Appl. Mech., Volume 2, Issue 4 (December 2021) – 24 articles

The advancements in the automotive, aviation, and aerospace industry have led to an increased usage of CFRP high-pressure gas tanks. In order to avoid any fatal accidents, the inspection procedures require accuracy, but also practicality, to be used in the industry. The presented work focuses on response-only metrics from vibrational experimental measurements of the CFRP tank. The power spectral density and transmittance function curves are both compared for the accuracy and ability to be used as metrics for damage detection. Along with the selection of the proper metric, an appropriate clustering algorithm that can accurately group similar states of the structure is of high importance. Two clustering algorithms, agglomerative hierarchical and spectral clustering, are employed and compared for their performance. A small Type V CFRP tank is used as an experimental structure on this benchmark problem. In order to create realistic material damage, the tank is placed on an impact system multiple times where different damage magnitudes are created. After each new state and damage magnitude on the tank, vibrational experimental data are collected. Using the collected data, all the combinations of the mentioned metrics and algorithms are executed and properly compared to evaluate their accuracy. Full article

Friction induced vibrations such as brake squealing, or juddering are still challenging topics in product engineering processes. So far, this topic was particularly relevant for the automobile industry because they were the main market for disc brake systems. However, since mobility habits change, disc brake system are more often to be found on bikes or e-scooters. In all of these systems, vibrations are excited in contacts on the micro scale but affect the user comfort and safety on the macro scale. Therefore, the aim of this cross-scale method is to analyze a system on a micro scale and to transfer the excitation mechanisms on a macro scale system. To address both scales, the current work presents a finite element model on the micro scale for the determination of the coefficient of friction, which is transferred to the macro scale and used in a multi-body simulation. Finally, a finite element modal analysis is conducted, which allowed us to evaluate the brake system behavior on base of an excitation. Full article

This paper presents a finite element implementation of plates and shells for the analysis of flexible multibody systems. The developments are set within the framework of the motion formalism that (1) uses configuration and motion to describe the kinematics of flexible multibody systems, (2) couples their displacement and rotation components by recognizing that configuration and motion are members of the Special Euclidean group, and (3) resolves all tensors components in local frames. The formulation based on the motion formalism (1) provides a theoretical framework that streamlines the formulation of shell elements, (2) leads to governing equations of motion that are objective, intrinsic, and present a reduced order of nonlinearity, (3) improves the efficiency of the solution process, (4) circumvents the shear locking phenomenon that plagues shell formulations based on classical kinematic descriptions, and (5) prevents the occurrence of singularities in the treatment of finite rotation. Numerical examples are presented to illustrate the advantageous features of the proposed formulation. Full article

The capabilities of detection and localization of damage in a structure, using a guided wave-based structural health monitoring (GWSHM) system, depend on the damage location and the chosen sensor array setup. This paper presents a novel approach to assess the reliability of an SHM system enabling to quantify localization accuracy. A two-step technique is developed to combine multiple paths to generate one probability of detection (POD) curve that provides information regarding the detection capability of an SHM system at a defined damage position. Moreover, a new method is presented to analyze localization accuracy. Established probability-based diagnostic imaging using a signal correlation algorithm is used to determine the damage location. The resultant output of the localization accuracy analysis is the smallest damage size at which a defined accuracy level can be reached at a determined location. The proposed methods for determination of detection probability and localization accuracy are applied to a plate-like CFRP structure with an omega stringer with artificial damage of different sizes at different locations. The results show that the location of the damage influences the sensitivity of detection and localization accuracy for the used detection and localization methods. Localization accuracy is enhanced as it becomes closer to the array’s center, but its detection sensitivity deteriorates. Full article

