orthotropic elastic material properties, providing a tailored metamaterial. The design variables are the coordinates of lattice skeleton nodes defined within the three-dimensional lattice cell space, and the connectivities between them resulting a strut-skeleton. Genetic algorithm (GA) is combined with posterior particle swarm optimization (PSO) algorithm to establish an integrated topology and shape optimization tool. For the calculation of the elastic properties of the individual lattice cells, an effective Timoshenko beam-based finite element calculation method was developed. The novelty of the work stems from its free topology optimization nature, excluding the strut diameters from the optimization variables. The method is demonstrated by four lattice cell optimization cases, where extreme orthotropic elastic properties were targeted and achieved. The tailored lattice cells represent a metamaterial, that can be used to build a structural component on the macroscopic scale, by stacking the cells periodically together, to fill the macroscopic 3D design space. This framework is a strong basis that can be extended to meet further nonlinear metamaterial requirements, such as energy absorption.

Numerical and experimental study of porous NiTi anisotropy under compression

Porous NiTi samples were obtained by self-propagating high-temperature synthesis (SHS) and cut to specific dimensions by electrical discharge machining. Quasi-static compression of the porous SHS-NiTi alloy demonstrated that the deformation was elastic-plastic. Three characteristic types of fracture surfaces of bridges can be distinguished. 1) Ductile fracture of the austenite phase in the form of a cup and cone relief. 2) Brittle fracture with the formation of cleavage steps. 3) Large areas of plastic shear, where cup and cone, and cleavage facets are nucleated. An algorithm for obtaining a porous framework model suitable for finite element method calculations has been developed. The effective moduli of elasticity and shear for the porous volume of the material were determined. It is shown that the studied porous volume has orthotropic elastic properties due to the geometry of the porous framework.

Anisotropy of elastic properties of SHS-synthesized porous titanium nickelide

Samples of porous NiTi were obtained by the method of self-propagating high-temperature synthesis. The mechanical characteristics of the porous ones were studied by quasi-static compression. When the samples of porous titanium nickelide were subject to quasi-static compression, the deformation was of an elastic-plastic nature. Three characteristic types of the fracture surface under quasi-static compression of the porous SHS – TiNi alloy were identified: 1) ductile fracture of the austenite phase in the form of a cup relief, 2) brittle fracture accompanied by the formation of cleavage steps, 3) large areas of plastic shear deformation, on which cups and cleavage facets were nucleated. To determine the anisotropy of the porous TiNi alloy properties, the volume of the porous sample was simulated, and estimated calculations were carried out. Based on the results of reconstructing 3D neutron high resolution tomography of the porous volume of titanium nickelide and the numerical parameters of the model porous medium, an algorithm was developed for obtaining a solid-state 3D model of the porous framework for using in finite element calculations. The studied porous titanium nickelide alloy, as well as spongy bone tissues, was shown to have orthotropic elastic properties conditioned by the geometric features of the porous framework. The effective moduli of elasticity and shear for the porous volume of the material were determined. The calculation results of the elastic moduli for the studied model of porous titanium nickelide numerically agree with the results obtained by compressing the samples of porous TiNi. The porous TiNi alloy under uniaxial compression was established to be destroyed under the action of tangential shear stresses at an angle of 45 degrees to the direction of uniaxial compression. The research was carried out with financial support of the Russian Science Foundation under the Grant No. 22-72-10037, https://rscf.ru/project/22-72-10037/.

Identification of anisotropic properties of polymer sheets from heterogeneous biaxial tests

The stretch blowing process for PET bottle induces the anisotropic mechanical properties due to the different elongation of macromolecular chains. For example, the Young's modulus can be multiplied by almost two in the longitudinal direction and more than 3 times in the hoop direction of the plastic bottle. However, the process is complex and the elastic properties present dispersions which depend on the process condition. Therefore, it is necessary that the 5 parameters from the orthotropic elastic properties can be all obtained during a single realization. The symmetry of the elasticity tensor reduces to 4 characteristics to be determined. To achieve this identification process, firstly, the displacement field is measured using image correlation and biaxial tests are carried out on a machine developed in our laboratory. Then, the virtual field method on a specific cruciform specimen with a hole is managed to identify the orthotropic elastic properties. The optimal position of the hole is also studied. Finally, the identified orthotropic constitutive parameters from this method are compared to the results obtained by classical methods.

