Multiscale Finite Element Research Articles

Digital twin-based identification of crystal plastic material parameters for weld joints of orthotropic steel decks

The identification of crystal plasticity (CP) material parameters is indispensable for using CP models to simulate and understand the microcrack initiation and propagation of orthotropic steel decks (OSD). This study proposes a digital twin (DT)-based framework for identifying CP material parameters of weld joints of OSD by fusing multiscale CP finite element model (CPFEM) with macroscale stress–strain material tests. The material tests of the specimen (physical entity) cut from the weld joints of OSD and sliced to the centimeter scale are carried out using the standard dynamic test system. The CPFEM simulation is used to develop a multiscale virtual entity to map the physical entity. The particle swarm optimization algorithm is used to fuse the CPFEM simulation with the material test data to identify CP material parameters and produce a DT. The results demonstrate that the CP material parameters identified by the proposed framework are more accurate than those identified by a single representative volume element method. The results also show that the DT-based identification of CP material parameters has high applicability.

Efficient phononic band gap optimization in two-dimensional lattice structures using extended multiscale finite element method

Efficient phononic band gap optimization in two-dimensional lattice structures using extended multiscale finite element method

Enhancing the pull-out behavior of ribbed steel bars in CNT-modified UHPFRC using recycled steel fibers from waste tires: a multiscale finite element study

In the current investigation, the effect of recycled steel fibers recovered from waste tires on the pull-out response of ribbed steel bars from carbon nanotube (CNT)-modified ultrahigh performance fiber reinforced concrete (UHPFRC) was considered using the multiscale finite element method (MSFEM). The MSFEM is based on three phases to simulate CNT-modified UHPC, recycled steel fibers (RSFs), and ribbed steel bars. For the first time, a bar ribbed has been simulated to make more realistic assumptions, and RSFs have been distributed in the form of curved cylinders of different lengths and with a random distribution within a concrete matrix. The interaction of the steel bar and the RSFs with the concrete is applied by the cohesive zone model (CZM). After confirming the simulation outcomes with the experimental results, the steel bar pull-out response is investigated using load-slip curves. The impact of the CNT content, RSFs and their aspect ratio on the bond strength of steel bars and CNT-modified UHPFRC was assessed. The results show that using RSFs with a lower aspect ratio (steel microfibers) significantly improves the pull-out characteristics of steel bars from concrete. Accordingly, the proposed MSFEM is considered for simulating the effects of different parameters on the pull-out response of ribbed steel bars from concrete without causing complex, time-consuming, or costly experiments. The results indicated that waste fiber or RSF can be used as a toughening component in CNT-modified ultrahigh-performance concrete and as a replacement for industrial steel fibers.

Stress-related discrete variable topology optimization with handling non-physical stress concentrations

The accuracy of stress calculation with a fixed mesh significantly affects the stress-based topology optimization, due to potential non-physical stress concentrations in voxel-based topology descriptions. This paper proposes a novel problem-independent machine learning enhanced high-precision stress calculation method (PIML-HPSCM) to address this challenge. As an immersed analysis method, PIML-HPSCM combines the high efficiency of fixed mesh with the accuracy of body-fitted mesh, without complex integration schemes of other immersed methods. PIML-HPSCM utilizes the extended multiscale finite element method to depict the material heterogeneity within high-resolution boundary elements. The accurate stress field can then be calculated conveniently by establishing stress evaluation matrices of high-resolution boundary elements. Moreover, the PIML is independent of problem settings and is applicable for various problems with the same governing equation type. Invoking the offline-trained neural network online can enhance stress calculation efficiency by 10–20 times. The stress-based discrete variable topology optimization, which naturally avoids singular stress phenomenon, is efficiently addressed by the sequential approximate integer programming method with PIML-HPSCM. Results from 2D and 3D examples demonstrate that the stresses calculated by PIML-HPSCM are consistent with those by body-fitted mesh, and optimized designs effectively eliminate stress concentrations of initial designs and have uniform stress distributions.