Electronic devices and their associated sensors are exposed to increasing mechanical, thermal and chemical stress in modern applications. In many areas of application, the electronics are completely encapsulated with thermosets in a single process step using injection molding technology, especially with epoxy molding compounds (EMC). The implementation of the connection of complete systems for electrical access through a thermoset encapsulation is of particular importance. In practice, metal pin contacts are used for this purpose, which are encapsulated together with the complete system in a single injection molding process step. However, this procedure contains challenges because the interface between the metallic pins and the plastic represents a weak point for reliability. In order to investigate the reliability of the interface, in this study, metallic pin contacts made of copper-nickel-tin alloy (CuNiSn) and bronze (CuSn6) are encapsulated with standard EMC materials. The metal surfaces made of CuNiSn are further coated with silver (Ag) and tin (Sn). An injection molding tool to produce test specimens is designed and manufactured according to the design rules of EMC processing. The reliability of the metal-plastic interfaces are investigated by means of shear and leak tests. The results of the investigations show that the reliability of the metal-plastic joints can be increased by using different material combinations. Full article

In order to analyze the dynamics of a structural problem accurately, a precise model of the structure, including an appropriate material description, is required. An important step within the modeling process is the correct determination of the model input parameters, e.g., loading conditions or material parameters. An accurate description of the damping characteristics is a complicated task, since many different effects have to be considered. An efficient approach to model the material damping is the introduction of fractional derivatives in the constitutive relations of the material, since only a small number of parameters is required to represent the real damping behavior. In this paper, a novel method to determine the damping parameters of viscoelastic materials described by the so-called fractional Zener material model is proposed. The damping parameters are estimated by matching the Frequency Response Functions (FRF) of a virtual model, describing a beam-like structure, with experimental vibration data. Since this process is generally time-consuming, a surrogate modeling technique, named Polynomial Chaos Expansion (PCE), is combined with a semi-analytical computational technique, called the Numerical Assembly Technique (NAT), to reduce the computational cost. The presented approach is applied to an artificial material with well defined parameters to show the accuracy and efficiency of the method. Additionally, vibration measurements are used to estimate the damping parameters of an aluminium rotor with low material damping, which can also be described by the fractional damping model. Full article

Different mechanical properties characterise the materials of 3D printed components, depending on the specific additive manufacturing (AM) process, its parameters, and the post-treatment adopted. Specifically, stereolithography (SLA) uses a photopolymerisation technique that creates solid components through selective solidification. In this study, 72 specimens were 3D printed using 12 commercial-grade methacrylate resins and tested under uniaxial tensile loads. The resin specimens were evaluated before and after curing. The recommended cure temperature and time were followed for all materials. The stress-strain curves measured during the testing campaign were evaluated in terms of maximum tensile strength, Young’s modulus, ductility, resilience, and toughness. The results reveal that the curing process increases the material stiffness and resistance to tensile loads. However, it was found that the curing process generally reduces the plasticity of the resins, causing a more or less marked brittle behaviour. This represents a potential limitation to the use of SLA 3D printing for structural elements which require some plasticity to avoid dangerous sudden failures. Full article

Various peening techniques have been used to improve the fatigue strength of steel structures. Among them, base metal impact hammer peening shows significant improvement in fatigue strength in ordinary steel, but the effect on high-strength steel has not been sufficiently studied. Accordingly, this study applied base material hammer impact peening to test specimens of 780 MPa grade high-strength steel (HT780) and 490 MPa grade ordinary steel (SM490), and the residual stress was measured and simulated. The experimental results clarified that a large compressive residual stress was introduced into the inner part of the plate thickness near the indentation in the high-strength steel, although the range of introduction of residual stress was equivalent in both the ordinary steel and high-strength steel. Full article

In cell structures, unlike in dense bodies, nonuniform deformation occurs from the impact end, even at velocities in the order of tens to hundreds of meters per second. In this study, we experimentally examine the nonuniform deformation mechanism of cell structures. They prepared two kinds of specimens: nickel foam (Ni foam) and silicone-rubber-filled nickel foam (Ni/silicone foam). As a dynamic and impact test method (compression velocity of 20 m/s or more), we used a dynamic and impact load-measuring apparatus with opposite load cells to evaluate the loads on both ends of the specimen in one test. At compression velocities of 20 m/s or less, no nonuniform deformations were observed in the Ni foam and the Ni/silicone foam, and the loads on the impact and the fixed ends achieved force equilibrium. The Ni foam showed no change with an increasing strain rate, and the Ni/silicone foam showed a strong strain rate dependence of the flow stress. At a compression velocity of approximately 26 m/s, the loads differed at the two ends of the Ni/silicone foam, and we observed nonuniform deformation from the impact end. The results of the visualization of the load and deformation behavior obtained from both ends of the specimen revealed that the velocity of the plastic stress wave and the length of the specimens are important for nonuniform deformation. Full article

