Rigorous Finite Element Research Articles

Chip warpage and stress analysis in power modules of different substrate configurations

Purpose This paper aims to use rigorous finite element simulations to investigate the impact of different substrate systems on the warpage behavior of silicon (Si) chips of power modules exposed to thermal loading. Design/methodology/approach Three common substrate systems: direct copper bonded (DCB), insulated metal substrate (IMS) and printed circuit board (PCB) configurations examined. In addition, three lead-free bonding materials: silver-tin transient liquid phase (TLP), sintered silver (Ag) and sintered copper (Cu). This results in nine assembly configurations. Finite element models of the electronic modules are developed using ANSYS to apply thermal loads from room temperature to 250°C to induce deformations, strains and stresses in the electronic structure. Accordingly, the silicon chip deformations and maximum principal stresses of each assembly configuration are thoroughly examined. Findings The results indicate that DCB-based power modules markedly reduce Si die warpage and maximum principal stresses, suggesting enhanced resistance to thermal loads. In contrast, IMS systems exhibit the highest levels of die warpage and out-of-plane deformation. PCB substrates, however, induce the highest maximum principal stress values in the silicon die, potentially leading to accelerated crack initiation and propagation. While the die attach system has a minimal effect on die warpage, the silver-tin TLP bonds generate significantly higher die stresses compared with sintered Ag and sintered Cu, which both result in reduced stresses. Originality/value Power electronics exceptionally rely on ceramic-based and polymer-based substrate systems due to their superior thermal conductivity, heat resistance and electrical insulation properties. The strategic selection of substrate structures can significantly enhance the robustness of power. Ultimately, the findings of this research provide valuable insights for the design of highly reliable and efficient power modules subjected to thermal stress.

Integrating product design principles to design a smart assistive cane

This paper presents the design of a smart assistive cane using the principles of product design and quality assurance. The smart cane is aimed at improving the safety and independence of individuals with walking difficulties. The proposed cane incorporates advanced features such as GPS navigation, fall detection, adjustable height, and integrated storage. A comprehensive design process was employed, including a thorough analysis of user needs through a Kano analysis, followed by the selection of appropriate materials and manufacturing methods. The cane's structural integrity and functionality were assessed through rigorous testing and finite element analysis. This research contributes to the development of assistive technologies that can incorporate user’s necessities and builds quality into the product with the design process, significantly enhancing the quality of life for individuals with mobility challenges. It serves as a potential demonstration to designers and researchers to incorporate product design, optimization, and quality assurance principles in design of similar assistive technologies and products.

Development and Characterization of a Flexible Soundproofing Metapanel for Noise Reduction

This study addresses the critical challenge of developing lightweight, flexible soundproofing materials for contemporary applications by introducing an innovative Flexible Soundproofing Metapanel (FSM). The FSM represents a significant advancement in acoustic metamaterial design, engineered to attenuate noise within the 2000–5000 Hz range—a frequency band associated with significant human auditory discomfort. The FSM’s novel structure, comprising a box-shaped frame and vibrating membrane, was optimized through rigorous finite element analysis and subsequently validated via comprehensive open field tests for enclosure-type soundproofing. Our results demonstrate that the FSM, featuring an optimized configuration of urethane rubber (Young’s modulus 6.5 MPa) and precisely tuned unit cell dimensions, significantly outperforms conventional mass-law-based materials in sound insulation efficacy across target frequencies. The FSM exhibited superior soundproofing performance across a broad spectrum of frequency bands, with particularly remarkable results in the crucial 2000–5000 Hz range. Its inherent flexibility enables applications to diverse surface geometries, substantially enhancing its practical utility. This research contributes substantially to the rapidly evolving field of acoustic metamaterials, offering a promising solution for noise control in applications where weight and spatial constraints are critical factors.