Prediction of the failure behavior of pseudo-ductile composites using a multi-scale finite element model

The hybridization technique has recently been used to produce a new generation of composites called pseudo-ductile composites, which have shown higher failure strain compared to conventional composites, minimizing the risks of the occurrence of a catastrophic failure. The pseudo-ductility behavior in these composites is obtained by hybridization of fibers with high and low failure strains. In this study, a multi-scale finite element (FE) model incorporating micro and macro-scales is proposed to predict the failure behavior of pseudo-ductile composites. A micro-scale representative volume element (RVE), consisting of randomly distributed fibers, was generated using a Python code. Periodic boundary conditions (PBCs) were applied to the RVE generated with a periodic geometry. To account for fiber failure and ply fragmentation, the tensile strength of fibers was distributed based on the Weibull distribution function and a user-defined UMAT subroutine was developed. Tensile loading was then applied to the RVE to simulate the composite’s mechanical behavior. For validation, an RVE was developed based on experimental data from recent research on thinply and conventional thickness composites. Numerical results were compared to experimental data, demonstrating acceptable agreement. In the final step, following a sequential multi-scale modeling approach, a macro-scale model was constructed based on the outputs of the micro-scale model subjected to tensile and shear loads. The results were compared with experimental data, revealing good agreement. The proposed model allows for the optimization of pseudo-ductile composite structures to achieve a desired set of mechanical properties without the need for conducting extensive experimental material tests.

Multi-scale moisture diffusion modeling and analysis of carbon/Kevlar-fiber hybrid composite laminates under the hygrothermal aging environment

Hybrid fiber reinforced polymer (HFRP) can have more complex micro moisture diffusion process than single fiber composite, owing to diverse hygroscopic properties of dissimilar fibers. Thus, elucidating the multi-scale moisture diffusion mechanism of HFRP through experimental method becomes a challenging endeavor. To this end, a multi-scale moisture diffusion modeling approach is proposed to investigate the moisture diffusion behavior of carbon/Kevlar HFRP under the hygrothermal aging environment. Leveraging Fick's law as a foundation, a combination of multi-scale moisture diffusion model and finite element method is employed. To validate the effectiveness of model, accelerated aging experiments are conducted on HFRP samples with various stacking sequences. By SEM characterization, the surface aging on aged Kevlar fibers and the debonding of aged fiber/matrix interface are conspicuously observed. Based on this model, the moisture diffusion behaviors in different HFRP configurations are simulated and analyzed to reveal the micro-, meso‑ and macro-scale moisture diffusion and resistance mechanisms. Our findings highlight the profound influence of factors such as fiber type, fiber content, fiber placement, hygroscopic properties of constituents, and their synergistic effects on moisture absorption and saturated moisture absorption rates. Finally, the hygroscopic properties of HFRP laminate with different stacking sequences are predicted by multi-scale model. This work endeavor furnishes valuable insights and guidelines for the design and analysis of moisture-resistant HFRP.

Seismic behavior of looseness-induced inclined mortise and tenon joints in ancient timber structures: Experimental tests, multi-scale finite element model, and behavior degradation