A new multi-scale topology optimization framework for optimal combinations of macro-layouts and local gradings of TPMS-based lattice structures

In this work, optimal combinations of macro-layouts and local gradings of triply periodic minimal surface (TPMS)-based lattice structures are obtained by using multi-scale topology optimization. A new innovative framework is proposed by using two density variables in each finite element. The first variable is the local relative lattice density and it sets the effective orthotropic elastic properties of the element, which in turn are obtained by using numerical homogenization of representative volume elements of the particular TPMS-based lattice structure of interest. The second variable is a standard topology optimization macro density variable, which defines if the element should be treated as a void or contain the graded lattice structure by letting this variable be governed by the rational approximation of material properties (RAMP) model. By using such density variables for all elements, the compliance is minimized by separately constraining the volume of lattice structure and the volume of macro-layout by using two independent constraints. For benchmarks in 3 D, it is demonstrated that the stiffness is increased significantly by including local grading of the lattice structure compared to using a constant lattice density. It is also demonstrated how ultra-lightweight designs can be generated using the multi-scale formulation, and how the optimal multi-scale solutions easily can be realized to printable stl-files by using implicit based geometry modeling. Finally, the new multi-scale topology optimization framework is utilized to generate an optimal design combination of macro-layout and local grading of frame-based Gyroid structure for the established GE-bracket benchmark.

An improved mean-field homogenization model for the three-dimensional elastic properties of masonry

Accurate assessment of the overall mechanical behavior of masonry, composed of bricks and mortar joints, remains challenging due to its inhomogeneous and orthotropic nature. In this study, the feasibility of various mean-field homogenization schemes for the three-dimensional orthotropic elastic properties of masonry is comprehensively investigated. Three kinds of masonry patterns are considered, including the stack bonded pattern, the running bonded pattern and the double-leaf Flemish bonded pattern that has received limited attention so far. Special attention is paid to the homogenization schemes which have not been applied to the masonry case, such as Lielens’ interpolative double inclusions (D-I) and the interaction direct derivative (IDD) schemes. After a comparison between the well-known mean-field homogenization schemes, an improved micro-mechanical model is proposed by combining the advantages of the IDD and D-I models. The validation of the proposed model is conducted through a comparison against experimental data from literature and numerical results obtained via finite element analyses (FEA). The results show that the proposed model can accurately evaluate the orthotropic elastic properties of the three masonry typologies for a wide range of stiffness ratios between brick and mortar, ranging from 1 to 1000. The proposed model also shows better performance than the classical schemes especially when the stiffness ratios between brick and mortar are higher than 10, which is of major importance for the application of mean-field homogenization based multiscale methods to the nonlinear analysis of masonry. Furthermore, the presented homogenization method can be of interest for other anisotropic materials, e.g., laminate materials.

Modelling of in-plane seismic behaviour of one-way steel or timber jack arch floors in existing buildings. Application to the Eixample district of Barcelona

The type of floor system has a decisive role in the seismic performance of unreinforced masonry buildings. The in-plane stiffness of the floors has to be adequately represented in the numerical modelling of existing buildings, as it can influence their seismic capacity. This paper investigates the seismic behaviour of one-way arch floor systems composed of steel or timber beams, and ceramic tile vaults. The main objective of the research is to provide a numerical procedure for the simplified modelling of jack arch floor systems in the seismic assessment of unreinforced masonry buildings. The presented approach aims to provide values for the orthotropic properties of simplified floor models composed of elastic 2D shell elements. The orthotropic elastic properties are computed and calibrated by means of comparisons with detailed 3D nonlinear models of the floors. The case study is a multi-storey existing masonry building of the historical “Eixample” district in Barcelona, which includes one-way arch floor systems. The Finite Element Method has been used for the numerical simulation of the seismic performance through nonlinear static (pushover) analyses. The results of the study contribute to a better understanding of the effect of the behaviour of one-way floors with steel or timber beams and tile vaults on the seismic response of masonry buildings. This work provides indicative values for the proper modelling of these particular floor slabs. The proposed methodology is also applicable to the numerical simulation of any other one-way floor system.

Design and Characterization of Asymmetric Cell Structure of Auxetic Material for Predictable Directional Mechanical Response.

A three-dimensional auxetic structure based on a known planar configuration including a design parameter producing asymmetry is proposed in this study. The auxetic cell is designed by topology analysis using classical Timoshenko beam theory in order to obtain the required orthotropic elastic properties. Samples of the structure are fabricated using the ABSplus fused filament technique and subsequently tested under quasi-static compression to statistically determine the Poisson’s ratio and Young’s modulus. The experimental results show good agreement with the topological analysis and reveal that the proposed structure can adequately provide different elastic properties in its three orthogonal directions. In addition, three point bending tests were carried out to determine the mechanical behavior of this cellular structure. The results show that this auxetic cell influences the macrostructure to exhibit different stiffness behavior in three working directions.