3D-printed topological-structured electrodes with exceptional mechanical properties for high-performance flexible Li-ion batteries

A vital aspect in advancing flexible batteries is the development of flexible electrodes capable of enduring repeated stretching while upholding satisfactory electrochemical performance. Thus, adopting a systematic and efficient approach to structural design and fabrication becomes imperative. In this study, we introduce an optimal structural design achieved through topology optimization and fabricate flexible electrodes via 3D printing, representing a departure from traditional design and manufacture methodologies in the development of flexible electrodes for batteries. Our research underscores the impressive mechanical strength of these topologically-structured electrodes (TSEs), validated through rigorous finite element analysis (FEA) and tensile strength testing. The results of both the stretch deformation and twist deformation analysis on the TSEs and the conventional mesh-structured electrodes (MSEs) show that the peak strain and stress of TSEs are much lower than those of MSEs. Notably, even under 50 % stretching, the TSEs maintain structural integrity, contrasting sharply with conventional mesh-structured electrodes (MSEs) and flat film electrodes which often crack under similar conditions. Moreover, after enduring 50 cycles of stretching, the TSEs retain an outstanding 98 % of their original capacity, surpassing MSEs which retain only 80 % of their capacity. These findings highlight the significant potential of topologically designed flexible electrodes, offering promising avenues for the development of stretchable and flexible energy storage devices such as wearable tech and bio-integrated electronics.

Broadband ultrasonic transducer based on nested composite structure with gradient acoustic impedance

This study introduces an innovative Broadband Ultrasonic Transducer employing a Nested Composite Structure with Gradient Acoustic Impedance, significantly enhancing the performance in medical diagnostics and non-destructive testing. The developed transducer, based on a unique nested PZT/epoxy composite design, achieves an optimized acoustic impedance gradient from 36.56 MRayls to 4.53 MRayls. This strategic design effectively addresses the impedance mismatch, a long-standing challenge in ultrasonic imaging. Rigorous Finite Element Analysis (FEA) using PZFlex software indicates that the transducer offers a −6 dB bandwidth of 69.31%, a substantial improvement over the existing models. Experimental results corroborate with theoretical predictions, demonstrating enhanced bandwidth (∼71.24%) and transmission efficiency. This advancement highlights the potential of gradient impedance in fabricating high-performance ultrasonic transducers, setting a new benchmark for ultrasonic imaging applications.

Numerical and theoretical analysis on soil arching effect of prefabricated piles as deep foundation pit supports

This study presents a detailed investigation into the soil arching effects within deep foundation pits (DFPs), focusing on their mechanical behavior and implications for structural design. Through rigorous 3D finite element modeling and parameter sensitivity analyses, the research explores the formation, geometric characteristics, and spatial distribution of soil arching phenomena. The investigation encompasses the influence of key parameters such as elastic modulus, cohesion, and internal friction angle on the soil arching effect. The findings reveal that soil arching within DFPs exhibits distinct spatial characteristics, with the prominent arch axis shifting as excavation depth progresses. Optimal soil arching is observed when the pile spacing approximates three times the pile diameter, enhancing soil retention and minimizing deformation risks. Sensitivity analyses highlight the significant impact of soil parameters on soil arching behavior, underscoring the critical role of cohesive forces and internal friction angles in shaping arching characteristics. By elucidating the interplay between soil parameters and soil arching effects, the research provides insights for optimizing pile spacing and structural stability.

Effect of Strain Gradient on Elastic and Plastic Size Dependency in Polycrystalline Copper

This study unveils the presence of size effect not only in the plastic regime but also in the elastic regime under strain gradient. This discovery emerges from a comprehensive set of experiments encompassing micro-cantilever bending and micro-pillar compression tests. Subsequent finite element analysis serves to not only expose the limitation of classical continuum theory but also to effectively demonstrate the enhanced predictive capabilities of couple stress theory in both elastic and plastic size effects. To incorporate couple stress theory, a systematic and rigorous finite element analysis-based optimization was devised to determine length scale parameters, which are additional material properties in couple stress theory. The resulting length scale parameters for polycrystalline copper were found to be 0.536 and 0.669µm in the elastic and plastic regimes, respectively. The study also explores the physical interpretation of these length scale parameters in both regimes.

