Time-dependent Finite Element Model Research Articles

Running-specific prosthesis' performance characterization by dynamic finite element approach.

Composite running-specific prostheses (RSP) are widely used by athletes with lower limb amputations to simulate the spring-like behavior of biological legs. However, the effect of these devices on the biomechanics of athletes with transtibial amputations remains uncertain. To address this issue, this study proposes a time-dependent finite element model that uses angles and dynamic loads during ground contact to evaluate RSP performance parameters such as stiffness and energy efficiency. The study also examines the impact of running speed and RSP geometry on performance. The in-silico characterization approach used in this study takes into account both the intrinsic characteristics of the RSP and the athlete's biomechanics to identify the influence of fundamental geometric variables of the RSP on performance. The model is verified by comparing its results with experimental data. The study found that as running speed increases, RSP stiffness, vertical ground reaction force (vGRF), and contact time decrease. The force-displacement profiles of RSP are nonlinear, but a linear function can be used to accurately represent their behavior at high sprinting speeds. Using higher RSP reduces energy efficiency and vGRF due to their lower stiffness. J-curve RSP result in higher stiffness, vGRF, and strain energy, while C-curve RSP are associated with longer contact times and higher energy efficiency.

Biomechanical analysis of combi-hole locking compression plate during fracture healing: A numerical study of screw configuration.

Locking compression plates (LCPs) have become a widely used option for treating femur bone fractures. However, the optimal screw configuration with combi-holes remains a subject of debate. The study aims to create a time-dependent finite element (FE) model to assess the impacts of different screw configurations on LCP fixation stiffness and healing efficiency across four healing stages during a complete fracture healing process. To simulate the healing process, we integrated a time-dependent callus formation mechanism into a FE model of the LCP with combi-holes. Three screw configuration parameters, namely working length, screw number, and screw position, were investigated. Increasing the working length negatively affected axial stiffness and healing efficiency (p < 0.001), while screw number or position had no significant impact (p > 0.01). The time-dependent model displayed a moderate correlation with the conventional time-independent model for axial stiffness and healing efficiency (ρ ≥ 0.733, p ≤ 0.025). The highest healing efficiency (95.2%) was observed in screw configuration C125 during the 4-8-week period. The results provide insights into managing fractures using LCPs with combi-holes over an extended duration. Under axial compressive loading conditions, the use of the C125 screw configuration can enhance callus formation during the 4-12-week period for transverse fractures. When employing the C12345 configuration, it becomes crucial to avoid overconstraint during the 4-8-week period.

Dynamic behavior of a zero-group velocity guided mode in rail structures.

Important characteristics of a zero-group velocity (ZGV) mode in a standard rail are investigated through numerical simulation and experiment. First, the semi-analytical finite element analysis is implemented to compute dispersion curves for the rail structure and the first ZGV point is identified. Backward waves are identified through opposing senses of group and phase velocities. Next, a time-dependent finite element model is used to understand the dynamic response of the rail. Finally, experimental measurements confirm that ZGV modes in rail structures are formed through interferences between two opposite-traveling waves, which is analogous to the S1-S2b ZGV Lamb mode in plate structures.

Investigating the relationship of hardness and flow stress in metal forming

Hardness is routinely utilised to link the bulk material properties to surface contact mechanics. Besides possible differences in the material properties between bulk and surface, there is no established relation between hardness and the thermo-viscoplastic flow stress of materials used in the context of metal forming processes. The purpose of this study is to investigate such relationship using 6061 and 6016 aluminium alloys manufactured by hot rolling. Optical microscopy and Vickers hardness tests at different loads and temperatures ranging from 22°C up to 450°C were carried out. A time-dependent Finite Element model of an indentation using thermo-viscoplastic material model based on bulk samples was developed and compared with experiments. Overall, no significant difference between bulk and surface for neither alloy was experimentally identified. The hardness decrease with temperature of the alloys is quantified and ready-to-use constraint factor maps associating the thermo-viscoplastic flow stress with hardness of the materials are presented. The numerical model allowed visualisation of viscoplastic effects, whereas comparisons to the experiments in terms of hardness and topography validated the model and constitutive equations. Constitutive equations derived from compression tests of bulk samples can confidently describe deformation at the surface level and so, be used to develop a contact model in the tribological context of metal forming.