In engineering, metaheuristic algorithms have been used to solve complex optimization problems. This paper investigates and compares various algorithms. On one hand, the study seeks to ascertain the advantages and disadvantages of the newly presented heuristic techniques. The efficiency of the algorithms is highly dependent on the nature of the problem. The ability to change the complexity of the problem and the knowledge of global optimal locations are two advantages of using synthetic test functions for algorithm benchmarking. On the other hand, real-world design issues may frequently give more meaningful information into the effectiveness of optimization strategies. A new synthetic test function generator has been built to examine various optimization techniques. The objective function noisiness increased significantly with different transformations (Euclidean distance-based weighting, Gaussian weighting and Gabor-like weighting), while the positions of the optima remained the same. The test functions were created to assess and compare the performance of the algorithms in preparation for further development. The ideal proportions of the primary girder of an overhead crane have also been discovered. By evaluating the performance of fifteen metaheuristic algorithms, the optimum solution to thirteen mathematical optimization techniques, as well as the box-girder design, is identified. Some conclusions were drawn about the efficiency of the different optimization techniques at the test function and the transformed noisy functions. The overhead travelling crane girder design shows the real-life application. Full article

Laser peening introduces compressive residual stresses on the surfaces of various materials and is effective in enhancing fatigue strength. Using a small microchip laser, with energies of 5, 10, and 15 mJ, the authors applied laser peening to the base material of an HT780 high-strength steel, and confirmed compressive residual stresses in the near-surface layer. Laser peening with a pulse energy of 15 mJ was then applied to fatigue samples of an HT780 butt-welded joint. It was confirmed that laser peening with the microchip laser prolonged the fatigue life of the welded joint samples to the same level as in previous studies with a conventional laser. Full article

The production demand of high-performance polymer composites utilizing natural and renewable resources, especially agricultural waste fibres, is rapidly growing. However, these polymers’ mechanical properties are strain rate-dependent due to their viscoelastic nature. Particularly, for natural fibre-reinforced polymer composites (NFPCs), the involvement of fillers has caused rather complex failure mechanisms under different strain rates. Moreover, unevenly and micro-sized bagasse-reinforced polymer composites often cause the formation of micro-cracks and voids in composites. Consequently, the rates of crack initiation and propagation of these composites become extremely sensitive. This, in turn, causes low and unpredictable tensile performance at higher tensile crosshead speeds, even within the low strain rate range. In this study, single-walled carbon nanotubes (SWCNTs) were applied to enhance the bagasse-epoxy composites’ strength. The effects of the weightage in the SWCNT loadings on the composites’ tensile properties were subsequently investigated under low strain rates of 0.0005 s⁻¹, 0.005 s⁻¹ and 0.05 s⁻¹. The composites’ failure shifted to a higher distribution (65.7% improvement, from 37.23 to 61.68 MPa, across strain rates) due to the addition of 0.05% SWCNTs, as indicated in a Weibull distribution plot. The high aspect ratio and strong interface adhesion of SWCNTs in and toward the epoxy matrix contributed significantly to the composites’ strengths. However, a further increase in SWCNT content in the tested composites caused early embrittlement due to agglomeration. The toughness and characteristic strength improved significantly as the strain rate increased. A scanning electron microscopic (SEM) analysis revealed that the SWCNTs’ high aspect ratios and large surface areas improved the interface bonding between the filler and matrix. However, higher SWCNT loadings (0.15% and 0.25%) caused a reverse effect in the same properties of these composites under the same strain rate variations, due to agglomeration. Finally, an empirical relationship was developed to describe the strain rate effect of tensile properties containing 0.05% SWCNT-reinforced bagasse-epoxy composites. Full article

