Finite Element Method Model Research Articles

Experimental Assessment of Force Redistribution in Elements of Damaged Bridge Model under Temporary Load from Rolling Stock

The relevance of the work lies in the fact that properties of damaged structures were sufficiently studied. Therefore, there is a high risk of their unpredictable behavior, which can lead to malfunctions, including serious accidents and man-made disasters. The risk of such danger increases significantly in the extreme climate of Siberia and the North. Damage and destruction of structures are confirmed by many facts.Purpose: The aim of the work is to experimentally simulate the bridge bearing capacity after damage in order to understand how the bridge behaves in various conditions and what measures can be taken to restore it.Methodology: The finite element method and experimental modeling in the PASCO digital laboratory were used to determine forces in the truss rods.Research findings: The redistribution of forces in the rods of the superstructure was detected when some of its elements are out of operation, and critical destruction is identified.

Evaluating the thermal stability of an interior permanent magnet synchronous machine through iterative multi‐physics simulation

AbstractThis paper investigates the thermal operating capability of an interior permanent magnet synchronous machine. An iterative workflow is presented, combining electromagnetic modeling, control, power‐loss modeling, and thermal modeling to identify maximum thermal stable operating points. Special attention is given to the critical temperatures of winding and permanent magnets. A nonlinear reduced order model based on finite element method model was used to simulate the system, including an inverter model with space vector pulse width modulation in combination with field‐oriented control. Furthermore, an advanced iron core loss model and thermal lumped parameter model were employed. The presented approach allows for evaluating losses and their impact on steady‐state temperatures. The obtained results highlight the significant influence of space vector pulse width modulation on iron core losses and the importance of considering both advanced power‐loss models and adequate thermal models when analyzing the machine's thermal state. This research emphasizes the concept of a thermally stable envelope, providing a comprehensive understanding of the thermal boundaries under various operating conditions.

Texture Evolution of High-purity Tantalum during 90°Clock Rolling

Abstract When fabricating high-purity tantalum targets for the sputtering procedure of integrated circuit manufacturing, a through-thickness texture gradient can form in the rolled tantalum (Ta) plate. This texture gradient hinders the target sputtering performance, reducing chip reliability. This study investigated the texture evolution during the 90°clock rolling through experimental and simulation methods. Balancing the plane strain deformation with the surface shear strain deformation during fabrication and limiting the total rolling reduction to no more than 85% can weaken the through-thickness texture gradient in the Ta plate. A crystal plasticity finite element method (CPFEM) model was developed to simulate the 90°clock rolling procedure in the ABAQUS/Explicit software. The simulation and the experimental results are in agreement, with slight differences in texture type and intensity due to tantalum’s complex slip behaviors.

A New Method for Temperature Dependent COM Parameters Extraction and Its Application to Simulation of SAW Devices

Abstract Surface Acoustic Wave (SAW) filters are widely used in mobile communication systems due to their superior performance. Yet, application scenarios for these SAW devices can be limited by temperature stability. The coupling of modes (COM) model is proved to be an efficient modeling approach to design SAW devices at present. However, temperature dependent COM parameter extraction is still absent. This work proposed a new method combining COM model with quasi-3D periodic finite element method (FEM) model coupled with thermal field, which can accurately and rapidly simulate and optimize the temperature stability of SAW devices. The COM parameters extraction method used in this study mainly depends on harmonic admittance. For a given temperature (T), the thermal effect can be computed by incorporating the linear thermal expansion coefficients and temperature coefficients of elasticity into the model. For validation, the admittance responses of a finite-length SAW resonator and the S-parameter of a double-mode SAW (DMS) for 42º YX-LiTaO3 piezoelectric substrate are calculated by using P-Matrix with the extracted COM parameters. For validation, the admittance responses of a SAW resonator on 42º YX-LiTaO3 under different temperature conditions is calculated. Furthermore, the temperature behaviors of a DMS filter on 42º YX-LiTaO3 are also analyzed based on the proposed method. Accurate predictions of the temperature behaviors for both resonator and filter were achieved and discussed. This investigation provides guidelines for design of high-performance SAW devices with good temperature stability.

