Multi-scale Finite Element Model Research Articles

Thermo-mechanical effects and microstructural evolution-coupled numerical simulation on the hot forming processes of superalloy turbine disk

Abstract Macroscopic deformation and microstructural evolution simultaneously exist in the hot forming processes of superalloy. In order to effectively and accurately study the hot forming processes of superalloy turbine disk with the numerical simulation method, a multi-scale finite element model of GH4065 superalloy turbine disk involving macroscopic and microscopic aspects was established by defining macro- and micromaterial model of superalloy, hot forming processing parameters, and boundary conditions. Via the numerical simulations of superalloy turbine disk, the macroscopic material flow and microstructural evolution behaviors in the hot forming processes of superalloy turbine disk were studied. Besides, the macroscopic deformation and microstructure distribution states after the hot forming processes were revealed and analyzed. A corresponding hot forming physical test of superalloy turbine disk was conducted to verify the results of the numerical simulation. Via the qualitative and quantitative analyses, it was concluded that the macroscopic deformation and microstructural evolution in the hot forming processes of superalloy turbine disk can be accurately predicted by the numerical simulation method.

Impact of fault slip induced by water injection on casing deformation: a numerical study

Fluid injection can cause fault reactivation and slip due to weakened cementation strength. The resulting fault slippage poses significant challenges to wellbore and casing integrity. To address this, we developed a multi-scale 3D finite element model, integrating reservoir, and near-wellbore components and applied to an offshore well in China’s ZD Reservoir, an area that has experienced fault reactivations (and casing deformations of wells intersecting reactivated faults) due to routinely water injection in nearby wells. Based on the actual formation’s wellbore-fault angle, a full-size fault is inserted into the model. The traction–separation law (TSL) describes progressive fault damage induced by waterflooding. The model also simulates the impact of fault slippage on cement failure and casing deformation. Research findings indicate that fluid injection reduces friction and shear cementation strength between faults, leading to reactivated fault slippage. The slip process involves three stages: low-level, sharply rising, and high-level stages, each exhibiting reduced fault friction and shear cementation strength. These outcomes provide insights to prevent casing damage during water flooding, optimizing injection points, or using better cement recipes at minimal cost.

Novel modification strategy via GO and polyurethane for epoxy nanocomposites: Simultaneous enhancements of fracture toughness and liquid oxygen compatibility for cryotank applications

Fracture toughness and liquid oxygen (LOX) compatibility of epoxy nanocomposites for liquid oxygen composite cryotank applications are two main concerns. In this work, a novel rigid-and-soft hybrid-microstructure modification strategy is proposed to improve these two properties simultaneously. Graphene oxide (GO) nanosheets are physically incorporated, and polyurethane (PU) particles are formed through phase-separation process. When 10 parts of PU and 0.1 parts of GO are added into 100 parts of epoxy (i.e., 10 phr PU and 0.1 phr GO), the fracture toughness is enhanced by 207.26 % at room temperature and 243.02 % at 90 K, respectively. Meanwhile, no sensitivity phenomena such as explosion, burning, flash, or charring for the nanocomposite are observed during liquid oxygen impact testing. Consequently, experimental characterizations and multiscale finite element models are utilized to reveal the synergistic effects of GO and PU on fracture behaviors and impact energy absorption.

Multi-scale study on the mechanical properties of concrete based on crack propagation under hygrothermal coupling

