Multi-scale Finite Element Model Research Articles

Experimental and numerical study on the mechanical behavior of 3D printed re-entrant auxetic structure filled with carbon nanotubes-reinforced polymethylmethacrylate foam

The present study aimed to develop the finite element method to examine the mechanical behavior of 3D printed re-entrant auxetic structure filled with nanoparticle-reinforced foams under in-plane uniaxial quasi-static compressive loading. A multi-scale finite element model of the nanocomposite is created by considering the randomly distributed carbon nanotubes (CNT) in the Polymethylmethacrylate (PMMA) polymer matrix for a specific volume fraction. The interaction between CNT and PMMA foam was simulated using the cohesive zone model (CZM). The effect of the volume fraction of carbon nanotubes and the geometric characteristics of the structure on the performance of these structures is examined. Results from the finite element study are validated by the samples manufactured using 3D printing and experimental testing results. The results show that the addition of carbon nanotubes to the re-entrant auxetic structure avoids the sharp reduction of force after the peak point, while the use of 2 wt.% of carbon nanotubes increases the maximum fracture force up to 75%. Results indicate optimal values for carbon nanotube volume fraction and the thickness of the cell walls, for which energy absorption has the highest value. It is concluded that adding 2 wt.% carbon nanotubes to the PMMA foam increases the energy absorption up to 130%.

Multiscale model construction and modulus prediction of needle-punched carbon/carbon composites

In this paper, the modulus prediction of NP-C/C is completed by establishing a multiscale finite element model, and the influence weight analysis of the modulus is carried out by using the analytical homogenization method. Firstly, three Micro-RVE, including unidirectional composites, short fiber reinforced composites and porous matrix, are established to characterize the layers of NP-C/C. Then, the finite element model is used for homogenization and passed upward into Meso-RVE, and the modulus prediction is completed. Finally, the analytical homogenization method is used combined with the MATLAB® script to analyze the influence weight of the modulus by adjusting the parameters. The results show that the average errors of stiffness coefficient prediction values obtained based on the analytical homogenization method are only 6.0% relative to the experimental values, which are lower than 25.3% of the finite element model. The modulus prediction method given in this study does not need to establish a micromechanical model with complex structure, and can be directly completed by computer script when the prediction accuracy is met, which is simple and feasible.

Progressive failure analysis of needle-punched C/SiC composites based on multiscale finite element model

Progressive failure analysis of needle-punched C/SiC composites based on multiscale finite element model

A new multi-scale modeling method for needled C/C composites

Needled composites have stronger interlaminar properties compared to two-dimensional fiber composite structures due to the introduction of z-directional fibers in the fiber composite layup. An effective multi-scale finite element model is developed in this paper for the complex structure of needle-punched composites. Three scales, namely fRVE, pRVE, and lRVE, are modeled from the fiber scale, the delamination scale, and the laminate scale. using ABAQUS, periodic boundary conditions are applied to the RVEs at different scales to obtain the effective mechanical properties of various RVEs. Meanwhile, the effect of needling density on the needled composites is predicted by applying the above multi-scale model. The increase of needling density can enhance the out-of-plane effective mechanical properties of the composites, but it also weakens the in-plane effective mechanical properties. The maximum error of the elastic modulus calculation is 17.68% with that of the reference, thus verifying the rationality of the multi-scale model.

Numerical Investigation of Effects of Camlock System on Thermal Conductivity of Structural Insulated Panels

Structural insulated panels (SIPs) are widely used in residential and commercial buildings due to their reliable mechanical and thermal performance. However, using framing members and nails to join SIPs causes thermal bridging across the insulation and thus increases heat losses from the building envelope. Alternatively, SIPs joined with embedded camlock systems can overcome this issue. In this paper, a parametric study of the effects of the camlock system material and SIP geometric design on the thermal performance of SIP walls was investigated using a multi-scale finite element modeling approach. The model considers the structural design details of the camlock system. In addition, the effects of the SIP materials, SIP thickness, and the number of camlock systems per unit area on the through-thickness thermal conductivity of the SIP walls are examined. It was found that the SIP thickness is a dominating factor influencing the thermal performance of the SIP. The through-thickness (overall) thermal conductivity of the SIP wall increases linearly with the increase in the number of camlock systems used per unit area. However, it rises exponentially with the increasing SIP thickness. The reduction in the overall R-value of the SIP caused by the camlock system embedded in the SIP did not exceed 13.8%.