Meso-crack propagation of RC induced by non-uniform rebar corrosion and the predictive model of time to concrete cover cracking

Non-uniform corrosion expansion in reinforced concrete (RC) structures will lead to concrete cracking, bond degradation, and an overall reduction in load-bearing capacity, severely threatening structural safety and durability. Accordingly, meso-crack propagation of RC induced by non-uniform rebar corrosion and the predictive model of time to concrete cover cracking are investigated in this paper, and the theoretical solutions for the critical corrosion rate and the corresponding time are proposed for structural durability evaluation and design. Firstly, based on the mesh-mapping technique of multi-shape random aggregates, a finite-element generation method for three-dimensional concrete three-phase meso-scale model is proposed, with modeling corrosion-expanded cracking of RC, reproducing the crack morphology and propagation process of concrete cracking due to non-uniform rebar corrosion. Subsequently, single factor influence analysis and multi-factor orthogonal test were employed to reveal the degrees of influence of various factors on the critical corrosion rate as follows: concrete strength > cover thickness > interface layer strength > aggregate content > aggregate grading > aggregate shape. A theoretical predictive model for the corrosion expansion cracking time of the RC cover was proposed, considering the influence of key factors including concrete strength and cover thickness. Finally, the validity of theoretical prediction method and the numerical model’s damage mode are verified through accelerated corrosion tests of RC.

Response prediction and damage assessment of CFST column after explosion via ANN

Concrete-filled steel tubes (CFSTs) have been extensively employed in pressurized structural members, such as high-rise buildings, large-span bridges or offshore structures. Accurately and reliably assessing the damage of CFST column subjected to explosion is helpful for designers to optimize the structural performance and construction cost. Currently, peak displacement, the damage indicator, is generally estimated via finite element method (FEM) and single degree of freedom (SDOF) oscillator model. However, the computational overhead of FEM is high, while the computational accuracy of SDOF model is low. In this paper, artificial neural network (ANN) is used to overcome the above drawbacks. A dataset of 270 experiments and numerical simulations is collected from existing literatures to develop the ANN model. The performance of this model is compared with the conventional methods, i.e., FEM and SDOF model. And its prediction accuracy and efficiency are better in the comparison by experimental results. The damage evaluation and parameter research are carried out to reveal insight into the factors on the CFST column under explosion, including the property of column and its cross-section properties, the axial compression condition, and the explosive. To support the explosion resistance design of a CFST column, an explicit equation and an excel calculation table are introduced based on the ANN model.

Thermal transfer characteristics and thermoelasticity analysis of direct-steam-generation parabolic trough collector

Parabolic trough solar direct-steam-generation technology integrates clean energy with green carriers and is one of the favorable low-carbon technologies. However, the non-uniform heat flow distribution and flow stratification of collectors are susceptible to variations in climatic conditions, causing dry spots and raising the failure risk, and there are fewer studies on their influence laws based on three-dimensional two-fluid modeling. Therefore, the three-dimensional optical-thermal-stress-hydrodynamic model of the collector is built in this work based on Monte Carlo Ray Tracing method, finite volume method, finite element method and Eulerian two-fluid modeling method, and the model validation results agree with the experimental results. The impacts of direct solar radiation (I) and inlet pressures (Pin) on heat transfer performance and thermoelasticity characteristics of the three flow stages are analyzed. The results revealed that heat transfer performance in two-phase flow is better than single-phase flow at the same working conditions. The elevation of I effectively improves the Nusselt number and collector efficiency, but also dramatically raises the circumferential temperature difference (CTD) and thermal stresses. Especially, the CTD, maximum deformation, and maximum equivalent stresses in the superheated stage are as high as 54.37 K, 32.82 mm, and 38.23 MPa at Pin = 3 MPa and I = 1000 W m−2, similarly the maximum equivalent stress is also as high as 32.96 MPa in the stratified flow. The results serve as a reminder to pay particular attention to the superheated stage and the laminar flow, particularly at low Pin and high I. Furthermore, the lower the Pin, the higher the deformation and equivalent stresses in the stratified flow phase and the higher the risk of induced failure. Therefore, this implies that higher operating pressures are more appropriate for stratified flow, but this may be limited by high heat loss and low collector efficiency.