During the long-term service of structures, the environmental temperature and humidity fields can lead to the evolution of the pore structure within concrete materials, thereby affecting changes in mechanical properties. However, the mechanisms of their influence still need further clarification and are challenging to correlate for prediction. Addressing this specific issue, the current study focuses on evaluating 78 cubic concrete specimens with C30 and C40 strength grades. These specimens were subjected to a 95 % humidity environment at temperatures of 40 °C, 60 °C, and 80 °C for durations of 30, 60, and 90 days. The research involved conducting both microstructural and macroscopic mechanical tests to quantify the evolution of internal hydrates, pore structures, and pore distribution, as well as to assess the changes in the macroscopic mechanical properties of the specimens. To accurately predict the process, a multiscale finite element model (FEM) based on the bilinear continuum cohesive damage model was established. This model quantifies the changes in mechanical properties of mesoscopic three-phase concrete due to microcrack evolution under hygrothermal coupling. To facilitate multiscale simulations between the Representative Volume Element (RVE) and macroscopic scale models, relevant subroutines were written using Umath, and parallel computing was employed to reduce the computational burden. For the macroscopic model in this study, a homogenized concrete cube model with dimensions identical to the experimental specimens was selected. The effectiveness of the parallel computational model was validated by comparing and analyzing the simulation results under uniaxial compression with the experimental data. The findings indicate that hygrothermal action leads to the initiation and expansion of microcracks within the concrete, thereby impacting the alteration of its mechanical properties. In addition, the parallel computing-based multiscale FEM can more accurately quantify the typical damage process of crack propagation while reducing the computational load and may provide relatively accurate predictions of the mechanical characteristics of concrete under the influence of hygrothermal coupling, ensuring effective modeling of macroscopic structural specimens in various temperature and humidity environments.

An efficient parameterized neural network enhanced multiscale finite element modeling for triply periodic minimal surface meta-structures and its applications for femur

Triply periodic minimal surface (TPMS) multiscale structures are meta-structures known for their low-weight-high-strength property. Because of their delicate geometry and sheet-networks feature, a fine mesh is required for finite element analysis, which is computationally expensive for conventional direct numerical simulation. To resolve this issue, this study develops a neural network enhanced finite element method (NN-FEM) for parameterized TPMS multiscale meta-structures. The multiscale homogenization approach replaces the complicated representative volume elements (RVEs) with a surrogate homogenized material model. The surrogate process is accomplished by deep learning of artificial neural networks (NN) with an effective boundary displacement gradient and the Helmholtz free energy of RVEs. The NN-trained surrogate material model is deployed on the macroscale Galerkin finite element model for various field tests. The parameterized structural information of TPMS can also be embedded into the NN model to resolve the hidden constitutive relation of RVEs with unique geometries. Numerical examples are provided to benchmark the efficacy and efficiency of NN-FEM on the parameterized TPMS structure. The proposed model can be applied to femurs for rapid stress analysis and osteoporosis detection.

Shaking table tests on inclined collapse mechanism of RC frame structures subjected to earthquakes

Inclined collapse of structures under strong earthquakes threatens the adjacent infrastructures. The collapse mode and collapse direction should be considered with caution to curb the secondary disaster in the urban area. However, current studies on the inclined collapse mechanism are predominantly limited to the qualitative and intuitive understanding. To fill this gap, this study presents an insight into the inclined collapse mechanism of the reinforced concrete (RC) frame structures with two typical features subjected to earthquakes, i.e., the structures with slab opening on one side of the first floor and the structures with disparate axial compression ratios of the first story columns on the opposite sides. First, shaking table tests were performed on two 1/10-scale three-story RC frame structure models undergoing inclined collapse. Then the multi-scale finite element models were established, validated against the test results and used for parametric studies. In the parametric studies, two coefficients were considered to describe the typical features of the RC frame structures, i.e., the strong column-weak beam ratio η and differential rate of the axial compression ratios λ. The test and numerical results found that the inclined collapse mechanism was attributed to the different distributions and discrepant resistance deterioration of the plastic hinges among the first story columns of the RC frame structures with the two features. This causes the inconsistent damage levels among the first story columns, the dominant direction of the lateral displacement, and the inclined collapse of the structures. Finally, the collapse mode and collapse direction can be controlled by appropriately adjusting the two coefficients η and λ for the structures with the typical features concerned in this study.