Pharmacokinetic Study of Triptolide Nanocarrier in Transdermal Drug Delivery System-Combination of Experiment and Mathematical Modeling.

Compared with traditional oral and injection administration, the transdermal administration of traditional Chinese medicine has distinctive characteristics and advantages, which can avoid the "first pass effect" of the liver and the destruction of the gastrointestinal tract, maintain a stable blood concentration, and prolong drug action time. However, the basic theory and technology research in transdermal drug delivery are relatively limited at present, especially regarding research on new carriers of transdermal drug delivery and pharmacokinetic studies of the skin, which has become a bottleneck of transdermal drug delivery development. Triptolide is one of the main active components of Tripterygium wilfordii, which displays activities against mouse models of polycystic kidney disease and pancreatic cancer but its physical properties and severe toxicity limit its therapeutic potential. Due to the previously mentioned advantages of transdermal administration, in this study, we performed a detail analysis of the pharmacokinetics of a new transdermal triptolide delivery system. Triptolide nanoemulsion gels were prepared and served as new delivery systems, and the ex vivo characteristics were described. The metabolic characteristics of the different triptolide transdermal drug delivery formulations were investigated via skin-blood synchronous microdialysis combined with LC/MS. A multiscale modeling framework, molecular dynamics and finite element modeling were adopted to simulate the transport process of triptolide in the skin and to explore the pharmacokinetics and mathematical patterns. This study shows that the three-layer model can be used for transdermal drug delivery system drug diffusion research. Therefore, it is profitable for transdermal drug delivery system design and the optimization of the dosage form. Based on the drug concentration of the in vivo microdialysis measurement technology, the diffusion coefficient of drugs in the skin can be more accurately measured, and the numerical results can be verified. Therefore, the microdialysis technique combined with mathematical modeling provides a very good platform for the further study of transdermal delivery systems. This research will provide a new technology and method for the study of the pharmacokinetics of traditional Chinese medicine transdermal drug delivery. It has important theoretical and practical significance in clarifying the metabolic transformation of percutaneous drug absorption and screening for appropriate drugs and dosage forms of transdermal drug delivery.

On the possibility of estimating myocardial fiber architecture from cardiac strains.

The myocardium is composed of a complex network of contractile myofibers that are organized in such a way as to produce efficient contraction and relaxation of the heart. The myofiber architecture in the myocardium is a key determinant of cardiac motion and the global or organ-level function of the heart. Reports of architectural remodeling in cardiac diseases, such as pulmonary hypertension and myocardial infarction, potentially contributing to cardiac dysfunction call for the inclusion of an architectural marker for an improved assessment of cardiac function. However, the in-vivo quantification of three-dimensional myo-architecture has proven challenging. In this work, we examine the sensitivity of cardiac strains to varying myofiber orientation using a multiscale finite-element model of the LV. Additionally, we present an inverse modeling approach to predict the myocardium fiber structure from cardiac strains. Our results indicate a strong correlation between fiber orientation and LV kinematics, corroborating that the fiber structure is a principal determinant of LV contractile behavior. Our inverse model was capable of accurately predicting the myocardial fiber range and regional fiber angles from strain measures. A concrete understanding of the link between LV myofiber structure and motion, and the development of non-invasive and feasible means of characterizing the myocardium architecture is expected to lead to advanced LV functional metrics and improved prognostic assessment of structural heart disease.