A machine learning approach to determine the elastic properties of printed fiber-reinforced polymers

This work focuses on the simultaneous determination of the elastic constants and the fiber orientation state for a short fiber-reinforced polymer composite by performing a minimum of experimental tests. We introduce a methodology that enables the inverse determination of fiber orientation state and the in-situ polymer properties by performing tensile tests at the composite coupon level. We demonstrate the approach for the extrusion deposition additive manufacturing (EDAM) process to illustrate one application of the methodology, but the development is such that it can be applied to short fiber-reinforced polymer (SFRP) systems processed via other methods. Currently, developing composites additive manufacturing digital twins require extensive material characterization. In particular, the mechanical characterization of the orthotropic elastic properties of a composite involves extensive sample preparation and testing, therefore the elasticity tensor is generally populated using a micromechanics model. This, however, requires measuring the fiber orientation state in addition to knowing the constituent material properties. Experimentally measuring the fiber orientation state can be tedious and time consuming. Further, optical methods are limited to resolving the orientation of cylindrical fibers or cluster of non-cylindrical fibers, and computed tomography (CT) methods scan regions of volume that are much smaller than a full printed bead. Therefore, we propose a methodology, accelerated by machine learning, to identify the anisotropic mechanical properties and fiber orientation state at the same time. Early results show that inference of the fiber orientation and composite properties is possible with as few as three tensile tests. Our results show that a combination of the choice of the micromechanics model and reliable set of experiments can yield the nine elastic constants, as well as, the fiber orientation state.

Identification of Orthotropic Elastic Properties of Wood by a Synthetic Image Approach Based on Digital Image Correlation.

This work aims to determine the orthotropic linear elastic constitutive parameters of Pinus pinaster Ait. wood from a single uniaxial compressive experimental test, under quasi-static loading conditions, based on two different specimen configurations: (a) on-axis rectangular specimens oriented on the radial-tangential plane, (b) off-axis specimens with a grain angle of about 60° (radial-tangential plane). Using digital image correlation (DIC), full-field displacement and strain maps are obtained and used to identify the four orthotropic elastic parameters using the finite element model updating (FEMU) technique. Based on the FE data, a synthetic image reconstruction approach is proposed by coupling the inverse identification method with synthetically deformed images, which are then processed by DIC and compared with the experimental results. The proposed methodology is first validated by employing a DIC-levelled FEA reference in the identification procedure. The impact of the DIC setting parameters on the identification results is systematically investigated. This influence appears to be stronger when the parameter is less sensitive to the experimental setup used. When using on-axis specimen configuration, three orthotropic parameters of Pinus pinaster (, and ) are correctly identified, while the shear modulus () is robustly identified when using off-axis specimen configuration.

Identification of orthotropic elastic properties of wood by digital image correlation and finite element model updating techniques

Computer-aided engineering systems rely on constitutive models and their parameters to describe the material behaviour. The identification process, however, grows in complexity for more elaborated material models, increasing the number of experimental tests needed, therefore time and cost consuming. Recently, with the development of digital image technology, there has been a growing interest in the use of full-field deformation measurements. This advancement has highlighted a new methodology on inverse identification techniques such as the finite element model updating method. This work aims to identify orthotropic linear elastic constitutive parameters of Pinus pinaster Ait. wood based on a single uniaxial compressive experimental test. Clear wood specimens oriented in the radial-tangential plane were used and tested under quasi-static loading condition. Full-field displacement and strain maps were obtained using digital image correlation and used to simultaneously identify the whole set of elastic properties through finite element model updating methodology.

Non-Destructive Assessment of the Elastic Properties of Low-Grade CLT Panels

The use of cross-laminated timber panels (CLT) made of low-grade structural timber has steadily increased in developing countries. These panels usually present several natural defects, which can cause a high local variation of their orthotropic elastic properties, generating future structural serviceability problems. Our work aims to estimate the local variability of the elastic properties in low-grade CLT panels by combining nondestructive transverse vibration testing, numerical simulations, and regional sensitivity analysis (RSA). Four three-layer Radiata pine CLT panels were subjected to transverse vibration tests with supports at four points. Besides, a series of numerical simulations of the panels, considering the local variability of the elastic properties of the panels in eight zones, were carried out using the finite element method. Then, RSA analysis was performed to study in which ranges of values the panels’ elastic properties generated lower differences between the measured versus simulated dynamic properties. Finally, a structural quality control indicator was proposed for the CLT panels based on keeping low the probability that the elastic properties in the central zones do not exceed minimum acceptable values. The results obtained suggest that the proposed methodology is suitable for segregating CLT panels with high concentrations of defects such as pith presence.