In this study, we propose a method for predicting the occurrence of brittle fractures in the beam-to-column joints of steel structures, considering different crack opening modes. We conducted experiments on beam-to-diaphragm joint specimens with varying plastically constrained cracks to reproduce brittle fractures. The experiments’ results demonstrated the effectiveness of the toughness scale model and the Weibull stress approach. In addition, we propose the mixed-mode ratio, which is a quantitative index of the mode difference, and we applied it to the finite element models of the specimens. In this study, we evaluate the validity of the mixed-mode ratio and explore the differences in crack opening modes, as they pertain to the occurrence of brittle fractures. Full article

In a flexoelectric sensing element using bending mode, estimation of the flexoelectric coefficient was investigated using 3-D stress/strain analysis and experiments. The proposed method uses the results (deformation and strain) from the finite element analysis (FEA). The estimated flexoelectric coefficients were compared with those obtained via the conventional method (Euler’s beam theory) under the assumption of the quasi 1-D stress field. The results show that the RMS value and standard deviation of the estimated flexoelectric coefficient for the 3-D stress field case of the sensing element are 31.51 µC/m and 0.24%, respectively. In addition, we found that the flexoelectric coefficient obtained from the results of the 3-D stress analysis is 1.8% smaller than that of the quasi-1-D stress analysis. Therefore, in order to obtain a more reliable flexoelectric coefficient in the sensing element, the results of the 3-D numerical stress analysis should be used for accurate estimation of the flexoelectric coefficient. Full article

Existing reinforced concrete (RC) buildings in Europe have generally been designed without proper consideration of seismic actions and capacity design principles, and thus they tend to be vulnerable to earthquakes. Moreover, since a significant proportion of the aforementioned buildings were developed during the 1950s and 1960s, they are currently close to the end of their service life. Therefore, seismic assessment of existing RC building is a major issue in structural engineering and construction management, and the related seismic analyses should take into account the effect of material ageing and degradation. This paper proposes a practice-oriented procedure for quantifying seismic reliability, taking into account the main effects of carbonation-induced degradation phenomena. It summarizes the main aspects of the most up-to-date models for the seismic degradation of concrete and RC members and shows how nonlinear static (pushover) analyses can be utilized (in lieu of the most time-consuming non-linear time history analyses) in quantifying seismic reliability with respect to the performance levels of relevance in seismic engineering. A relevant case study is finally considered with the aim to showing how some parameters, such as exposure class and cover thickness, affect the resulting seismic reliability of existing RC buildings. Full article

Due to growing demands on newly developed products concerning their weight, sound emission, etc., advanced materials are introduced in the product designs. The modeling of these materials is an important task, and a very promising approach to capture the viscoelastic behavior of a broad class of materials are fractional time derivative operators, since only a small number of parameters is required to fit measurement data. The fractional differential operator in the constitutive equations introduces additional challenges in the solution process of structural models, e.g., beams or plates. Therefore, a highly efficient computational method called Numerical Assembly Technique is proposed in this paper to tackle general beam vibration problems governed by the Timoshenko beam theory and the fractional Zener material model. A general framework is presented, which allows for the modeling of multi-span beams with general linear supports, rigid attachments, and arbitrarily distributed force and moment loading. The efficiency and accuracy of the method is shown in comparison to the Finite Element Method. Additionally, a validation with experimental results for beam systems made of steel and polyvinyl chloride is presented, to illustrate the advantages of the proposed method and the material model. Full article

In many applications constant or piecewise constant refractive index profiles are used to study the scattering of plane electromagnetic waves by a spherical object. When the structured media has variable refractive indices, this is more of a challenge. In this paper, we investigate the morphology dependent resonances for the scattering of electromagnetic waves from two concentric spheres when the outer shell has a variable refractive index. The resonance analysis is applied to the general solutions of the radial Debye potential for both transverse magnetic and transverse electric modes. Finally, the analytic conditions to determine the resonance locations for this system are derived in the closed form of both modes. Our numerical results are provided with discussion. Full article