Multi-scale modeling and experimental study on electrosprayed multicore microcapsule-based self-healing polymers

In this study, we promote a multi-scale modeling to predict the healing efficiencies (HEs) of incorporated polymers with self-healing microcapsules. The Python scripts were employed to generate three representative volume elements (RVEs) with randomly dispersed 5, 7.5, and 10% volume fraction (VF) of alginate microcapsules. Three VUSDFLD subroutines were codded and supplemented with ABAQUS/Explicit solver to obtain the maximum tensile stresses (Sut) of virgin, damaged, and healed samples followed by calculating HF of self-healing polymers. Based on the simulation results, more incorporation of self-healing microcapsules increased the tensile after impact HF, so that HFs were increased from 46.31% for RVEs containing 5% VF up to 65.41% and 84.84% for 7.5% and 10% VF, respectively. The presence of more self-healing microcapsules could improve the chance of rupturing more filled microcapsules with healing agents after crack propagation due to impact damages in the matrix. Thus, more damaged elements would be healed by spread healing agents. To evaluate the reliability of simulation results, the specimens containing electrosprayed multicore self-healing microcapsules were fabricated, and experimental HFs were calculated. The same trend was obtained for experimental results, as acquired in the simulation of RVEs. The error of healing efficiencies were only 6.82%, 2.81%, and 7.74 for incorporated specimens with 5, 7.5, and 10% VF of electrosprayed multicore microcapsules, respectively, indicating the accuracy of introduced multi-scale finite element modeling. The fabrication defects of experimental specimens can be the reason of simulation errors.

Behaviour of non-ballast pre-stressed and precast track structures in high speed railway based on multiscale finite element model

In order to make further study on the mechanical property of CRTSIII type slab non-ballast track structures, which was self-designed in China, based on the method of the multiscale finite element model (FEM), the traditional FEM of slab non-ballast track structures was improved. The multiscale FEM of CRTSIII type slab non-ballast track structures was established based on the general finite element program ABAQUS. Then the comparative calculation was made between various FEMs, showing that the high solution precision, fast modelling speed and high solution efficiency could be obtained. Therefore, the multiscale FEM was suitable for the parametric study on mechanical behaviour of CRTSIII type slab non-ballast track structures, and then the key influence factor and constructions could be optimized.

A micromechanical based finite element model approach to accurately predict the effective thermal properties of micro-aerated chocolate

Micro-aeration is a method to modify the sensorial attributes of chocolate but also affects the material properties of chocolate, which in turn, determine its material response during manufacturing and oral processes. This study aims to define the effect of micro-aeration on the thermal properties of chocolate by considering the changes of chocolate microstructure due to micro-aeration. Micro-aeration was found to alter the chocolate microstructure creating a layer of a third phase at the porous interfaces, which is argued to consist of cocoa butter of higher melting properties. A multiscale Finite Element Model is developed, which was confirmed by macroscale heat transfer measurements, to parametrically simulate the structural changes of micro-porous chocolates at the microscale level and estimate their effective properties, such as thermal conductivity and specific heat capacity. The developed multiscale computational model simulates the porous chocolate as a two-phase (chocolate- pores) or three-phase material (chocolate-cocoa butter layer- pores). The investigation identified a new, complex transient thermal mechanism that controls the behaviour of micro-aerated chocolate during melting and solidification. The results showed a maximum 13% reduction of keff and 15% increase of Cpeff with 15% micro-aeration resulting to a slower transient heat transfer through the micro-aerated chocolate. The reason is that the micro-aerated chocolate can store a larger amount of thermal energy than its solid counterpart. This effect slows down the transient heat transfer rate in the chocolate and modifies melting/solidification rate and impacts sensorial attributes during oral processing and cooling during manufacturing.