Bayesian inference for predicting the long-term deflection of prestressed concrete bridges by on-site measurements

Predicting the long-term deflection of prestressed concrete bridges (PSCB) by the deterministic models is subject to significant epistemic uncertainties, and the Bayesian statistics provide a practical way to make more reliable prediction by use of the long-term measurements. In this paper, a comprehensive Bayesian inference frame was built, in which the model parameters associated with creep, shrinkage, dead load and prestress level were updated by the Bayesian inference of the deflection measurements. A 3-D time-dependent finite element model was constructed, based on which a surrogate model was built to enhance computation efficiency. The Markov Chain Monte Carlo (MCMC) algorithm was adopted to approximate the manifold of the posterior distribution. In the case study, two sets of deflection of the case bridge were utilized to perform the Bayesian inference in a sequential manner. The results revealed that the updated models could produced better fit to the measurements than the deterministic model, while the variance of the prediction was significantly reduced. The updated model revealed changing trends of the time-dependent deflection, which characterizes a later-age acceleration from the initial moderate trend. Based on the updated models, the time-dependent reliability associated with the limit states defined by deflection limits was computed. For such a task, the MCMC-based pre-sampling and the quasi-optimal importance sampling were adopted to reduce the variance of the computation.

Long-term deflection prediction in steel-concrete composite beams

This paper aims to improve the current state-of-the-art in long-term deflection prediction in steel-concrete composite beams. The efficiency of a time-dependent finite element model based on linear creep theory is verified with available experimental data. A parametric numerical study is then carried out, which focuses on the effects of concrete creep and/or shrinkage, ultimate shrinkage strain and reinforcing bars in the slab. The study shows that the long-term deformations in composite beams are dominated by concrete shrinkage and that a higher area of reinforcing bars leads to lower long-term deformations and steel stresses. The AISC model appears to overestimate the shrinkage-induced deflection. A modified ACI equation is proposed to quantify time-dependent deflections in composite beams. In particular, a modified reduction factor reflecting the influence of reinforcing bars and a coefficient reflecting the influence of ultimate shrinkage are introduced in the proposed equation. The long-term deflections predicted by this equation and the results of extensive numerical analyses are found to be in good agreement.

An equation-based multiphysics modelling framework for oxidative ageing of asphalt pavements

Long-term oxidative ageing occurs in asphalt pavements when they are exposed to the ambient environment for extended periods. This ageing phenomenon is dependent on multiple physical fields, including heat transfer, oxygen diffusion from air into interconnected air voids of asphalt pavement, oxygen diffusion from air void channels to asphalt mastic inside, and growth of oxidation products in bitumen. Most existing oxidative ageing models were established via coupling of limited physical fields. However, to accurately determine the oxidative ageing effect on pavement performance, there is a need to develop a multiphysics model that integrates all ageing-related physical fields comprehensively. The challenge lies in that the ageing-related physics are circularly dependent, time-dependent and highly nonlinear. This study developed a multiphysics and time-dependent finite element model that successfully addressed the issues of high nonlinearity and circular dependency of oxidative ageing in the asphalt pavements.Specifically, a differential equation-based approach was employed to efficiently couple the multiple physical fields into one integrated model. The multiphysics framework included a pavement temperature prediction model and an integrated ageing model. The model involved a variety of inputs such as site-specific hourly climate data, parameters for oxidation kinetics of bituminous binder, volumetric properties of asphalt mixture, thermal and diffusive properties of pavement materials, and pavement structure. The pavement temperature model was validated using the pavement temperature profiles for different climate regions in the Long-Term Pavement Performance (LTPP) database. The integrated ageing model was validated using the Fourier-transform infrared spectroscopy (FTIR) data of field-aged asphalt cores in the literature. Results showed that the model can accurately predict the change in pavement temperature profile on an hourly basis and reliably predict the degree of oxidative ageing across pavement depth for different climate zones.

Finite element simulation of friction and adhesion attributed contact of bio-inspired gecko-mimetic PDMS micro-flaps with SiO2 spherical surface

The remarkable tribological attributes of the gecko feet have grown much interest in the field of biomimetic tribology over the past two decades. It has been shown that the complexity of friction and adhesion phenomena made it difficult to transfer these exceptional properties into fully functional smart, dry, micro patterned adhesives. The latter, combined with the relative lack of literature on computational oriented studies on these phenomena, is the motive of the current work. Here, a 2D time-dependent finite element model of friction and adhesion attributed contact of polydimethysiloxane (PDMS) micro flaps with a smooth SiO2 spherical surface is presented. The model is tested through simulations concerning changes in the disc curvature, the flap density, as well as different disc mounting heights, representing the effect of preload. Furthermore, the effect of tribological parameters of adhesion and friction coefficient is discussed. Finally, the effect of the use of two hyperelastic material models was examined.