Investigating the Behaviour of Railway Track Ground Vibrations for Different Track Foundation Conditions Using FEM

High-speed trains are a useful friendly option for ground transportation. Railway-induced ground vibrations can have a severe impact on human health and the communities that surround rail lines. Current research is showing the problem and its solution as technology is advancing steadily, still, there are some misunderstandings. This is because the propagation of railway vibration in urban areas is complex. So, this work focuses on reducing vibration by enhancing the ballast, and sub-ballast qualities of the railway track through the use of insulation technologies. The Finite Element Method (FEM) model offers insight into how vibrations propagate over a railway track’s foundation. The FEM model can be used to forecast the frequency of vibrations. The Plaxis 3D model’s results show a reduction in vibration propagation. Sylomer is used as a damping material to absorb the vibration and block the propagation path. The application of damping material changes the track-bed system’s dynamic response, effectively decreasing vibration transmission to the surrounding soil. Stress on the surrounding soil and structure foundation is reduced by the process of vibration mitigation. Establishing a benchmark reference for soil parameters is crucial for the accurate analysis and prediction of ground behavior. By creating a detailed and standardized set of soil data, engineers and planners can better understand the characteristics and capabilities of the ground on which they intend to build.

Experimental and numerical investigation on failure behaviour of aluminum-polymer friction stir composite joints

Friction stir composite joints between an aluminum alloy (AA6082-T6) and reinforced polymer (NorylTM GFN2) were studied regarding their failure characteristics. A comprehensive analysis on the mechanical behaviour of the joints was carried out, assessing the resulting deformed shape, the associated strain field and the observed failure modes using a digital image correlation (DIC) system and comparing with a finite elements method (FEM) model. The numerical model evidenced a good fitness to the experimental results since both the displacements and strain fields were found to be very similar. Both numerical and experimental strain fields in the longitudinal direction exhibited a localized spot of highly strained material, clearly indicating the nucleation site. Since secondary bending occurs in structural elements under tension due to geometrical and stiffness asymmetries, as is the case of overlap composite joints, a bending stress is induced, increasing the local stress compared to the nominal tension stress values. The ultimate tensile stress of the joints was found to range between 60.2 and 70.4 MPa, leading to an average joint efficiency of 82.6 %. The bending factor (kb) at the failure region was found to be 2.0, which means that the bending stress accounts for 2/3 of the total stress, acting as main failure catalyst.

Topology optimization of adaptive sandwich plates with magnetorheological core layer for improved vibration attenuation.

In this study the optimum topology distribution of the magnetorheological elastomer (MRE) layer in an adaptive sandwich plate is investigated. The adaptive sandwich plate consists of an MR elastomer layer embedded between two thin elastic plates. A finite element model has been first formulated to derive the governing equations of motion. A design optimization methodology incorporating the developed finite element model has been subsequently developed to identify the optimum topology treatment of the MR layer to enhance the vibration control in wide-band frequency range. For this purpose, the dynamic compliance and density of each element are defined as the objective function and design variables in the optimization problem, respectively. The method of the solid isotropic material with penalization (SIMP), is extended for material properties interpolation leading to a new MRE-based penalization (MREP) model. Method of moving asymptotes (MMA) has been subsequently utilized to solve the optimization problem. The developed finite element model and design optimization method are first validated using benchmark problems. The proposed design optimization methodology is then effectively utilized to investigate the optimal topologies of the magnetorheological elastomer (MRE) core layer in MRE-based sandwich plates under various boundary and loading conditions. Results show the effectiveness of the proposed design optimization methodology for topology optimization of MRE-based sandwich panels to mitigate the vibration in wide range of frequencies.

A numerical model for assessing the effect of low clay content on wave-induced seabed liquefaction

In the marine environment, the seabed contains a certain amount of clay. Experimental studies show that the liquefaction susceptibility of the sandy seabed increases as clay content (CC) rises to a certain threshold, beyond which further increases in CC reduce liquefaction susceptibility. However, numerical models that describe the effect of CC on seabed liquefaction are very limited. This study proposed a dynamic poro-elasto-plastic finite element method model for analyzing liquefaction in the sandy seabed with CC below the threshold. Based on a series of undrained triaxial compression tests on sand-clay mixtures from existing literature, a unified constitutive framework was demonstrated to be effective for describing the liquefaction behavior of sand with low CC using one set of model parameters. Existing wave flume model tests validated the effectiveness of the proposed seabed model in describing the effect of low CC on excess pore water pressure (EPWP). Numerical results confirmed that adding a small amount of clay to the seabed increased the soil contraction and thus its liquefaction susceptibility. Wave-induced liquefaction was limited to a certain depth of the seabed, and the liquefaction depth was significantly affected by the CC. Adding a low content of clay the sandy seabed significantly increased both horizontal and vertical displacements under wave action, potentially leading to the instability of the seabed. This study provides a new method for accurately assessing the wave-induced stability of marine structures built on the sandy seabed containing certain amounts of clay.