Multi-scale modelling of deformation heterogeneities in explosively welded layered sheets

A multi-scale numerical investigation of local heterogeneities in the strain and stress fields occurring during forming of explosively welded layered metallic sheets is the main goal of the research. Explosive welding is a complex process involving various phenomena occurring in materials during an impact at high velocities and pressures, especially at the interfaces of colliding metals. As a result, the interface of the layered metallic sheets is often highly heterogeneous at the microscale level, what directly affects the sheet behaviour under subsequent forming conditions. To investigate this issue, the mesh-free numerical model of the explosive welding process is used first to recreate the characteristic features of the interface morphology. Various detonation velocities are used to provide diversified morphological features at the interface. Obtained results are then used as input data to develop the concurrent multi-scale finite element model of material behaviour under deformation conditions. The multi-scale modelling concept with explicit representation of the interface region is used. The highly refined heterogeneous FE mesh was generated in the interface region to capture local heterogeneities occurring at the microscale. Particular attention is put on numerical investigation of an influence of interface morphology in the welding zone on the development of the stress localisation that may directly lead to fracture initiation during forming.

A simplified method for fatigue life evaluation of welded joints in OSD considering welding residual stress relaxation

The welding residual stress at the welded joints of orthotropic steel decks (OSD) has a significant influence on the fatigue life, and welding residual stress relaxation (WRSR) occurs under vehicle loading. The existing fatigue evaluation method for steel bridges does not consider the WRSR on fatigue life and may cause a large deviation between the fatigue life prediction results and the fatigue cracking in the field. This paper proposes a simplified fatigue life evaluation method that can consider WRSR quantitatively. First, the initial welding residual stress (IWRS) distribution model is established based on residual stress tests and numerical simulation. Second, the simplified mechanical model of the coupled effect of IWRS and vehicle-induced structural stress as well as the law of WRSR are established via stress analysis at the weld toe section of DRWJs under external loading. Furthermore, the peak/valley value of the coupled effect of IWRS and vehicle-induced structural stress are determined, and a stress time-history simplification method considering WRSR is proposed. On this basis, a simplified fatigue life evaluation method considering the WRSR of DRWJs on OSDs is finally proposed and combined with the Q345 steel full-range SN curve model. The Jiangyin Yangtze River Highway Bridge is used as an example to demonstrate the fatigue life evaluation procedure of this proposed model in detail. Based on the multiscale finite element model (FEM) considering the coupling effect of the WRS and vehicle loading stress, the real stress time-history curves of DRWJs under vehicle loading cases are extracted and compared to those of the simplified method. Based on the full-range SN curve model considering IWRS and WRSR, the fatigue life of the welding joints of Jiangyin Bridge is finally calculated, and the results are more accurate and closer in value to the field observations of fatigue cracking when compared with the Eruocode3 standard. This provides a theoretical basis for fatigue analysis and lifetime assessment technology of large span highway steel box girder bridges.

Adaptive hierarchical multiscale modeling for concrete trans-scale damage evolution

This work presents an adaptive hierarchical multiscale approach for modeling the trans-scale damage evolution in concrete. The problem domain represented by an adaptive hierarchical multiscale finite element (FE) model is decomposed into two regions, namely the macroscopic elastic region and the multiscale critical region prone to damage. The former is simulated only by macroscopic elements, while the latter is modeled by both macroscopic elements and the coupled-volume mesoscopic FE samples assigned to the integration points belonging to these macroscopic elements. A model update criterion is proposed to adaptively identify the multiscale critical region during the loading process. Innovatively, the coupled-volume meso‑samples are randomly generated on the fly when the macroscopic integration points are first identified to be included in the multiscale critical region. Concrete damage at the macroscale is quantitatively characterized based on its mesoscopic counterpart thanks to the proposed partition-based averaging scheme. The numerical simulations demonstrate that the presented approach can track and quantify concrete trans-scale damage evolution. Importantly, in the simulation of a 480 mm-length dog-bone-shaped specimen, the number of degrees of freedom and computational time are only 8.35 and 17.57% of those of the direct mesoscale simulation, respectively.