Ultimate bearing capacity analysis of self-anchored suspension bridge with steel box girders considering local buckling

The local stability may dominate the design of a self-anchored suspension bridge with steel box girders. Due to geometric imperfections and welding residual stresses rarely considered for its ultimate bearing capacity analysis, the influences of the local buckling on the global structural behavior remain unknown. This paper presents a multi-scale finite element (FE) model for a self-anchored suspension bridge incorporating geometric imperfections and residual stresses in a steel box girder segment simulated by shell elements. Also, the pattern considering the defects in the shell FE model is validated by experiments. An extended parametric study is carried out via multi-scale FE models under various defects. Results illustrate that: ➀ the effects of local buckling on the ultimate bearing capacity of the bridge is small and can be ignored if geometric imperfections and residual stresses are not considered; ➁ the influences of local buckling becomes significant if geometric imperfections and residual stresses are included; and ➂ ultimate bearing capacity decreases with increase of defects, with geometric imperfection being the main factor influencing the ultimate bearing capacity of the bridge. Additionally, the thickness of steel plates has significant influences on the ultimate bearing capacity of the bridge. A comparison between the EN 1993–1-5 and the FE analysis results indicates that the former is conservative. This study provides useful insights for analyzing and designing local buckling from the perspective of steel bridge system.

The Use of Virtual Tissue Constructs That Include Morphological Variability to Assess the Potential of Electrical Impedance Spectroscopy to Differentiate between Thyroid and Parathyroid Tissues during Surgery.

Electrical impedance spectroscopy (EIS) has been proposed as a promising noninvasive method to differentiate healthy thyroid from parathyroid tissues during thyroidectomy. However, previously reported similarities in the in vivo measured spectra of these tissues during a pilot study suggest that this separation may not be straightforward. We utilise computational modelling as a method to elucidate the distinguishing characteristics in the EIS signal and explore the features of the tissue that contribute to the observed electrical behaviour. Firstly, multiscale finite element models (or 'virtual tissue constructs') of thyroid and parathyroid tissues were developed and verified against in vivo tissue measurements. A global sensitivity analysis was performed to investigate the impact of physiological micro-, meso- and macroscale tissue morphological features of both tissue types on the computed macroscale EIS spectra and explore the separability of the two tissue types. Our results suggest that the presence of a surface fascia layer could obstruct tissue differentiation, but an analysis of the separability of simulated spectra without the surface fascia layer suggests that differentiation of the two tissue types should be possible if this layer is completely removed by the surgeon. Comprehensive in vivo measurements are required to fully determine the potential for EIS as a method in distinguishing between thyroid and parathyroid tissues.

Study of the Impact of Varying Inclination Angles of Arch Ribs on the Seismic Behavior of Half-Through Steel Basket-Handle Arch Bridge

In the present study, multiscale finite element (FE) models of half-through steel basket-handle arch bridges were established. The eigenvalue analyses were conducted to explore the dynamic characteristics of the arch bridges based on the FE models. In addition, a parametric analysis was carried out to investigate the impact of the inclination angle of the arch rib (0°, 4°, and 7°) on the longitudinal and transverse seismic performances of arch bridges. The results show that with the increase in inclination angle, the out-of-plane stiffness of half-through steel basket-handle arch bridges increases, resulting in the natural period of the structure becoming shorter from 3.09 s to 2.93 s. Adjusting the inclination angle appropriately has a beneficial impact on the overall seismic performance of the structures, affecting both displacement and internal forces, in which the most significant improvements include a 42.8% decrease in displacement and a 62.6% reduction in internal forces. Adjusting the inclination angle can cause the arch springing and transverse brace to undergo larger plastic deformation. It is advisable to judiciously enlarge the sectional dimensions and enhance the material strength of both the arch springing and the transverse bracing in seismic designs.

Multiscale Static Compressive Damage Characteristics of Kiwifruit Based on the Finite Element Method.

