Orthotropic Material Properties Research Articles

The Effect of Ratio of Fiber Bundles in the Textile Composite Layer

Abstract The article shows how the orthotropic material properties of the textile composite layer change if the ratio of longitudinal and transversal fiber bundles in the textile is modified in the case of a composite reinforced with plain weave textile. I determine the material properties using model-cell and finite element simulation. The density of the longitudinal fiber bundles is the same in each of the five examined layer models. I change the ratio of the fiber bundles of the textile by varying the distance of the transversal roving’s in each model.

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.

Exploring the thermomechanical and dynamical mode switch transition of a reversible solid oxide cell

Reversible solid oxide cells (r-SOCs) are regarded as a solution form of clean energy generation towards a green hydrogen energy transition. However, during transportation, installation, and operation, they are required to withstand dynamic conditions as they face thermal, mechanical, and vibrational effects. Assessing the interplay of the thermomechanical and dynamical impacts on r-SOC materials during the mode-switch from electrolysis to fuel cell operation is the subject of this current comprehensive study. Advanced FEM-based homogenisation techniques have been harnessed in predicting and evaluating the detailed transients during static and dynamic loading. The intricate 3D thermal profiles throughout the transient reversible dual-modus operation from a typical r-SOC study have been derived using advanced image processing. Orthotropic material properties were incorporated into a unified macroscopic scale model by deriving the complex 3D microstructure geometry characteristics of the cell materials and component layers. The comprehensive thermomechanical and pre-stressed modal analysis results showed that the static and dynamic forces in fuel cell mode are more pronounced, whereas, in electrolysis operation, the dynamical behaviour highly depends on geometrical and operating conditions. Smaller component size shows higher natural frequencies and more intense vibration, leading to higher deformation attributed to complex mode shapes and reduced flexural rigidity. These insights are essential for optimizing r-SOC design parameters, enhancing their dynamic and structural reliability throughout their dual-mode operation lifespan.

Identification, uncertainty quantification and validation of orthotropic material properties for additively manufactured polymers

The mechanical behavior of polymeric parts manufactured by fused filament fabrication is often characterized as orthotropic because of the layer-wise extrusion of the material. To perform reliable simulations of the mechanical response of these parts subjected to certain loads, the material parameters have to be known. This leads to the task of material parameter identification from suitable experimental data. In this work, the identification of the material parameters for orthotropic material behavior is studied in detail with a focus on the specific characteristics of additively manufactured parts. This comprises working out the differences that arise compared to the parameter identification for classical orthotropic composite materials. Moreover, the material parameters are identified from tensile and shear test information together with full-field displacement data from digital image correlation measurements. Then, the obtained parameters are compared for analytical and numerical approaches, where a non-linear least-squares method with finite elements is drawn on. The parameters are not only identified, but also an uncertainty analysis is carried out and, subsequently, the different methods are validated. Further, a clear derivation of commonly applied analytical equations is provided with a special focus on the underlying assumptions. It turns out that the analytical parameter identification procedures cannot be easily transferred to numerical procedures, especially when using full-field data, because of correlations between the parameters. Moreover, the identified parameters are employed to prove the reasonability of orthotropic material behavior for specimens manufactured by fused filament fabrication. Finally, during validation it turns out that all parameter identification methods provide a good agreement with experimental data, showing only small differences between the results of the different calibration strategies.

Dynamic behavior of the orthotropic hollow cylinder under a magnetic field: a thermoelastic analysis

The present article focuses on the complete analytical solution of an orthotropic hollow cylinder using a proposed magneto-thermoelastic model and finite Hankel transformation. The study considers the Lord–Shulman and Green–Lindsay models of hyperbolic generalized thermoelasticity within the context of thermoelasticity theory. The analytical expressions of the field variables of the cylinder in a magnetic field were obtained under thermo-mechanical loadings. The study also offered closed-form field functions and measured the thermoelastic behavior concerning the magnetic field intensity of the cylinder based on thermoelastic theories involving a second sound. The inclusion of hyperbolic-type heat conduction models enhanced the visualization of the reflection of thermal waves into the cylinder. The study also investigated the impacts of orthotropic material properties on the considered medium and compared the results with the existing literature.