Effect of geometrical structure variations on strength and damage onset of cortical bone using multi-scale cohesive zone based finite element method

Three-dimensional multi-scale finite element models were designed to examine the effects of geometrical structure variations on the damage onset in cortical bone at multiple structural scales. A cohesive zone finite element approach, together with anisotropic damage initiation criteria, is used to predict the onset of damage. The finite element models are developed to account for the onset of microdamage from the microscopic length scales consisting of collagen fibres, to the macroscopic level consisting of osteons and the Haversian canals. Numerical results indicated that the yield strain at the initiation of microcracks is independent of variations in the local mineral volume fraction at each structural scale. Further, the yield strain and strength properties of cortical bone are dependent on its structural anisotropy and hierarchical structure. A positive correlation is observed between bone strength and mineral content at each length scale.

Multiscale modelling and simulation of subsurface carbide deformation during the formation of white etching areas

One of the main failure indications in rolling bearings subjected to rolling contact fatigue (RCF) is premature subsurface cracking accompanied by white etching areas (WEAs). The cracks that are linked with WEAs are called white etching cracks (WECs). The formation mechanisms of WEAs/WECs are still highly debatable according to international state of art. Often SAE 52100 steel is used for bearing rings. Its microstructure consists of a martensitic or bainitic matrix and homogeneously distributed chromium rich cementite precipitations. There are two main hypotheses based on what forms first, the cracks or WEAs (hypothesis 1 & 2 respectively). There are many numerical studies that examine non-metallic inclusions as a source of cracks that leads to WEAs (hypothesis 1), but none that considers carbides as the source of severe plastic deformation subjected to RCF that leads to WEAs and, eventually WECs (hypothesis 2). In this study, the testing was conducted on a ZF-type modified RCF test rig with hydrogen charged samples to reproduce WEAs/WECs formation. Later the influence of the microstructural features of the carbides on the steel matrix, during the formation of WEAs was investigated by microstructural investigations and multiscale finite element modelling. It was found that carbides can contribute to severe local plastic deformation which leads to formation of WEAs. Thus, it also supported the likelihood of hypothesis 2. Additionally, the surface traction and microstructural characteristics of carbides are correlated with the wide range of WEAs formation depths and timescales.

Prediction of internal mechanical damage in pineapple compression using finite element method based on Hooke's and Hertz's laws

Fruits are susceptible to damage from external loads during harvesting, transport and storage. Fruit damage is determined by its tissue mechanical properties. The aim of this study was to evaluate two theories (Hooke's and Hertz's Laws) on the apparent elastic modulus of pineapple and predict the internal mechanical damage of pineapple under compression. Two multi-scale finite element models (FEMs) were developed to predict the pineapple internal damage. One model, based on Hooke's Law contained three layers, including peel, pulp, and core. Another model, based on Hertz's Law, was a two layers model, including peel and pulp (containing core). The difference of these two FEMs was evaluated in terms of different compression displacements. The results showed that, when the compression displacement ≤10 mm, the Hooke three-layer model was closer to reality. But when the compression displacement >10 mm, the Hertz two-layer model was better in reflecting real pineapple compression. Simulated data confirmed the experimental results and predicted the internal mechanical damage of pineapple. Finite element results indicated that, when a force was applied to the fruit, pulp tissue suffered mechanical damage before peel and core tissue. When the compression level was ≤5% (5.5 mm; 86 N), there was no damage to pulp, core, and peel. But, if compression level >5%, the fruit was damaged. These results indicated that pineapple placed horizontally with an allowable numbers of stackable pineapples must be less than eight. Otherwise, the maximum allowable force of stacked fruit on the lowest one will reach the pulp failure force.