In the handling or processing process, fruits are easily crushed by external loads. This type of damage in fruit often leads to the internal pulp browning and rotting, with the severity largely dependent on the fruit tissue's geometric and mechanical properties. In kiwifruits, with their thin skin and dark-colored flesh, it is particularly challenging to observe and analyze the damage caused by extrusion through traditional experimental methods. The objective of this research is to construct a multi-scale finite element model encompassing the skin, flesh, and core by measuring the geometric and mechanical properties of kiwifruit, to assess and predict the damage characteristics under compression, and to verify the accuracy of the finite element model through experiments. The results indicated that kiwifruits demonstrated different compressive strengths in different directions during compression. The compressive strength in the axial direction was higher than that in the radial direction, and there was little difference between the long and short radial directions. The flesh tissue is the most vulnerable to mechanical damage under external compression, followed by the core. At strain levels below 5%, there was no noticeable damage in the axial or radial directions of the kiwifruit. However, when strain exceeded 5%, damage began to manifest in some of the flesh tissue. To maintain fruit quality during storage and transportation, the stacking height should not exceed 77 fruits in the axial direction, 48 in the long direction, and 53 in the short direction. The finite element analysis showed that the established model can effectively simulate and predict the internal damage behavior of kiwifruits under compression loads, which is helpful for a deeper understanding of the mechanical properties of fruits and provides a theoretical basis and technical guidance for minimizing mechanical damage during fruit handling.

Comparative study on fatigue evaluation of suspenders by introducing actual vehicle trajectory data

Suspenders play a crucial role in transmitting loads from the bridge deck to the main cable in a suspension bridge. They are susceptible to fatigue due to repeated dynamic loads, particularly traffic loads. Traffic Load Models (TLMs), typically created using Monte–Carlo simulation and Weigh-In-Motion (WIM) data, are employed to evaluate this fatigue. However, these models often overlook practical vehicle trajectories and spatio-temporal distribution, which compromises the precision of fatigue assessments. In this study, we introduce a novel 2D Intelligent Driver Model (2D-IDM) that incorporates actual vehicle trajectories, with a particular focus on transverse vehicle movement. This enhancement aims to improve the fidelity of existing TLMs. To provide a clear, qualitative, and quantitative understanding of the effects of fatigue evaluation with or without actual trajectory characteristics, we have structured this paper as a comparative study. We compare our proposed model, denoted as TLM S-3, with two observation-based models (O-1 and O-2) and two simulation-based models (S-1 and S-2). We conducted an experimental case study on a long-span suspension bridge, where the actual traffic load trajectory was obtained using a WIM-Vision integrated system. To calculate fatigue damage considering both longitudinal and transverse directions, we established a multi-scale Finite Element Model (FEM) using solid element types to simulate the bridge girder. This model can generate the stress influence surface of the bridge and has been verified in both static and dynamic aspects. Our detailed comparative analysis demonstrates the consistency of the proposed 2D-IDM with the actual measured traffic load trajectories. This indicates that our approach can enhance the fidelity and precision of fatigue evaluations for bridge suspenders.

Multiscale Finite Element Modeling of the Effect of Macro-Encapsulated Phase-Change Materials on the Thermal Performance of Hydronic Floor Heating Systems

Phase-change materials (PCMs) are commonly employed in building service equipment to regulate indoor temperatures and reduce energy consumption. This study conducted multi-scale finite element modeling to analyze the steady-state and dynamic thermal behavior of a hydronic radiant floor heating system integrated with macro-encapsulated PCMs. It predicted performance values for hydronic floor heating with and without macro-encapsulated PCMs. The study assessed the impact of the PCM volume fraction, heating water temperature, capsule thermal conductivity, and shape on the thermal performance of hydronic floor heating through various finite element models. The predictive capability of the finite element model was validated using experimental data, showing good agreement. Although the inclusion of PCMs lowered the floor temperature, it improved temperature distribution and retained heat when the system was inactive. The PCM volume fraction significantly influenced the performance of the hydronic floor. However, the shape of the macro-encapsulated PCM and thermal conductivity of the shell had minimal effects in the studied case. For instance, increasing the thermal conductivity of the shell of the PCM capsule fifty times from 0.3 to 15 W m−1 K−1 resulted in an increase in surface temperature by 1.2 °C.

Computational Optimization of Sandwich Silicone Rubber Composite for Improved Thermal Conductivity and Electrical Insulation.