Analyzing the effect of infill density on the mechanical compression of ASA in additive manufacturing: a FEM perspective

Additive manufacturing (AM) represents a novel method for parts manufacturing, revolutionizing the design principles and processes. Among the different AM methods, fused filament fabrication (FFF) is one of the most widely employed and affordable, with numerous applications across a broad range of fields. Inherently, due to the fundamental physical mechanisms occurring during part building, the material acquires different properties compared to those of bulk material. Simultaneously, parameters such as the infill pattern and infill density significantly affect the overall behavior of the part. An efficient and effective tool to minimize the necessity for experimental investigations and to define the mechanical properties with respect to these parameters (i.e., infill density and pattern) is the finite element method (FEM). In the current study, accurate FEM models were developed and presented, considering the precise geometry of compression specimens for simulating the compression behavior of FFF-printed ASA polymer. More specifically, honeycomb infill patterns with different infill densities were simulated, and the results were validated by direct comparison to respective experimental results. It was deduced that utilizing an appropriate mesh size leads to higher precision and also increases the stability of the numerical simulation, while the FEM models can predict the loads as well as the deformed geometric shapes for different infill densities. As an overall conclusion, it is proved and reasoned that employing FEM and a proper modeling approach is indeed a feasible and efficient way to predict and define the compressive behavior of FFF parts.

Optimizing the Electrode Geometry of an In-Plane Unimorph Piezoelectric Microactuator for Maximum Deflection

Piezoelectric microactuators have been widely used for actuation, sensing, and energy harvesting. While out-of-plane piezoelectric configurations are well established, both in-plane deflection and asymmetric electrode placement have been underexplored in terms of actuation efficiency. This study explores the impact of asymmetric electrode geometry on the performance of slender unimorph actuators that deflect in-plane, where actuator length is much larger than width or thickness. After validating the finite element modeling method against experimental data, the geometric parameters of the proposed unimorph model are manipulated to explore the effect of different electrode geometries and layer thicknesses on actuation efficiency. Four key findings were that (1) the fringing field within the piezoelectric material plays a measurable role in performance, (2) symmetry in electrode placement is generally nonoptimal, (3) optimal electrode geometry is independent of scale, and (4) the smaller the ratio of width to thickness, the larger the deflection. The findings contribute to the development of efficient design strategies that optimize the performance of planar actuators for potential implications for microelectromechanical systems (MEMS). To aid designers of piezoelectric unimorph actuators in determining the optimal electrode geometry, three types of parameterized figures and two types of simulation apps are provided.

Seismic Behavior of Composite Columns with High-Strength Concrete-Filled Steel Tube Flanges and Honeycomb Steel Webs Subjected to Freeze-Thaw Cycles

To investigate the seismic behavior of composite columns with high-strength concrete-filled steel tube flanges and honeycomb steel webs (STHHC) after being subjected to freeze-thaw cycles, 36 full-scale STHHCs were designed with the following main parameters: the shear span ratio (λs), the axial compression ratio (n0), the number of freeze-thaw cycles (Nc), the concrete cubic compression strength (fcu), and the steel ratio of the section (αs). Compared with existing experimental data, the validity of the finite element modeling method was verified. Parameter analysis was conducted on 36 full-scale STHHCs to obtain the hysteresis curve of the composite columns and to clarify the impact of the different parameters on the skeleton curve, the energy dissipation capacity, the stiffness degradation, and the ductility of the composite columns. The results showed that the hysteresis curves of all specimens after freeze-thaw cycles exhibited an ideal shuttle shape, reflecting that this kind of composite column has good energy dissipation ability and freeze-thaw resistance. The specimens’ maximum bulging deformation and maximum stress both occurred at the column base. Finally, the restoring force model of this kind of composite column is therefore established, and design recommendations based on these results are proposed.