Generalized magneto-thermoelasticity problem in an orthotropic hollow sphere under thermal shock

This article addresses the magneto-thermoelasticity problem within an orthotropic hollow sphere. The governing equations are formulated based on the Lord-Shulman coupled theory of thermoelasticity. Time-dependent thermal and mechanical boundary conditions are imposed on the inner and outer surfaces of the hollow sphere. The analytical solution is obtained using the finite Hankel transform. A thermal shock in the form of heat flux is prescribed on the sphere’s inner surface, and subsequently, the transient thermal response of the sphere, along with radial displacement and radial, tangential, and circumferential stresses, are derived. The influence of different magnetic field values, orthotropic material properties, and relaxation time is investigated and presented graphically. The obtained results exhibit excellent agreement with existing literature, validating the robustness of the proposed model. The findings not only contribute to the fundamental understanding of magneto-thermoelasticity but also offer practical insights for engineering applications involving orthotropic materials in complex thermal and magnetic environments. The availability of an exact solution facilitates the validation of numerical models, ensuring their accuracy and reliability in capturing the intricate behavior of orthotropic materials under coupled fields.

Estimation of thermophysical properties of a pouch-type Li-ion battery using an inverse methodology

The growing popularity of electric vehicles highlights the crucial role of batteries. Effective battery thermal management is crucial for improving performance, reliability, and safety, especially in tropical areas where overheating is a key challenge. This necessitates a comprehensive understanding of the thermophysical properties of batteries. The present study concerns the estimation of the temperature-dependent orthotropic thermophysical properties (kx , ky , kz , cp ) of the active material in a pouch-type Li-ion battery using an inverse methodology. An experimental study is conducted on a commercial AMP20M1HD-A Li-ion battery to measure the surface temperature at various locations using thermocouples. The forward model consists of the three-dimensional unsteady conduction problem and is solved in COMSOL using experimental boundary conditions. The data generated is used to train an Artificial Neural Network, which acts as a replacement for the forward model. The Metropolis Hasting-Markov Chain Monte Carlo algorithm along with the Bayesian inference inverse model is used for analyzing the posterior distribution and the average estimates for thermophysical properties are obtained. The temperature dependence study shows a significant correlation between temperature and battery thermophysical properties. The accuracy of the employed inverse model is validated by obtaining the surface temperature using the estimated thermophysical properties and comparing it with the measured surface temperature.

Cylindrical single-wall and double-wall structures with or without internal water subjected to underwater shock loading

A series of experimental studies were conducted for cylindrical structures subjected to underwater shock loading to understand their dynamic responses and failure characteristics. All tests were performed inside an anechoic water tank. The submerged test cylinders were freely suspended, and an underwater shock loading was generated by the Compressed Air Shock Pipe Underwater Release (CASPUR) system. Cylinders were made of two different materials. The first group of cylinders was fabricated from carbon fiber and resin using the filament winding technique. The winding angles were ± 45° resulting in the same properties along axial and hoop directions. The second group of cylinders was constructed using a 3-D printer with polylactic acid (PLA) material. The 3-D printed cylinders had an orthotropic material property with different values in the axial and hoop directions. Both single-wall and double-wall cylindrical structures were tested. The latter consisted of two concentric cylinders of different diameters with uniform spacing between them. In addition, within the single-wall cylinders and the annuli of double-wall cylinders, the water fill was varied at 0%, 50%, or 100%. Pressure and strain gages were used to measure the shock pressure and deformation of the cylinders. The number of cylinders such as single-wall or double-wall and the internal water resulted in significant effects on the measured dynamic response (i.e., strain gage response) as well as the failure loading and failure characteristics including major failure locations. Internal water reduced the strain on the cylinders and made them withstand greater shock loading for both single-wall and double-wall cylinders.

Mechanobiochemical bone remodelling around an uncemented acetabular component: influence of bone orthotropy.