Mechanical behavior of large-diameter pipe elbows under low-cyclic loading

Large-diameter steel pipes are often used for transmitting and distributing water, gas, and oil products from the source to the end user. These pipelines are mainly oriented by using pipe el- bows due to their high flexibility along their routes. It is important to understand the mechani- cal behavior of these critical infrastructure components to promote material sustainability. For this purpose, a rigorous 3D finite element model is employed to investigate the mechanical behavior of large-diameter pipe elbows with varying elbow angles such as 90°, 60°, and 30°. Moreover, geometrical and material nonlinearities capture the pipes’ ratcheting behavior even under pressurized and unpressurized scenarios. It is seen that the pipes with a larger elbow angle can endure a higher number of cycles before they reach their limit states. In addition, pipe elbows behave similarly to straight pipes as the elbow angle decreases and becomes more vulnerable to plastic deformations such as kink and buckling under bending loads.

Dual-polarization strong nonreciprocal thermal radiation under near-normal incidence

Performance of irreversible radiation is limited by the single polarization and large incident angles. Given potential applications of nonreciprocal thermal radiation, the implementation of irreversible radiation for both TE and TM polarizations at small angles is highly demanded. A solution that combines periodic silicon-based nanopore arrays with magneto-optical material (InAs) is proposed in this work. The results show that the absorptivity and emissivity of two polarizations are close to 98% with an incident angle of 1.5° and a high Q factor over 1680. By adjusting the applied magnetic field, the emissivity and transverse magneto-optical Kerr effect can be dynamically tuned. The validity of the calculation results is verified by the rigorous coupled-wave analysis and finite element method. Impedance matching theory and coupled mode theory are adopted to further analyze the physical origin. The proposed scheme and thermal radiator that allow nonreciprocal thermal radiation for both TE and TM polarizations at an extremely small incident angle offer valuable guidance to the development of dual-polarization nonreciprocal radiation devices.

Reconfigurable Polarized Photodetector with Centrosymmetric Silicon Enabled by Flexoelectric Effect for Encrypted Communication

AbstractIn the rapidly evolving digital landscape, secure communication is crucial, and polarization‐sensitive photodetectors offer a promising approach to enhance security and efficiency. However, conventional devices face limitations in encoding capacity due to material‐specific anisotropic properties and geometric factors. In this study, the critical role of the flexoelectric effect in detecting polarized light in silicon and its effective utilization in secure communication systems are demonstrated. The device shows self‐biased photoresponse, which is modulated by up to 320% with the application of force by a sharp probe, a phenomenon attributed to the flexoelectric effect. The polarization sensing behavior is confirmed through comprehensive scanning photocurrent mapping, which is further supported by rigorous finite element simulations. As a potential application, the device is implemented to sense Morse code and effectively modulate it using the flexoelectric effect and light polarization angle, offering more sophisticated encryption methods for secure communication. This research provides valuable insights for advancing secure communication technologies and overcoming the inherent challenges associated with silicon‐based photodetectors.

Kinematic bending of piles in made ground

This work explores earthquake-induced kinematic bending in the so far unresolved case of a pile embedded in a two-layer soil with a thin surface layer. The problem is treated analytically by means of a generalised Winkler model, which in addition considers the effect of boundary conditions at the pile head over earlier contributions on the subject. Novel analytical closed-form expressions of the kinematic bending moment at the pile head and at the interface between the two soil layers are provided for both fixed- and free-head piles. The analytical solutions are validated through a rigorous finite-element model, which proves a remarkable accuracy in the static regime. While for interface bending the past literature indications for the dynamic coefficient make the proposed formula accurate for both shallow and deep interface, a novel dynamic interaction factor, describing dynamic effects for pile-head bending, is introduced. A numerical example provides guidance on application of the formulae in real design scenarios.

Radial distribution of pump and signal intensities in step index EDFA for LP11 mode in Kerr nonlinear condition

Abstract In an all-optical communication system, an erbium-doped fiber amplifier performs a very significant role. The effectiveness of the operation of this kind of amplifier depends on different parameters of the amplifier. Variation of the intensities of pump and signal with distance along the radius of the fiber from the core axis is one such significant parameter. In our present case, we have studied the distribution of the intensities of both the pump and signal along the radius of the fiber in an erbium-doped dual-mode fiber amplifier for the LP11 mode. In the present case, some step-index fibers of different normalized frequencies have opted. Our study is an application of the Chebyshev technique expressing the LP11 modal field in the form of a power series. A little computation is required for the prediction of the concerned results by this technique. Results obtained from this study show an excellent match with those found by the rigorous finite element method establishing its accuracy. This study using such a user-friendly and accurate technique will be helpful to the optical engineers involved in this domain.