The inclination damage of mortise and tenon (M-T) joints, caused by the looseness between the mortise and tenon, has an detrimental impact on the overall safety of structures. To investigate the effects of varying inclination rotation on the seismic behavior of ancient M-T joints, four 1/3.2-scaled straight M-T joints with different inclination rotation, one intact joint for comparison and three looseness-induced inclined joints, were cyclically tested. Typical failure modes of the damaged joints were identified. The influence of the tilt deterioration on the joint's hysteretic and rotational behavior was evaluated. The test results showed that with an increase in the inclination rotation, the size of the hysteretic loops of the inclined joints was increasingly smaller, the negative initial slippage and pinching effects were more apparent, the ultimate moment-resisting, initial elastic stiffness, and ductility of the specimens degraded significantly. Furthermore, the multi-scale finite element models of the looseness-induced inclined M-T joints were established using the ABAQUS. Based on the validated numerical model, the parameter analysis was performed. The influence of the frictional coefficient of wood, inclined rotation, and horizontal gap between the tenon and mortise on the joint's hysteretic behavior and energy dissipation mechanism was quantified. It is found that with a friction coefficient of 0.6, the positive and negative ultimate moments-resisting of the joint improved 65.99 % and 35.89 %, respectively; the joint's slip moment and energy dissipation increased by 12.18 and 3.78 times, respectively. With a 0.043 rad inclined rotation, the positive and negative ultimate moments of the joint decreased 23.32 % and 30.46 %, respectively; the joint's positive and negative initial elastic stiffnesses and cumulative energy dissipation reduced 49.12 %, 28.96 %, and 56.33 %, respectively. When the inclined rotation remained at 0.022 rad, the positive and negative ultimate moments of the joint including a 6 mm horizontal gap reduced 26.63 % and 34.20 %, respectively; the joint's positive and negative initial elastic stiffnesses, and accumulative energy dissipation decreased 42.42 %, 59.43 %, and 79.50 %, respectively.

An efficient multi-scale method for failure mechanism analysis of SiCf/Ti composites with experimental validation

This study focuses on developing and validating a high-precision concurrent multi-scale finite element model considering the progressive damage model (PDM) and the cohesive zone model (CZM) for predicting the damage evolution of SiCf/Ti composites. At the macro-scale, a constitutive model describing the anisotropic damage criterion of SiCf/Ti composites was implemented by means of a user-defined subroutine (VUMAT). Meanwhile, based on the submodelling, a representative volume element (RVE) model was developed to systematically analyze the failure modes of the SiC fibers, the matrix, and the interface, respectively. Specifically, the crack initiation and propagation in the stress concentration zones were further discussed. Simultaneously, experimental methods were employed to verify the feasibility of the current model. During the uniaxial compression, the brittle fracture of the SiC fibers and ductile fracture of the matrix are the predominant failure modes of SiCf/Ti composites, with fiber fracture being the dominant factor. The crack initiates at the fibers, propagates rapidly to the fiber-matrix interface, and then extends into the matrix. Moreover, the fracture locations are suscepticle to stress concentrations, leading to the crack initiation and propagation. The predicted results show that the local damage has a significant effect on the failure mechanism of SiCf/Ti composites and this multi-scale model provides a scientific reference for the design and optimization of composites.

Thermokinetics driven microstructure and phase evolution in laser-based additive manufacturing of Ti-25wt.%Nb and its performance in physiological solution

A bio-compatible Ti-25 wt% Nb alloy fabricated from a blend of pure elemental powders using laser powder bed fusion additive manufacturing technique. The present work investigated the effects of processing conditions on the evolution of microstructures and its consequential material attributes, such as mechanical properties and corrosion performance. Thermal management strategies comprising laser powers of 200 W and 300 W in complement with a shorter scan length (1 mm) and substrate preheating above β-transus temperature (1123 K) were considered to achieve complete dissolution of niobium particles. The microstructure in the 200 W sample showed thin α′′ martensite needles in β matrix while martensite laths in the 300 W condition appear coarse and were twice the area fraction compared to that in 200 W build. On the other hand, microstructures in the heated substrate sample exhibited the evolution of α and β phases. A multi-scale finite element method based thermo-kinetic model spanning from melt pool scale to the component scale was incorporated to understand the mechanism of the evolution of microstructures during liquid–solid and solid–solid state transformation. Electrochemical performance in the simulated body fluid of the printed alloys was found to be significantly affected by the presence of martensite fractions. Both mechanical and corrosion behaviors were favorably influenced by adoption of the substrate preheating during additive manufacturing due to promotion of diffusional transformation of β to α at the expense of martensitic transformation.