The efficient dissipation of heat has emerged as a crucial concern for modern electronic devices, given the continuous increase in their power density and consumption. Thus, the utilization of thermally conductive but electrically insulating silicone rubber composites as a thermal interface material has garnered significant interest. In this study, the effects of the filler volume fraction, filler orientation, layer volume fractions, layer configuration, and a number of layers on the thermal conductivity and electrical resistivity of silicone rubber composites were examined using a multiscale finite element modeling strategy. The results demonstrated that modification of the filler orientation can change the thermal conductivity by 28 and 21 times in the in-plane and through-thickness directions, respectively. The in-plane thermal conductivities of silicone rubber/boron nitride and silicone rubber/expanded graphite layers exhibit a percolation phenomenon at filler volume fractions of 35% and 30%, respectively. The electrical resistivity of the composite increases exponentially with a decrease in the number of layers.

Tensile mechanical behavior and failure mechanism of 2.5D woven fabric reinforced aluminum matrix composites involving residual stress

The tensile behavior of two and a half-dimensional (2.5D) woven fabric reinforced Al matrix composites involving residual stress was investigated experimentally and numerically. The residual stress and subsequent tensile behavior of the composites were predicted by multiscale finite element modeling. And the correctness of numerical simulation is verified by residual stress, tensile curve, surface strain diagram and fracture morphology. The results show that the inhomogeneous residual stress leads to the damage of the matrix and interface in the interweaving area of yarns. During the tensile process, the surface strain exhibits an obvious periodic distribution characteristic, which is related to the arrangement of yarns. With the increase of tensile strain, local matrix and interface damage accumulate and expand leading to the weft yarn cracking, matrix failure and interface debonding successively. The abrupt fracture of the composite can be attributed to the axial fracture of warp yarn, which exhibits obvious fiber fracture and pull-out characteristic.

In-silico simulation of nanoindentation on bone using a 2D cohesive finite element model

This study proposed and validated a 2D finite element (FE) model for conducting in-silico simulations of in-situ nanoindentation tests on mineralized collagen fibrils (MCF) and the extrafibrillar matrix (EFM) within human cortical bone. Initially, a multiscale cohesive FE model was developed by adapting a previous model of bone lamellae, encompassing both MCF and EFM. Subsequently, nanoindentation tests were simulated in-silico using this model, and the resulting predictions were compared to AFM nanoindentation test data to verify the model's accuracy. The FE model accurately predicted nanoindentation results under wet conditions, closely aligning with outcomes obtained from AFM nanoindentation tests. Specifically, it successfully mirrored the traction/separation curve, nanoindentation modulus, plastic energy dissipation, and plastic energy ratio obtained from AFM nanoindentation tests. Additionally, this in-silico model demonstrated its ability to capture alterations in nanoindentation properties caused by the removal of bound water, by considering corresponding changes in mechanical properties of the collagen phase and the interfaces among bone constituents. Notably, significant changes in the elastic modulus and plastic energy dissipation were observed in both MCF and EFM compartments of bone, consistent with observations in AFM nanoindentation tests. These findings indicate that the proposed in-silico model effectively captures the influence of ultrastructural changes on bone's mechanical properties at sub-lamellar levels. Presently, no experimental methods exist to conduct parametric studies elucidating the ultrastructural origins of bone tissue fragility. The introduction of this in-silico model presents an invaluable tool to bridge this knowledge gap in the future.

Simulation-based evaluation of effects of fabric structure on thermal conductivity of various 2D woven composites

The thermal conductivities of woven composites are strongly affected by the anisotropic properties of the reinforcing fibers, and thus by the fabric structure. In this study, the thermal conductivity of 2D woven composites was investigated by optimizing the fabric structures to enhance the through-thickness and in-plane thermal conductivities. Multiscale finite element models were developed to simulate the thermal behavior of various 2D fabric structures and evaluate their thermal performance under varying conditions, focusing on the effects of fiber tow undulation, dry-zone porosity, and matrix-rich zones. Fabric architectures were selected based on common 2D weavings of composites. The results showed that the tow undulation substantially enhanced the through-thickness conductivity and mitigated the impact of porosity. In addition, a higher tow anisotropy increased the effect of undulation. Moreover, the plain-weave fabric structures exhibited the highest through-thickness and in-plane thermal conductivities among the evaluated 2D woven fabrics in porous composites. Finally, the matrix-rich zones showed a stronger effect on the through-thickness than on the in-plane thermal conductivity of the 2D woven composites.