The chamfered bend two, four and eight-way SIW power dividers analysis for millimeter wave applications using the quick finite element method

In this paper, we propose three kinds of substrate-integrated waveguide (SIWs) based chamfered bend power divider junctions provide equal power distribution to all output ports while maintaining high isolation and operating in the 54 GHz to 60 GHz frequency band. The advantages of the SIW technology are ease of design, fabrication and low form and full integration with planar printed circuits. In this case, the concept of the SIW H-plane power divider is implemented using a rigorous two-dimensional quick finite element method (2D-QFEM) programmed by MATLAB software. The numerical performance of this method is the Quick simulation time for using the mesh with Delaunay regularization in two dimensions, if we increase the mesh the FEM gives better results. This paper presents the transmission coefficient, return loss and the electric field distribution. The results obtained from QFEM were compared with those provided by HFSS for validation. When using the discretization with the Delaunay procedure only in two dimensions, we notice that the calculated simulation time decreases with good precision.

A fictitious pile method for interaction factor of two laterally loaded piles in multilayered isotropic soils

An efficient fictitious pile method based on elasticity theory is presented for the analysis of interaction factor of two laterally loaded piles embedded in non-homogeneous soils. The problem is decomposed into two systems, namely the two fictitious piles acted upon by (partial) external loading, and an extended multilayered soil continuum acted upon by a system of pile-soil interaction forces at imaginary positions of the piles. The behavior/responses of the multilayered isotropic soils are analyzed through a computationally effective transfer matrix solution procedure. A Fredholm integral equation of the second kind is then deduced for the load-deformation relationship of a two-pile group system, by considering the equilibrium of the pile-soil interaction forces and the displacement compatibility between the fictitious pile and the extended soil. Comparison of the results calculated by the present fictitious pile method for displacement interaction factor between two piles embedded in multilayered isotropic soils has shown good agreement with the previous ones obtained by using the more rigorous finite element approach. The parametric numerical study demonstrates that the soft-over-stiff-over-soft soil layers have a profound effect on the pile-to-pile displacement interaction factor for the case of moment loading, which should be carefully considered in the practical design.

Radial Differentiation of Pump and Signal Intensities in Trapezoidal index EDFA for LP11 mode in Kerr nonlinear state

An Erbium-Doped Fiber Amplifier (EDFA) is an in-line component in modern all –optical telecommunication infrastructure. Different parametric characteristics of an EDFA express the suitability and excellency of performance in its real field application. Intensities of pump and signal vary with distance from the core-axis along the radius of the fiber which is one of the significant characteristics of an EDFA. Change of behavior of pump and signal intensities along the radius of the fiber in an erbium-doped dual-mode trapezoidal index fiber made amplifier due to Kerr nonlinearity phenomenon originating from launching and transmission of intense light from LASER beam inside the amplifier for the LP_11 mode has been exercised in this case. In the present case, some trapezoidal-index fibers of different normalised frequencies have been opted. This exercise is an implementation of the reliable and easy mathematical instrument, the Chebyshev technique. Results derived in this exercise exhibit a fantastic similarity with those derived by the rigorous finite element method. This study with implementation of such a reliable and easy technique may help the interested optical engineers.

Unidirectional invisibility in a PT-symmetric structure designed by topology optimization.

This study designs a piecewise homogeneous dielectric structure with parity-time (PT) symmetry that realizes the unidirectional invisibility of a perfect electric conductor in two dimensions. We apply topology optimization and design a PT-symmetric material that minimizes the total scattering cross section for a given plane wave to achieve unidirectional invisibility. A rigorous mode-matching finite element method is used to perform all computations. The designed PT-symmetric structure suppressed plane-wave scattering by approximately 99% for the given incident direction, whereas the reversed incident wave experienced 83 times larger scattering intensity. The proposed method provides a novel approach, to the best of our knowledge, to promote various applications of PT symmetry.