Model order reduction of time-domain acoustic finite element simulations with perfectly matched layers

This paper presents a stability-preserving model reduction method for an acoustic finite element model with perfectly matched layers (PMLs). PMLs are often introduced into an unbounded domain to simulate the Sommerfeld radiation condition. These layers act as anisotropic damping materials to absorb the scattered field, of which the material properties are frequency- and coordinate-dependent. The corresponding time-domain model size is often very large due to this frequency-dependent property and the number of elements needed per wavelength. Therefore, to enable efficient transient simulations, this paper proposes a two-step method to generate stable reduced order models (ROMs) of such systems. Firstly, the modified and stable version of PMLs is projected by a one-sided split basis, which gives a stable intermediate ROM. Secondly, the intermediate ROM is modified to satisfy the stability-preserving condition by applying the modal transformation. Applying any one-sided model order reduction method on this modified model leads to a stable and small ROM. This two-step method is further extended to account for the locally-conformal PML model by reformulating it in curvilinear coordinates, which works for arbitrary convex truncated domains. The proposed method is successfully verified by several numerical simulations.

Experimental and numerical investigation on the in-plane performance of nail-laminated timber floor

Existing research has shown that the nail-laminated timber (NLT) floor has the potential to achieve considerable out-of-plane flexural performance at a relatively lower cost. However, though the in-plane performance of structural floors greatly impacts the seismic resistance of the overall structure, research on the in-plane behavior of NLT floors is still insufficient. In this paper, an in-plane shear test was carried out on twelve NLT floor specimens of four subgroups. A finite element model (FEM) method was established and verified using the experimental results. A parametric analysis was performed based on the FEM method to quantify the influence of sheathing nails on the in-plane performance of the NLT floor in both planar directions. Experimental results indicate that sheathing nail spacing and loading direction showed significant influence on the in-plane performance of NLT, while the orientation of sheathing did not. Main failure modes include dislocation of adjacent sheathings, sheathing nail failure, and lamina nail failure. Verification of the proposed FEM method showed good agreement with the experimental results, both on performance characteristics and deformation patterns. Parametric result indicates that the elastic stiffness and shear strength were linearly correlated to the quantity of sheathing nails.

Evaluation of finite element modeling methods for predicting compression screw failure in a custom pelvic implant.

Introduction: Three-dimensional (3D)-printed custom pelvic implants have become a clinically viable option for patients undergoing pelvic cancer surgery with resection of the hip joint. However, increased clinical utilization has also necessitated improved implant durability, especially with regard to the compression screws used to secure the implant to remaining pelvic bone. This study evaluated six different finite element (FE) screw modeling methods for predicting compression screw pullout and fatigue failure in a custom pelvic implant secured to bone using nine compression screws. Methods: Three modeling methods (tied constraints (TIE), bolt load with constant force (BL-CF), and bolt load with constant length (BL-CL)) generated screw axial forces using functionality built into Abaqus FE software; while the remaining three modeling methods (isotropic pseudo-thermal field (ISO), orthotropic pseudo-thermal field (ORT), and equal-and-opposite force field (FOR)) generated screw axial forces using iterative physics-based relationships that can be implemented in any FE software. The ability of all six modeling methods to match specified screw pretension forces and predict screw pullout and fatigue failure was evaluated using an FE model of a custom pelvic implant with total hip replacement. The applied hip contact forces in the FE model were estimated at two locations in a gait cycle. For each of the nine screws in the custom implant FE model, likelihood of screw pullout failure was predicted using maximum screw axial force, while likelihood of screw fatigue failure was predicted using maximum von Mises stress. Results: The three iterative physics-based modeling methods and the non-iterative Abaqus BL-CL method produced nearly identical predictions for likelihood of screw pullout and fatigue failure, while the other two built-in Abaqus modeling methods yielded vastly different predictions. However, the Abaqus BL-CL method required the least computation time, largely because an iterative process was not needed to induce specified screw pretension forces. Of the three iterative methods, FOR required the fewest iterations and thus the least computation time. Discussion: These findings suggest that the BL-CL screw modeling method is the best option when Abaqus is used for predicting screw pullout and fatigue failure in custom pelvis prostheses, while the iterative physics-based FOR method is the best option if FE software other than Abaqus is used.