Parametric study of CNT waviness effect in CNT/polymer nanocomposites using multiscale finite element modeling

The effect of CNT waviness on the elastic properties of CNT-reinforced polymer nanocomposites is investigated using multiscale finite element modeling. CNT and the interphase are modeled at the nanoscale as discrete structures of beams and trusses, and the polymer matrix is treated as a microscale continuum medium. Using the model, a parametric study of the effect of CNT waviness is carried out. The effect of CNT waviness is also calculated using a three-phase Mori-Tanaka micromechanical model, and the results are compared. The model is validated with molecular dynamics simulation results and experimental data available in the literature.

Mechanical properties prediction of ductile iron with spherical graphite using multi-scale finite element model

In this paper, using the multi-scale finite element method, the effect of graphite particles on the mechanical behavior of ductile iron has been investigated under tensile loading. For this purpose, taking into account the spherical geometric shape of the graphite phase and considering a specific volume fraction, these spheres are randomly placed in the whole body and a two-component composite material is created. As a next step, a micromechanical model of these materials is developed by defining the mechanical properties of the matrix and graphites as well as their interfaces. The mechanical properties of the matrix are simulated using the Ramberg-Osgood elastic-plastic model. By simulation in ABAQUS software and using nonlinear dynamic analysis, the effects of volume percentages and adhesion of graphite particles with matrix on the direct tensile load-displacement behavior of ductile iron were investigated. The results of experimental tests were used to verify the results of the numerical model. The weight percentage of graphite particles has a significant effect on the tensile strength and elastic modulus of these cast irons. The results show that with the increase in the amount of graphite particles, the tensile strength of cast iron increases up to a certain value and then reverses. With 21% graphite particles, the maximum tensile strength of ductile iron is 601 MPa. Compared with a pure sample of cast iron, the tensile strength increases by approximately 13.4% for this weight percentage of graphite particles.

Distribution and evolution of low-energy twin boundary density in time−space domain during isothermal compression for Ni80A superalloy

Adjusting the density of low-energy boundary, i.e., Σ3n twin boundary, in a thermal-plastic deformation process is a significant approach to enhance grain boundary-related properties for an alloy. In order to uncover the distribution and evolution of twinboundary density in a current-heating forming process, and their inner mechanisms dependent on grain size and stored-energy, an electrical−thermal−mechanical multi-field coupling and macro-micro multi-scale coupling finite element model was established. Simulation results of isothermal compression processes for Ni80A superalloy show that twin-boundary density keeps constant in the heating and holding stages, while it increases quickly and then intends to decrease in the compressing stage. Its distribution gets more homogeneous under high temperature and medium strain rate. The processing parameter domains corresponding to finer grain size and higher stored-energy, as well as higher dynamic recrystallization degree, contribute to promoting the twinboundary density.

Prediction of elastic properties of 3D4D rotary braided composites with voids using multi-scale finite element and surrogate models

The conventional evaluation of 3D braided composites' mechanical properties through numerical and experimental methodologies serves as a hindrance to material application owing to the considerable expenses, time constraints, and laborious efforts involved. Moreover, the presence of void defects induced during the processing exacerbates this challenge. In this study, a multi-scale finite element model (FEM) and a surrogate model are established for predicting elastic properties of three dimensional four directional (3D4D) rotary braided composites with voids for the first time. Based on the established FEM, a comprehensive dataset containing 768 data points is formed, covering the ranges of both design parameters and void defect parameters. The influence of braiding angle, yarn width, and porosity, on the elastic constants of 3D4D rotary braided composites is accurately analyzed. A genetic algorithm-optimized back propagation neural network (GABPNN) model is developed, which possess the capability to replicate FEM outcomes with a commendable R-value of 0.99. The remarkable concordance between the anticipated outcomes and experimental datasets corroborates the triumphant implementation of the present method in unraveling the interconnections between microstructure and properties in 3D4D rotary braided composites containing voids. Consequently, this offers a propitious instrument for expediting the intelligent conception and refinement of composite materials.