Stress intensity factor analysis for multiple cracks in orthotropic steel decks rib-to-floorbeam weld details under vehicles loading

In recent years, it has been found that multiple cracks coexist in the existing steel bridge orthotropic steel decks (OSDs) longitudinal rib-to-floorbeam (RF) details. The synergistic expansion mechanism of multiple cracks in the orthotropic steel bridge deck panel is still unclear. This paper proposes a multiscale extension finite element method based on ABAQUS and FRANC 3D interactive technology to simulate the fatigue crack propagation behavior of steel bridge RF details under dynamic vehicle loading. The effectiveness of this method is verified by comparing experimental data. The crack propagation behavior of longitudinal rib weld toes, transverse diaphragm weld toes, and transverse diaphragm arc notches is studied, and the influence of fatigue crack length and angle on the initial crack stress intensity factor (SIF) of adjacent details is discussed.

Multiscale model reduction for the time fractional thermoporoelasticity problem in fractured and heterogeneous media

In this paper, we consider the time fractional thermoporoelasticity problem in fractured and heterogeneous media. The mathematical model with a time memory formalism is described by a coupled system of equations for pressure, temperature and displacements. We use an implicit finite difference approximation for temporal discretization. We present a fine grid approximation based on the finite element method and Discrete Fracture Model (DFM) for two-dimensional model problems. Further, we use the Generalized Multiscale Finite Element Method (GMsFEM) for coarse grid approximation. The primary concept behind the proposed method is to streamline the complexity inherent in the thermoporoelasticity problem. Given that our model equation incorporates multiple fractional powers, leading to multiple unknowns with memory effects, we aim to address this intricacy by optimizing the problem’s dimensionality. As a result, the solution is sought on a coarse grid, a strategic choice that not only simplifies the computational cost but also contributes to significant time savings. We present numerical results for the two-dimensional model problems in heterogeneous fractured porous media. We derive relative errors between the reference fine grid solution and the multiscale solution for different numbers of multiscale basis functions. The results confirm that the proposed method is able to achieve good accuracy with a few degrees of freedoms on the coarse grid.

Advanced Fatigue Assessment of Riveted Railway Bridges on Existing Masonry Abutments: An Italian Case Study

Riveted railway bridges with already long structural lives can still be commonly found in service in Europe. In light of their peculiarities, they are often prone to fatigue damage; nevertheless, very few prescriptions regarding fatigue assessment of these structures can be found in current European provisions. Within this framework, the present paper illustrates the advanced fatigue assessment of an Italian riveted railway bridge selected as a case study. For this purpose, multi-scale finite element modelling of the bridge was developed, and the most critical details were assessed through application of the advanced strain energy density (SED) method. The obtained outcomes were compared both with other studies in the literature and prescriptions from the current and upcoming versions of EN1993-1-9.

Development of an optimal adaptive finite element stabiliser for the simulation of complex flows

An optimal adaptive multiscale finite element method(AMsFEM) for numerical solutions of flow problems modelled by the Oldroyd B model is developed. Complex flows experience instabilities due to a phenomena known as the high Weissenberg number problem. The stabilisers are terms in-cooperated into the variational formulation when applying the finite element method. For the selected few stabilisers, numerical experiments are performed to study the convergence of the solutions. These demonstrate that adaptive strategies reduce the computational load of flow simulation. A best performing combination of choice of stabiliser and adaptive strategy is suggested.

Local Deformation Analysis and Optimization of Steel Box Girder during Incremental Launching

Due to the significant weight of the steel box girder and the substantial gap between temporary piers, the stress concentration and localized deformation of the girder’s bottom plate are pronounced during the incremental launching construction process. In this study, the multi-scale finite element method was employed to simulate the incremental launching process of the steel box girder, analyze the pattern of localized deformation in the bottom plate contact area, and propose corresponding optimization control measures. Additionally, the entire incremental launching process was monitored, and the improvement in localized deformation before and after the optimization of the incremental launching scheme was analyzed. The results illustrate that the original incremental launching scheme led to substantial localized deformation in the bottom plate contact area of the steel box girder. Optimal control measures were implemented for the four incremental launching construction schemes. The optimal scheme significantly mitigated the localized deformation of the steel box girder’s bottom plate, with an average decrease in deformation of 48.32%. These findings can provide robust technical guidance and data support for the control of localized deformation in large-span steel box girders during the incremental launching construction process.