Heat and Temperature Localization via Fabry–Pérot Resonances at the Tip of a Nanofocusing Cone

AbstractNanofocusing of electromagnetic (EM) energy is an emblematic effect that guides EM energy along plasmonic conical structures, effectively focusing it at its nanometer‐sized extremity. However, EM energy nanofocusing could also be accompanied by (often disregarded) heating. Here, rigorous 3D finite element method simulations of a plasmonic conical structure were performed with a finite‐size apex excited by a continuous wave radially polarized beam over visible and near‐infrared wavelengths. Together with broadband nanofocusing the presence of narrowband Fabry–Pérot (FP) like resonances is demonstrated. Importantly, FP‐like resonances yield strong temperature localization that adds to the broadband nanofocusing component, providing an extra degree of freedom in tuning the temperature localization through proper selection of the structure dimensions suitable for applications in Raman, electron emission spectroscopies or sharp‐tip nanofabrication strategies.

An accurate but simple method for estimation of the influence of kerr nonlinearity on the far field pattern of LP11 mode in dispersion-shifted and dispersion-flattened fibers

Abstract In this paper, we have presented the far field pattern in presence and absence of Kerr type nonlinearity for the first higher order mode in Dispersion shifted and dispersion flattened type optical fibers. Our analytical results are based on simple power series expressions for the first higher order (LP11) mode of aforesaid fibers, which have been formulated by Chebyshev formalism. Using the analytical expressions for the linear case, method of iteration is applied in order to predict the concerned propagation parameters in presence of Kerr type nonlinearity. We have taken some typical trapezoidal index, step W and Parabolic W fibers for our study. Our results for the far field pattern have been shown to be in excellent agreement with the exact numerical results computed by rigorous finite element technique. The simplicity and accuracy of our formalism will prove helpful to the designers for setting up of efficient low dispersion optical link.

Novel design of inter-module joint in reinforced concrete modular construction using high-strength fiber-reinforced cementitious composites (HSFRCC)

The development of modular construction is surging in recent years. It has been popularized worldwide due to better quality control, environmental-friendliness and potential construction time and cost savings. A specific challenge associated with reinforced concrete modular construction is the design of inter-module joint. Minimizing the size of in-situ cast joint between prefabricated units is of great importance for improving construction efficiency. In addition, reinforcement details should be as simple as possible to enhance constructability. This study proposes a novel connection design for wall-to-wall inter-module joint using high-strength fiber-reinforced cementitious composites (HSFRCC) and steel plate-induced confining stresses. Small-scale direct tension pull-out tests were performed with specially designed loading fixtures to simulate the bond behavior between HSFRCC and high-yield steel bars in the proposed joint design. The effects of joint material properties, embedment length and confinement conditions were evaluated. Results showed that the combined use of HSFRCC with plate confinement greatly improves bond capacity. The preferred rebar yielding failure (rather than bond failure) was achieved with embedment length of only 8d (d being the bar diameter). A rigorous finite element model was established by incorporating explicit geometry of rebar and mechanical properties of joint material, and the numerical results showed good agreement with test observations. Therefore, the applicability of the FE analysis in facilitating the proposed inter-module joint is demonstrated.

Guided-Mode-Resonance Reflectors for Performance Enhancement of Sapphire Based Fabry-Perot Sensors in Harsh Environment

This paper presents a guided-mode resonance (GMR) reflector for sapphire based Fabry-Perot (F-P) sensors that enables tunable or wideband high reflectance with high temperature resistance,which is expected to effectively regulate the performance of F-P sensors and offer a novel approach for designing F-P sensors in harsh environments. Intrinsic and extrinsic GMR gratings are proposed, and their optical and thermal properties are investigated and compared through numerical simulations, such as rigorous coupled-wave analysis and finite element analysis methods. The quantitative results indicate high feasibility for harsh environment applications and the potential for adopting different demodulation methods. Significant enhancement in the F-P sensor performance is obtained through analysis based on the F-P interference model, and the spectrum fineness and sensor sensitivity can be enhanced by at least one order of magnitude. The GMR reflector can be extended to other types of F-P sensors, demonstrating significant potential in high-temperature applications.