Mechanical loosening of an implant is often caused by bone resorption, owing to stress/strain shielding. Adaptive bone remodelling elucidates the response of bone tissue to alterations in mechanical and biochemical environments. This study aims to propose a novel framework of bone remodelling based on the combined effects of bone orthotropy and mechanobiochemical stimulus. The proposed remodelling framework was employed in the finite element model of an implanted hemipelvis to predict evolutionary changes in bone density and associated orthotropic bone material properties. In order to account for variations in load transfer during common daily activities, several musculoskeletal loading conditions of hip joint corresponding to sitting down/up, stairs ascend/descend and normal walking were considered. The bone remodelling predictions were compared with those of isotropic strain energy density (SED)-based, isotropic mechanobiochemical and orthotropic strain-based bone remodelling formulations. Although similar trends of bone resorption were predicted by orthotropic mechanobiochemical (MBC) and orthotropic strain-based models across implanted acetabulum, more volume (10-20%) of bone elements was subjected to bone resorption for the orthotropic MBC model. Higher bone resorption (75-85%) was predicted by the orthotropic strain-based and orthotropic MBC models compared to the isotropic MBC and SED-based models. Higher bone apposition (35-160%) across the implanted acetabulum was predicted by the isotropic MBC model, compared to the SED-based model. The remodelling predictions indicated that a reduction in estrogen level might lead to an increase in bone resorption. The study highlighted the importance of including mechanobiochemical stimulus and bone anisotropy to predict bone remodelling adequately.

An ICME framework for short fiber reinforced ceramic matrix composites via direct ink writing

A manufacturing-driven ICME framework is proposed to model short fiber reinforced ceramic matrix composites (CMCs) via direct ink writing. Currently, there lacks efforts to investigate the effects of properties of short fiber reinforced CMCs due to fiber alignment variance. A multi-scale modeling approach is presented to use representative volume elements to capture the homogenized mechanical behavior at various fiber aspect ratios and volume ratios. The orthotropic material properties are mapped to model the printing process. A series of tensile tests simulations show that with 20∘ standard deviation in fiber alignment, the fracture plane has the maximum local tensile stress range at a printing angle of 30∘ and has the minimum local tensile stress range at 90 ∘ . When the standard deviation increases from 20∘ to 40∘, the average tensile strength across the fracture plane decreases by 2%, but the stress variations increase 27.6%.

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.

Bending and torsion induced stresses in cylindrically orthotropic and inhomogeneous timber beams

The structural design of timber beams subject to bending often relies on the application of the simple Euler–Bernoulli beam theory. However, the simplistic formulas for stress calculations overlook the inherent characteristics of the wood material and the true distribution of the annual rings within the cross-sectional area. This paper introduces a method for determining all six stress components for a cantilever-type beam that is subjected to concentrated end loads. The method considers an inhomogeneous cross-section and employs cylindrically orthotropic material properties. Notably, this approach does not necessitate prior knowledge of elastic and shear centres. It is founded on the formulation of a displacement field incorporating unknown in-plane distortion and warping functions. These are then solved through a straightforward finite element procedure. The efficacy of the method is validated by a series of numerical examples that align with analytical results. Furthermore, a benchmark example for cylindrically orthotropic cross-sections is proposed. As a practical demonstration, an analysis is performed on a real sawn timber cross-section with material parameters representative of Norway spruce. The findings reveal significant disparities in the maximum stresses when compared to conventional engineering approaches. In this specific instance, the maximum longitudinal normal stress resulting from bending is approximately 20 % higher than the outcomes of typical engineering methods. This emphasizes the critical role played by the actual distribution of annual rings across the specific beam cross-section.

Dynamic Analysis of a High-Performance Prosthetic Leg: Experimental Characterisation and Numerical Modelling