Control of long-term deflections of RC beams using reinforcements and low-shrinkage concrete

An experimentally based programme was conducted to assess the influence of heterogeneity on the long-term deflection of reinforced concrete (RC) elements with compression reinforcement and low-shrinkage concrete. These two structural measures are usually employed by designers to mitigate deflection of concrete beams, slabs and bridge decks due to creep and shrinkage effects. Control of creep and shrinkage deflections is important for successful design of concrete elements as the deflections influence their sizing and thus the associated costs. A 5 year experimental study was undertaken to address the most common alternative design approaches to alleviate long-term deflections of concrete. These included variable reinforcement ratios within the compressive zone, variable tensile reinforcement ratios, low-shrinkage concrete within the compressive zone and a combination of these measures. In total, 12 cantilever beam specimens were tested in the laboratory under controlled environmental conditions, supported by a time-dependent finite-element model. Both numerical and experimental results showed RC beam deflection reductions of up to 85% could be achieved when both compressive reinforcement and low-shrinkage concrete were employed.

On discrepancies between time-dependent nonlinear 3D and 2D finite element simulations of deep tunnel advance: A numerical study on the Brenner Base Tunnel

A numerical study on a stretch of the Brenner Base Tunnel, characterized by high overburden and driven according to the New Austrian Tunneling Method, is presented. At first, a 3D time-dependent nonlinear finite element model is developed, taking into account the construction process, nonlinear material behavior of the surrounding rock mass, and the time-dependent nonlinear material behavior of shotcrete. Next, the prognosis capabilities of a simplified time-dependent 2D model are investigated, since in engineering practice 3D computations are often not feasible due to their computational expense. For this model, a thorough calibration of a particular stress release scheme based on the 3D model is performed, aiming at a good fit of the displacements. Hence, the remaining discrepancies of the response of the two models can be attributed to the simplifying assumptions inherent in the 2D model. The computed displacements are validated by comparison with in situ measurement data. It will be demonstrated that both the 3D model and the calibrated 2D model together with the nonlinear constitutive models allow a good correspondence of the predicted displacements with the measured ones at the tunnel site. However, striking discrepancies are observed for the predicted evolution of the stress state in the shotcrete shell.

Loss estimation of magnetic gears

Reduction in losses is essential for the efficiency enhancement of magnetic gears. In this paper, the power losses of a coaxial magnetic gear are estimated, based on a developed convenient approach for loss analysis using a time-dependent finite element model. The results are confirmed by a sophisticated measurement system for magnetic gear testing. Eddy current losses in permanent magnets and magnetic cores, magnetic flux reluctance and harmonic distortion in magnetic materials during magnetic gear operation are determined. The output torque reduction, especially at high rotational speeds and high gear ratios caused by losses, is analyzed. Different permanent magnet material grades are utilized in order to evaluate the eddy currents and the torque transmission losses during the magnetic gear performance.

Temperature field and residual stress distribution for laser metal deposition

Laser metal deposition (LMD) process has been widely used in many industrial applications such as automotive, defense, aerospace, and so on. Modeling has to address physical phenomena like laser-powder interaction, heat transfer, fusion, solidification, and track formation. LMD induces a complex thermal stress field that results in residual stress distributions. Depending on its magnitude and nature (i.e., whether tensile or compressive), the residual stresses can cause unpredicted in-service failures. Therefore, the prediction of its distribution in the deposited structure as a function of the process strategy is essential to improve the process and the part quality. LMD represents mathematically a free boundary value problem. This means that the track geometry is part of the solution. The authors developed a three-dimensional time-dependent finite element model for LMD with coaxial powder feeding supply. The model encompasses the powder stream, its interaction with the laser radiation, and the melt pool computation. The model was validated by a comparison of the experimental and computed shapes of the melt pool surfaces concerning cross section, longitudinal section and high-speed photographs [Pirch et al., in Proceedings of the ICALEO Conference, 16–20 October 2016]. In this paper, the model was applied to overlapping tracks for single and multilayer processing for different process strategies. The simulation allows us to analyze the time- and space-resolved evolution of temperature and stresses. The influence of the powder feed rate on the residual stresses is investigated.