Microstructure-sensitivity of CPFEM models on fretting fatigue crack initiation of AA2024-T351 alloy

The AA2024-T351 alloy is widely used in civil engineering, machinery, and aerospace industries for bolts, rivets, and thin plate components. When in service within these fields, the components are susceptible to performance degradation and fracture failure due to fretting fatigue. In this study, a crystal plastic finite element method (CPFEM) model incorporating microstructure sensitivity is employed to predict the fretting fatigue crack initiation (FFCI) location and lifetime. The submodel method is utilized to simulate various microstructures in the contact region of the specimen under fretting fatigue. This research focuses on two fatigue indicator parameters (FIPs): accumulated plastic slip p and FIPFS, used to determine the hotspots for crack nucleation on the contact surface and subsurface in fretting fatigue. The study explores the impact of different grain size and orientation on crack nucleation and analyzes how various microstructural characteristics influence the crack initiation lifetime. The findings indicate that the influence of grain orientation distribution in fretting fatigue on the initiation location of contact surface cracks is not significant, but it has a notable impact on subsurface cracks. Different grain textures combinations exhibit a more pronounced anisotropy based on the accumulated plastic slip p than FIPFS. Additionally, the effect of grain orientation distribution on the FFCI lifetime is influenced by the average grain size, showing remarkable influence within a specific range of grain sizes.

3D Shape Reconstruction of Ge Nanowires during Vapor-Liquid-Solid Growth under Modulating Electric Field.

Bottom-up growth offers precise control over the structure and geometry of semiconductor nanowires (NWs), enabling a wide range of possible shapes and seamless heterostructures for applications in nanophotonics and electronics. The most common vapor-liquid-solid (VLS) growth method features a complex interaction between the liquid metal catalyst droplet and the anisotropic structure of the crystalline NW, and the growth is mainly orchestrated by the triple-phase line (TPL). Despite the intrinsic mismatch between the droplet and the NW symmetries, its discussion has been largely avoided because of its complexity, which has led to the situation when multiple observed phenomena such as NW axial asymmetry or the oscillating truncation at the TPL still lack detailed explanation. The introduction of an electric field control of the droplet has opened even more questions, which cannot be answered without properly addressing three-dimensional (3D) structure and morphology of the NW and the droplet. This work describes the details of electric-field-controlled VLS growth of germanium (Ge) NWs using environmental transmission electron microscopy (ETEM). We perform TEM tomography of the droplet-NW system during an unperturbed growth, then track its evolution while modulating the bias potential. Using 3D finite element method (FEM) modeling and crystallographic considerations, we provide a detailed and consistent mechanism for VLS growth, which naturally explains the observed asymmetries and features of a growing NW based on its crystal structure. Our findings provide a solid framework for the fabrication of complex 3D semiconductor nanostructures with ultimate control over their morphology.

Investigating the effect of rolling deformation on the electro-mechanical limits of Nb3Sn wires produced by RRP® and PIT technologies

Future high-field magnets for particle accelerators hinge on the crucial development of advanced Nb3Sn wires engineered to withstand the large stresses generated during magnet assembly and operation. The superconducting properties of Nb3Sn enable the design of compact accelerator-quality magnets above 10 T, but at the same time the brittleness and strain sensitivity of the material impose careful consideration of the mechanical limits. In addition, accelerator magnets are wound using Rutherford cables and the cabling process generates deformations in the wire that can affect its electro-mechanical performance. This paper reports on the impact of the rolling deformation on the transverse stress tolerance of high-performance restacked-rod-process (RRP®) and powder-in-tube (PIT) Nb3Sn wires. Rolling deformation was used to mimic the effect of cabling on the wire shape. Deformed samples were compared to reference round wires in term of stress dependence and irreversible limit (σ irr) of the critical current (I c) under transverse compressive loads up to 240 MPa. Experiments were performed at 4.2 K, 19 T, on resin-impregnated single wires that imitate the operating conditions in a Rutherford cable of an accelerator magnet. The results show that rolling deformation has a detrimental effect on the initial I c of PIT wires, but it does not influence the behavior of the wire under stresses above 70 MPa. On the other hand, the deformation of RRP® wires leads to an improved σ irr without affecting the initial I c. Additionally, a 2D-mechanical finite element method model of the RRP® wire was developed to investigate the impact of the wire geometry on the plastic deformation of the copper matrix, which induces residual stresses on Nb3Sn and is the main cause for the permanent reduction of I c. Based on the model results, an alternative layout of the wire was proposed that improves its stress tolerance without affecting its electrical transport properties.