A Multiscale Modeling and Experimental Study on the Tensile Strength of Plain-Woven Composites with Hybrid Bonded-Bolted Joints.

CFRP hybrid bonded-bolted (HBB) joints combine the advantages of traditional joining methods, namely adhesive bonding, and bolting, to achieve optimal connection performance, making them the most favored connection method. The structural parameters of CFRP HBB joints, including overlap length, bolt-hole spacing, and fit clearance relationships, have a complex impact on connection performance. To enhance the connectivity performance of joint structures, this paper develops a multiscale finite element analysis model to investigate the impact of structural parameters on the strength of CFRP HBB joint structures. Coupled with experimental validation, the study reveals how changes in structural parameters affect the unidirectional tensile failure force of the joints. Building on this, an analytical approach and inverse design methodology for the mechanical properties of CFRP HBB joints based on deep supervised learning algorithms are developed. Neural networks accurately and efficiently predict the performance of joints with unprecedented combinations of parameters, thus expediting the inverse design process. This research combines experimentation and multiscale finite element analysis to explore the unknown relationships between the mechanical properties of CFRP HBB joints and their structural parameters. Furthermore, leveraging DNN neural networks, a rapid calculation method for the mechanical properties of hybrid joints is proposed. The findings lay the groundwork for the broader application and more intricate design of composite materials and their connection structures.

Nonlinear properties of uni-directional cellulose nanofiber-reinforced poly (lactic acid) composite filaments: a multiscale computational study

In the quest to elevate the mechanical properties of cellulose nanofiber-reinforced poly (lactic acid) composite materials for robust industrial applications, we conducted multiscale nonlinear finite element analysis rooted in homogenization theory. Our study delved into the intricate web of mechanical mechanisms and their pivotal influencers. This paper zeroed in on three paramount factors: the distribution of fibers, the fiber–matrix interface, and the aspect ratio of the fibers. For fiber distribution, we assumed fiber orientation control in fused filament fabrication and clarified the limit of material improvement by setting one-dimensional orientation as the upper limit. Our analysis of the fiber–matrix interface proposed a comprehensive three-scale structure, encompassing microstructures featuring intricate interfacial phases around the fibers, sub-microstructures with myriad dispersed fibers, and macrostructures subjected to external loads. The profound impact of the fiber–matrix interface on material properties was unveiled through a meticulous two-step homogenization process. Furthermore, we examined the substantial influence of the fiber aspect ratio on material properties. By unraveling the complex interplay among these critical factors, this research provided new design guidelines for fiber morphology to the performance of cellulose composites.

Multi-scale Modeling and Finite Element Analyses of Thermal Conductivity of 3D C/SiC Composites Fabricating by Flexible-Oriented Woven Process

Thermal conductivity is one of the most significant criterion of three-dimensional carbon fiber-reinforced SiC matrix composites (3D C/SiC). Represent volume element (RVE) models of microscale, void/matrix and mesoscale proposed in this work are used to simulate the thermal conductivity behaviors of the 3D C/SiC composites. An entirely new process is introduced to weave the preform with three-dimensional orthogonal architecture. The 3D steady-state analysis step is created for assessing the thermal conductivity behaviors of the composites by applying periodic temperature boundary conditions. Three RVE models of cuboid, hexagonal and fiber random distribution are respectively developed to comparatively study the influence of fiber package pattern on the thermal conductivities at the microscale. Besides, the effect of void morphology on the thermal conductivity of the matrix is analyzed by the void/matrix models. The prediction results at the mesoscale correspond closely to the experimental values. The effect of the porosities and fiber volume fractions on the thermal conductivities is also taken into consideration. The multi-scale models mentioned in this paper can be used to predict the thermal conductivity behaviors of other composites with complex structures.