Optimal Design of Galvanic Corrosion Protection Systems for Offshore Wind Turbine Support Structures

The current work addresses a mass/cost-optimization procedure for galvanic anode cathodic protection systems based on both cathodic protection (CP) standards and numerical simulation. An approach is developed for optimizing the number and dimensions of the galvanic anodes, distributing the optimized anodes on the support structure, and finally evaluating the protective potential on the structure during the lifetime by using finite element (FE) software. An algorithm based on sequential quadratic programming is used for optimizing the number and dimensions of the anodes. Both simplified and detailed models are suggested for calculating the protective potential on the structure. The simplified model is selected based on its advantages in terms of calculation time and compatibility with DNV standard data. A time-dependent FE model is used to take into account the electrical isolation degradation of the structure coating as well as the mass reduction of the anodes during the CP lifetime. The performance of the proposed optimization process is examined on a mono bucket inspired (with some simplifications) by the Dogger Bank metrological mast in England. The optimized designs for different coating and anode types are compared and the best designs in terms of both cost and protective potential during the lifetime are suggested. The achieved results show that the proposed optimization procedure can reduce the cost of the CP system around 70% compared to the original non-optimized CP design of the Dogger Bank metrological mast. Furthermore, evaluating the time-evolution performance of the CP systems can reduce their lifetime uncertainty.

Maskless X-Ray Writing of Electrical Devices on a Superconducting Oxide with Nanometer Resolution and Online Process Monitoring

X-ray nanofabrication has so far been usually limited to mask methods involving photoresist impression and subsequent etching. Herein we show that an innovative maskless X-ray nanopatterning approach allows writing electrical devices with nanometer feature size. In particular we fabricated a Josephson device on a Bi2Sr2CaCu2O8+δ (Bi-2212) superconducting oxide micro-crystal by drawing two single lines of only 50 nm in width using a 17.4 keV synchrotron nano-beam. A precise control of the fabrication process was achieved by monitoring in situ the variations of the device electrical resistance during X-ray irradiation, thus finely tuning the irradiation time to drive the material into a non-superconducting state only in the irradiated regions, without significantly perturbing the crystal structure. Time-dependent finite element model simulations show that a possible microscopic origin of this effect can be related to the instantaneous temperature increase induced by the intense synchrotron picosecond X-ray pulses. These results prove that a conceptually new patterning method for oxide electrical devices, based on the local change of electrical properties, is actually possible with potential advantages in terms of heat dissipation, chemical contamination, miniaturization and high aspect ratio of the devices.

Time-dependent nonlinear finite element modeling of the elastic and plastic deformation in SiGe heterostructured nanomaterials

The study of strain and stress distributions and relaxation mechanisms during epitaxial deposition of ultra-thin film heterostructures is of critical importance for nanoelectronic materials. It provides guidance for the control of structures at the nanometer scale and insights into the underlying physics. In this paper, we present a time-dependent nonlinear finite element model, which realistically simulates the evolution of elastic and plastic deformation in SiGe heterostructured nanomaterials during epitaxial deposition. Dynamic elements have been used to simulate the layer-by-layer deposition and growth rate as well as chemical-mechanical polishing (CMP) planarization. The thickness of add-on and etched-off layers was limited to few nanometers depending on the final epitaxial layer thickness and its growth rate. The material plastic behavior is described by the Von Mises yield criterion coupled with isotropic work hardening conditions and the Levy-Mises flow rule. The model has been successfully applied to the growth of ultra-thin (15 nm) strained-Si/Si1-xGex/Si(001) heterostructures. Depth and time dependent elastic and plastic stress and strain in the growing layers are quantified and the relaxation mechanisms are deduced. From the calculated elastic and plastic strain fields, we derived the relaxation factor, plastic strain rate, dislocation glide velocity, misfit, and threading dislocation density as well as several structural properties such as lattice parameters and misfit dislocation spacing and length. These were found in close agreement with published experimental data. The simulation was able to show at which step of the growth process and how often yielding events occur. Plastic deformation and so the nucleation and multiplication of dislocations appeared to occur consistently during growth of the graded-layer. The simulation was also able to predict that CMP of the SiGe-cap followed by a regrowth step will indeed further relax the graded layer. This two-phase relaxation mechanism is expected from the growth process but experimentally difficult to verify. Results from the simulation also show that rapid cooling is favored over slow cooling in order to retain the maximum amount of elastic strain in the strained-Si device layer.

Landslide Kinematical Analysis through Inverse Numerical Modelling and Differential SAR Interferometry

The aim of this paper is to propose a methodology to perform inverse numerical modelling of slow landslides that combines the potentialities of both numerical approaches and well-known remote-sensing satellite techniques. In particular, through an optimization procedure based on a genetic algorithm, we minimize, with respect to a proper penalty function, the difference between the modelled displacement field and differential synthetic aperture radar interferometry (DInSAR) deformation time series. The proposed methodology allows us to automatically search for the physical parameters that characterize the landslide behaviour. To validate the presented approach, we focus our analysis on the slow Ivancich landslide (Assisi, central Italy). The kinematical evolution of the unstable slope is investigated via long-term DInSAR analysis, by exploiting about 20 years of ERS-1/2 and ENVISAT satellite acquisitions. The landslide is driven by the presence of a shear band, whose behaviour is simulated through a two-dimensional time-dependent finite element model, in two different physical scenarios, i.e. Newtonian viscous flow and a deviatoric creep model. Comparison between the model results and DInSAR measurements reveals that the deviatoric creep model is more suitable to describe the kinematical evolution of the landslide. This finding is also confirmed by comparing the model results with the available independent inclinometer measurements. Our analysis emphasizes that integration of different data, within inverse numerical models, allows deep investigation of the kinematical behaviour of slow active landslides and discrimination of the driving forces that govern their deformation processes.