Material-efficient, highly load-bearing members made of high-performance compressive concretes are often exposed to cyclical loads because of their slender construction, which can be relevant to the design. When investigating the fatigue behaviour of high-performance concretes in pressure swell tests, however, the specimen temperature rises strongly owing to the elevated loading rate at frequencies higher than 3 Hz. This leads to a negative influence on the achieved number of load cycles compared to tests carried out at slow speeds and calculated values, for example, according to fib Model Code 2010. This phenomenon, which was already observed, must be considered when generating design formulae or Wöhler lines for component design, as the test conditions with high constant load frequencies as well as sample storage in a climate chamber at constant conditions are prerequisites that cannot be expected in real material applications. Therefore, laboratory testing influences must be eliminated in order to avoid underestimating the material. Instead of adjusting the test conditions to prevent or control temperature development, as was the case in previous approaches, this article shows how the temperature effects can be corrected when analysing the results, considering both the applied stress and the maximum temperature reached. For this purpose, a calculation method was developed that was validated on the basis of a large number of fatigue tests. Thus, in the future, the application of one temperature sensor to the test specimen can effectively advance the extraction of values for Wöhler curves, even with high test frequencies. Full article

Polymer electrolyte coated carbon fibres embedded in polymeric matrix materials represent a multifunctional material with several application scenarios. Structural batteries, thermal management materials as well as stiffness adaptive composites, made from this material, are exposed to significant joule heat, when electrical energy is transferred via the carbon fibres. This leads to a temperature increase of up to 100 K. The thermal behaviour of this composite material is characterized in this numerical study based on a RVE representation for the first time. Compared to classical fibre reinforced plastics, this material comprises a third material phase, the polymer electrolyte coating, covering each individual fibre. This material has not been evaluated for effective thermal conductivity, specific heat and thermal behaviour on the microscale before. Therefore, boundary conditions, motivated from applications, are applied and joule heating by the carbon fibres is included as heat source by an electro-thermal coupling. The resulting temperature field is discussed towards its effect on the mechanical behaviour of the material. Especially the temperature gradient is pronounced in thickness direction, leading to a temperature drop of $1 \frac{{}^{°}\mathrm{C}}{\mathrm{mm}}$, which needs to be included in thermal stress analysis in future thermo-mechanically coupled models. Another important emphasis is the identification of suitable homogenization and model reduction strategies in order to reduce the numerical effort spent on the thermal problem. Therefore, traditional analytical homogenization methods as well as a newly proposed “Two-Level Lewis-Nielsen” approach are discussed in comparison to virtually measured effective quantities. This extensive comparison of analytical and numerical methods is original compared to earlier works dealing with PeCCF composites. In addition, the accuracy of the new Two-Level Lewis-Nielsen method is found to fit best compared to classical methods. Finally, a first efficient and accurate 2D representation of the thermal behaviour of the PeCCF composite is shown, which reduces computational cost by up to 97%. This benefit comes with a different Temperature drop prediction in thickness direction of $1.5 \frac{{}^{°}\mathrm{C}}{\mathrm{mm}}$. In the context of future modelling of multifunctional PeCCF composite materials with multiphysical couplings, this deviation is acceptable with respect to the huge benefit for computational cost. Full article

A series of experiments were carried out for developing a paint coating removal method for high-strength bolted joints in steel bridges. The paint-coated bolted joint specimens were heated to the target temperature of 200 °C by using a sheet-type ceramic heater. The maximum temperature of specimens could be controlled within 10% of the target value. The paint coating was easily removed by using general tools after heating. The behaviour of bolts with thermal expansion and shrinkage was monitored by strain gauges attached to the bolts during heating. It was estimated that the axial forces of the bolts were reduced by 2.6% of the initially installed axial forces, on average. Full article