In recent years, significant improvements in the design of leg blade prosthetics have been carried out. After several advances in material and topological optimisations, sport-purpose feet prosthetics have reached high-level performances, allowing athletes with limb loss to participate in various sport activities at a competitive level. Since the knowledge of prosthetic mechanical behaviour is crucial for its optimal design, specific studies are required to meet the anthropometric characteristics of the athlete. This research work is focused on investigating the dynamic behaviour of a running blade prosthetic and developing a validated prosthetic model, placing particular emphasis on the definition of suitable material properties. An experimental modal analysis is performed on the Cheetah Xcel, Össur lower limb prosthetic. In contrast with what has already been presented in the literature, a roving hummer test under free–free conditions is proposed here to avoid the uncertainties due to constraint conditions. For the first time, blade prosthetic dynamic characteristics in free–free conditions are presented. Additionally, a novel Finite Element model of the prosthetic is developed and tuned on the basis of the experimental results. The modal assurance criterion index is exploited to compare experimental and numerical mode shapes. Starting from frequency response functions, the first six mode shapes are experimentally identified in the frequency range up to 750 Hz, including both bending and torsion. As expected, the bending in the vertical plane constitutes the primary mode shape: this kind of flexion enhances energy storage, enabling athletes to achieve an optimal running gait. This study shows the dynamic modal behaviour of a lower limb prosthetic in free–free conditions and demonstrates that a traditional isotropic material is not suitable in describing its dynamic features. The development of a model that exploits orthotropic material properties improves the alignment between experimental and numerical outcomes. This result is in agreement with the material composition of the prosthetic, which consists of carbon fibre layers.

Development and validation of lumbar spine finite element model.

The functional biomechanics of the lumbar spine have been better understood by finite element method (FEM) simulations. However, there are still areas where the behavior of soft tissues can be better modeled or described in a different way. The purpose of this research is to develop and validate a lumbar spine section intended for biomechanical research. A FE model of the 50th percentile adult male (AM) Total Human Model for Safety (THUMS) v6.1 was used to implement the modifications. The main modifications were to apply orthotropic material properties and nonlinear stress-strain behavior for ligaments, hyperelastic material properties for annulus fibrosus and nucleus pulposus, and the specific content of collagenous fibers in the annulus fibrosus ground substance. Additionally, a separation of the nucleus pulposus from surrounding bones and tissues was implemented. The FE model was subjected to different loading modes, in which intervertebral rotations and disc pressures were calculated. Loading modes contained different forces and moments acting on the lumbar section: axial forces (compression and tension), shear forces, pure moments, and combined loading modes of axial forces and pure moments. The obtained ranges of motion from the modified numerical model agreed with experimental data for all loading modes. Moreover, intradiscal pressure validation for the modified model presented a good agreement with the data available from the literature. This study demonstrated the modifications of the THUMS v6.1 model and validated the obtained numerical results with existing literature in the sub-injurious range. By applying the proposed changes, it is possible to better model the behavior of the human lumbar section under various loads and moments.

Investigation of modelling approaches to study the structural performance of 3D printed plain wall under uniform axial compression

This study reports an experimental and numerical examination performed on a 3D printed (3DP) wall subjected to vertical axial compression. A detailed investigation of material property and full-scale testing of the 3DP plain wall was performed to explore the structural performance of the 3D printed wall. To obtain the mechanical properties of mortar, test prisms obtained by printing mortar as layers resulted in undesirable failure modes. Hence, this study proposes a unique methodology to obtain the mechanical property of mortar with an assumption of mortar material as isotropic. However, to consider the effect of the interface within the printed layers, interface strength tests in terms of normal and shear strength were performed. Likewise, the behavior of 3DP wall being anisotropic, a unique analysis concept was adopted in a current study comprising of modelling the printed layers as in actual thickness and cross-section and providing material property obtained from an assumption of mortar material as isotropic. Moreover, orthotropic material properties of the printed material were provided to FE models via testing of the 3D printed specimens parallel and normal to the interface. The full-scale test specimen was modeled as layers in a numerical tool and results from the test and simulation were compared in terms of load-displacement behavior, distribution of strain on the wall surface, and damage pattern of the wall. Moreover, recommendation on the selection of the suitable material model and contact algorithm is provided in the current study for simulating the behavior of 3DP structures.

Biomechanical influence of plate configurations on mandible subcondylar fracture fixation: a finite element study.