Validated numerical modeling of galvanic corrosion of zinc and aluminum coatings

A time-dependent finite element model was developed to simulate the corrosion of zinc and aluminum coatings, galvanically coupled to a mild steel substrate in deaerated 0.01 M H2SO4 electrolyte. The simulations of galvanic corrosion for each of the coatings were compared to experimental measurements of open circuit potential, and changes in coating geometry measured via surface profilometry. Good agreement between the model predictions and corrosion tests were observed initially for both coatings. However, in the case of the zinc coating, divergence was observed between the simulation and the corrosion test after approximately 40min, due to a decrease in the reactivity of the zinc surface.

A computational model for the simulation of dynamic fracture in laminated composite plates

A mesoscopic, time-dependent finite element model for the simulation of dynamic fracture in laminated composite plates is presented. The computational model allows for the simulation of mesh-objective multiple matrix cracking and delamination in laminated composite plates. The analyses are performed with an emphasis on the quantification of the effect of the loading rate on interacting damage mechanisms, i.e. matrix cracking and delamination. In particular, rate effects on damage initiation, propagation, and interaction between matrix cracking and delamination under low and high velocity impact are studied. Moreover, the paper addresses computational issues related to time continuity in stress/strain and velocity fields, during dynamic simulation, at the time of incorporation of new degrees of freedom in a mesh-objective crack modeling approach. Illustrative numerical examples are presented to show the performance of the model. The model is validated with a fast crack growth simulation in a unidirectional laminate. An impact test on a cross-ply laminated plate is performed in order to study the rate effects on structural response and damage mechanics.

Towards an efficient numerical simulation of complex 3D knee joint motion

We present a time-dependent finite element model of the human knee joint of full 3D geometric complexity together with advanced numerical algorithms needed for its simulation. The model comprises bones, cartilage and the major ligaments, while patella and menisci are still missing. Bones are modeled by linear elastic materials, cartilage by linear viscoelastic materials, and ligaments by one-dimensional nonlinear Cosserat rods. In order to capture the dynamical contact problems correctly, we solve the full PDEs of elasticity with strict contact inequalities. The spatio-temporal discretization follows a time layers approach (first time, then space discretization). For the time discretization of the elastic and viscoelastic parts we use a new contact-stabilized Newmark method, while for the Cosserat rods we choose an energy-momentum method. For the space discretization, we use linear finite elements for the elastic and viscoelastic parts and novel geodesic finite elements for the Cosserat rods. The coupled system is solved by a Dirichlet---Neumann method. The large algebraic systems of the bone---cartilage contact problems are solved efficiently by the truncated non-smooth Newton multigrid method.

A Finite Element Model for Spherical Debris Denting in Heavily Loaded Contacts

The objective of this study is to develop models to investigate the effects of contaminants (debris denting process) in heavily loaded rolling and sliding contacts. A dynamic time dependent finite element model (FEM) was developed to determine the elastic-plastic deformation and contact force generated between the mating surfaces and a spherical debris as debris passes through the contact region. The FEA model was used to obtain the effects of various parameters such as debris sizes, material properties, friction coefficients, applied loads, and surface speeds on the elastic-plastic deformation and contact force of the system. The FEM was used to predict debris and mating surfaces deformations as a function of debris size, material properties, friction coefficient, applied load, and surface speed. Using the FEM, a parametric study demonstrated that material properties (i.e., modulus of elasticity, yield strength, ultimate strength and Poisson’s ratio) and friction coefficients play significant roles on the height and width of dents on the mating surfaces. For lower friction coefficients μd&lt;0.3 the debris and mating surfaces slip more easily relative to one another and therefore the debris has lower aspect ratio. As friction coefficient is increased the debris and mating surfaces stick to one another and therefore the debris deforms less and has higher aspect ratio. The results indicate that the pressure generated between the debris and mating surfaces is high enough to plastically deform the debris and mating surfaces and cause a permanent dent on the surfaces and cause residual stresses around the dent. Based on the FEM results, a dry contact model (DCM) was developed to allow similar analyses as the FEM, however, in significantly shorter computational time.