A heat treatment is effective for reducing the residual stress of the welded structures. A post-weld heat treatment (PWHT) requires a large heating apparatus (furnace). It requires a high energy, a long time, and a high cost. For examining the possibility of cost and energy saving in PWHT work, an economical and mechanical investigation of the local PWHT to stiffened plate members in steel bridges was conducted. The expense of apparatus for the furnace PWHT was 1.5 times higher than that of local PWHT by sheet-type ceramic heaters. When the number of heater units was reduced and were repeatedly used, the expense for the apparatus became lower. However, it took longer to complete the heat treatment than with the furnace PWHT or the local PWHT with full heater units. The thermal elastic-plastic finite element (FE) analysis examined the effect of local PWHT. The tendency of the stress distribution after the local PWHT differed from the welding residual stress or the stress after the furnace PWHT because of the temperature difference between the heated and the non-heated parts of the local PWHT. However, the effect of residual stress relief by the local PWHT could be almost the same as that of the furnace PWHT. Full article

In this study, an innovative composite was fabricated in which the matrix is partially derived from natural sources and the filler from undervalued eggshell waste material. The effect of coating eggshells and mineral limestone with 2 wt.% stearic acid on the mechanical properties of a bio-epoxy matrix was investigated. Eggshells and limestone (untreated and stearic acid-treated) fillers were added to the bio-epoxy matrix in quantities of 5, 10, and 20 wt.% loadings using a solution mixing technique. The CaCO₃ content in eggshells was confirmed to be 88 wt.%, and the crystalline phase was found to be calcite. The stearic acid coating did not show any decrease in crystallinity of the fillers. Scanning electron microscopy (SEM) displayed changes in the fractured surfaces, which infers the fillers altered the bio-epoxy polymer. The mechanical property results showed enhancements in the composite tensile modulus and flexural modulus compared to the pure bio-epoxy, as expected. In contrast, despite the improvement in the tensile and flexural strengths of the stearic acid-treated fillers, the composite strength values were not higher than those of the unfilled bio-epoxy matrix. The energy absorbed by all composites in Charpy impact tests fell below that of the pure bio-epoxy and decreased with an increase in filler content for both untreated and stearic acid-treated fillers tested at 23 and −40 °C. Statistical analysis of the results was conducted using Statistical Analysis Software (SAS) with ranking based on Tukey’s method. The study identified that the addition of 5, 10, and 20 wt.% in a bio-epoxy matrix may be acceptable provided the end product requires lower tensile and flexural load requirements than those of the pure bio-epoxy. However, filler loadings below 5 wt.% would be a better choice. Full article

This paper deals with the modal analysis of optimized trapezoidal stiffened plates with simple supported conditions on the four edges of the base plate. The main objective of the finite element analysis is to investigate the natural frequencies and mode shapes of some stiffened structures subjected to lateral pressure and uniaxial compression in order to identify any potentially dangerous frequencies and eliminate the failure possibilities. The natural frequencies and mode shapes are important parameters in the design of stiffened plates for dynamic loading conditions. In this study, the numerical analysis is performed for such a design of this kind of welded plates which have already been optimized for lateral pressure and uniaxial compression. The objective function of the optimization to be minimized performed with the Excel Solver program is the cost function which contains material and fabrication costs for Gas Metal Arc Welding (GMAW) welding technology. In this study, the eigenvalue extraction used to calculate the natural frequencies and mode shapes is based on the Lanczos iteration methods using the Abaqus software. The structure is made of two grades of steel, which are described with different yield stress while all other material properties of the steels in the isotropic elastic model remain the same. Drawing the conclusion from finite element analysis, this circumstance greatly affects the result. Full article

The load-bearing capacity of a CC(T) specimen (Center-Cracked Tension) in the ductile fracture regime is usually controlled by plastic collapse. If the material’s tearing resistance is sufficiently low, the load-bearing capacity can drop below the plastic collapse value. Here, a recently developed simple fracture mechanics-based Charpy-V impact energy criterion for plastic collapse was used to provide a best estimate assessment of the CC(T) specimen load-bearing capacity. Full article