Enhancing mode-II delamination resistance of hybrid woven composite materials of glass/Kevlar fabrics by stitching with Kevlar threads

This study analyzes the effects of stitching a hybrid composite beam on its Mode-II delamination to enhance the bonding between a Kevlar-Kevlar interface. The material under investigation is a composite material manufactured from fiberglass and Kevlar fabrics stitched together with Kevlar threads before the infusion of epoxy resin. End-notched flexure tests and multiscale finite element simulations are conducted to validate a glass/epoxy composite with a glass-glass interface. Calibrated simulations are then used to perform a parametric study on stitching parameters, including stitch spacing, pitch, and direction on a composite with a Kevlar-Kevlar interface. The parametric study on Kevlar-Kevlar specimens revealed an average improvement of 17 % in maximum load capacity and 103 % in tangent stiffness in stitched specimens compared to unstitched specimens. Additionally, increasing stitch density up to 0.02 mm−2 significantly enhances mechanical performance, while higher densities do not provide significant additional improvements.

Influence of thermal conductivity on evolution of grain morphology during laser-based directed energy deposition of CoCrxFeNi high entropy alloys

A model CoCrxFeNi high entropy alloy system was chosen to investigate the effect of thermal conductivity on the evolution of spatial orientation of columnar grain morphology during laser directed energy deposition. The thermal conductivity of the alloy was varied by tuning the chromium content in CoCrxFeNi alloys. CoCrxFeNi alloys with chromium content ranging between 0 and 24 at% were produced under identical processing conditions of laser direct energy deposition method. Electron back scattered diffraction images of the cross-sections revealed that the spatial orientation of grain morphology transitioned from zigzag columnar grains from layer-to-layer to near-continuous columnar grains across multiple layers with increased content of chromium in CoCrxFeNi. A multi-scale multi-physics finite element based thermo-kinetic model with consideration to multi-track multi-layer nature of the laser direct energy deposition technique was adopted to correlate the process thermo-kinetics with the evolution of microstructure. The computation calculations revealed that the decrease in thermal conductivity from 36 W/m.K (CoFeNi) to 26 W/m.K (CoCr24FeNi) at the melting point reduced the cooling rate from 3.3 ×104 °C/s to 1.3 ×104 °C/s in CoFeNi and CoCr24FeNi alloys, respectively. This subsequently evolved into increased degree of remelting of previously deposited layers and caused the direction of resultant thermal gradient to reorient towards the build direction. Such reorientation in resultant thermal gradient contributed to transition of spatial orientation of grain morphology from columnar zigzag microstructures from layer-to-layer to near continuous columnar grains across multiple layers. The present observation was verified compared with other reported metallic systems exhibiting zigzag and continuous columnar grains, and a unified mechanism underlining the role of thermal conductivity on microstructure evolution was proposed.

Collimated beam formation in 3D acoustic sonic crystals

We demonstrate strongly collimated beam formation, at audible frequencies, in a three-dimensional acoustic phononic crystal where the wavelength is commensurate with the crystal elements; the crystal is a seemingly simple rectangular cuboid constructed from closely-spaced spheres, and yet demonstrates rich wave phenomena acting as a canonical three-dimensional metamaterial. We employ theory, numerical simulation and experiments to design and interpret this collimated beam phenomenon and use a crystal consisting of a finite rectangular cuboid array of 4×10×10 polymer spheres 1.38 cm in diameter in air, arranged in a primitive cubic cell with the centre-to-centre spacing of the spheres, i.e. the pitch, as 1.5 cm. Collimation effects are observed in the time domain for chirps with central frequencies at 14.2 kHz and 18 kHz, and we deployed a laser feedback interferometer or Self-Mixing Interferometer – a recently proposed technique to observe complex acoustic fields—that enables experimental visualisation of the pressure field both within the crystal and outside of the crystal. Numerical exploration using a higher-order multi-scale finite element method designed for the rapid and detailed simulation of 3D wave physics further confirms these collimation effects and cross-validates with the experiments. Interpretation follows using High Frequency Homogenization and Bloch analysis whereby the different origin of the collimation at these two frequencies is revealed by markedly different isofrequency surfaces of the sonic crystal.