Mandible subcondylar fractures have very high complication rate, yet there is no consensus on suitable plate design for optimal patient outcomes. Our study is aimed at comparing single mini, trapezoid, lambda, strut and double mini plates. A finite-element (FE) model of intact mandible was developed based on healthy CT-scan data, which was further virtually osteotomized and fixated with plates. The cortical and cancellous bones were assigned region-specific orthotropic and heterogenous isotropic material properties respectively. The models were subjected to six load cases representing the mastication cycle. Under opposite lateralities, the tensile and compressive mandibular strain distributions were found as the opposite, with tensile strains at the posterior border under ipsilateral molar clenching (RMOL) resulting in lesser mandibular strain in reconstructed mandible with single mini plate under RMOL but highest mandibular strain under the contralateral molar clenching (LMOL). Owing to the reduced mandibular strains under LMOL than RMOL, the contralateral chewing is preferred during the immediate post-surgery period for patients. Under LMOL, the peak von Mises stresses in the plate decreased with increase in the number of screws. Furthermore, the presence of two arms in double mini and trapezoid plates seems beneficial to neutralise the tensile and compressive strains across load cases.

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.

Prediction of moisture-induced cracks in wooden cross sections using finite element simulations

Wood absorbs and desorbs moisture due to its hygroscopic behavior, leading to moisture gradients in timber elements as well as swelling and shrinkage. These processes are constrained due to the orthotropic material properties of wood, leading to moisture-induced stresses, which can cause crack initiation and propagation. A significant amount of the damage in timber constructions indoors can be related to changes of the moisture content (MC). However, more information is needed about the correlation between moisture changes or gradients and specific damage characteristics, like crack depths. Thus, based on numerical simulations, the crack depth development within two solid timber and one glued laminated timber (GLT) cross section over time for different relative humidity (RH) reductions and initial MCs is analyzed. For this purpose, a multi-Fickian transport model is used to determine moisture fields, which are then used as loads in a subsequent stress simulation, where linear elastic material behavior is considered. An extended finite element approach, supported by a multisurface failure criterion defining the failure behavior, allows for the simulation of moisture-induced discrete cracking. Based on simulation results, correlations between potential maximum crack depths and moisture gradients in indoor climate conditions are derived, which enables the prediction of crack depths in wood. Finally, it is shown that the initial MC level significantly influences the maximum crack depth that can be expected.

Determining the influence of irradiation swelling on creep and damage in elements with orthotropic material properties

This paper reports a method that numerically models the deformation and accumulation of hidden damage in structural elements that are in an inhomogeneous thermal field and are exposed to radiation. Materials considered are those exhibiting orthotropy (transversal isotropy) of long-term properties. The problem is stated as an boundary – initial value one. To solve it, the finite element method and the initial-difference method of time integration are used. To simulate the anisotropy of the process of accumulation of hidden damage, a damage tensor is applied. The development of irradiation swelling strains is described using the equation for a limited temperature range and a specific fluence value. The results of numerical modeling of creep and damage in plates in tension with circular notches, which are in an inhomogeneous temperature field, are considered. The material of the plates is a titanium alloy VT1-0. It was found that the effect of irradiation significantly, up to 6‒7 %, increases the level of deformation in the plate. Radiation significantly, by almost 4 times, reduces the time until the completion of the hidden fracture of the plates. It was found that orthotropy of radiation swelling properties leads to redistribution of areas with significant strains and damage values. It has been established that the effect of irradiation swelling also qualitatively changes the nature of the distribution of maximum damage in the plate, which extends to a fairly large area. Such results are due to the additional effect of irradiation swelling strains on the rate of general irreversible deformation and redistribution of stresses

MODELING THE EARLYWOOD AND LATEWOOD GROWTH RINGS OF NORWAY SPRUCE TIMBER BEAMS FOR FINITE ELEMENT CALCULATION

The purpose of this research is to determine the orthotropic material properties oftheNorway spruce (Picea abies) and to develop a finite element modeling technique that, when applied to an individual specimen, can properly predict the outcome of the measurement results (i.e., deflection by a predefined loading) by simulation only. For the development ofthefinite element model of timber beams, their unique annual ring pattern is considered. TheHSV color spectrum of picture of the end grain pattern is analyzed with a photo analytical algorithm in order to separate the phases, earlywood and latewood. The determined surface ratio of thephases is used to hypothesize that the volume and surface ratios are equal. For thedescription of wood as a material the rule of mixtures is used. The results of thecompared measurements and FE models based on the introduced hypotheses show good agreement within the linear elastic limit.