Multiscale crystal plasticity finite element model for investigating the irradiation hardening and defect evolution mechanism of A508-3 steel

• A multiscale crystal plasticity finite element model (MCPFEM) is proposed. • This model combines molecular dynamics with crystal plasticity theory. • Evolution equations for partial- and full-absorption dislocation loops are utilized. • The absorption probability in the crystal plasticity framework is considered. • The proposed theory is applied to analyze irradiated BCC A508-3 steel. A multiscale crystal plasticity finite element model, which combines molecular dynamics with crystal plasticity theory, is proposed. In this model, the evolution equations for partial- and full-absorption dislocation loops are utilized. Furthermore, we introduce the absorption probability in the crystal plasticity framework using the parameters at the atomic scale, which connects the microscale and mesoscale. The proposed method is applied to analyze the mechanical behavior of irradiated body-center-cubic (BCC) A508-3 steel. It was found that the numerical results agree well with the experimental data, which demonstrates the feasibility and accuracy of this model. Irradiation hardening was captured by the proposed model. Considering parameter evolution, irradiation can accelerate the increase in mobile dislocations and impede the decrease of immobile dislocations. The proposed model may provide a theoretical guide for predicting the mechanical behaviors of irradiated BCC metals for the selection of structural materials in nuclear plants.

Description of Dynamic Recrystallization Behaviors and Grain Evolution Mechanisms during the Hot Forming Process for SAE 5137H Steel.

Describing the dynamic recrystallization (DRX) behaviors and grain evolution mechanisms in the hot forming process contributes to controlling microstructures and enhancing mechanical properties of materials. Here, the isothermal compression experiments for SAE 5137H steel were conducted under temperatures of 1123–1483 K and strain rates of 0.01–10 s−1. The DRX kinetics models, including DRX volume fraction and grain size models, and the meso-scale cellular automaton (CA) models, were established based on the obtained true stress–strain curves and microstructure observation results. In order to dynamically reveal DRX behaviors and grain morphology evolution, a multi-field and multi-scale coupling finite element (FE) model for the hot compression process was developed by embedding the solved DRX kinetics models and CA models. Results show that the DRX volume fraction and grain size increase with temperature increasing and strain rate decreasing. The DRX grains are easier to nucleate at the initial grain boundaries. As strain increases, DRX grains grow up by devouring the matrix grains until DRX occurs completely. The microstructures after compression are composed of equiaxed DRX grains. Finally, the comparisons of grain size between experimental results and simulation results were performed. The mean relative errors between experimental results and predicted results from DRX kinetics models, and between experimental results and predicted results from CA models, were evaluated as 6.5% and 6.0%, respectively. It proves that the developed FE model can well describe the microstructure evolution in the hot deformation process of SAE 5137H steel.

Phase field approach to damage and fracture in asphalt concrete using multiscale finite element modeling of an instrumented pavement section

This study presents a Multiscale Finite Element Model (MsFEM) and Phase Field Fracture (PFF) based approach to study the responses and damage behavior of the viscoelastic Asphalt Concrete (AC) based on the actual traffic loadings. AC is a multiphase heterogeneous material. Understanding the mechanical responses and damage accumulation in different phases of AC has been a challenge for the pavement research community. This study proposes a methodology to overcome this challenge by combining a two-way linked multiscale finite element model with phase-field fracture. A modified PFF degradation function is formulated to quantify the damage and fracture in the AC microstructure. Combining MsFEM with PFF, it is possible to take the material heterogeneity, anisotropic and viscoelastic damage accumulation in the AC microstructure into consideration to identify the overall performance of the macroscale pavement. The developed MsFEM with PFF is validated based on the responses from an instrumented pavement section under Falling Weight Deflectometer (FWD) test load. Model responses are in agreement with field sensor responses, demonstrating that MsFEM with PFF can be used to accurately and efficiently predict AC microstructure performances. The model is also used to perform parametric studies to determine the extent of damage in the microscale AC due to the movement of Super Heavy Loads (SHLs) which is computationally very expensive in a traditional single scale model. The results from the parametric study show that weaker and thinner unbound layers have the highest potential of initiating fatigue damage in the AC microstructure.

Control of multi-scale cracking for improvement of the reliability of carbon/carbon composites via design of interlaminar stress

Controlled cracking at micro/mesoscale is crucial for decreasing the strength scatter and improving the reliability of carbon/carbon composites (C/Cs). In this work, the controlled cracking is realized by a designed interlaminar residual thermal stress (RTS), which is introduced inside the C/Cs by the alternate stacking of two types of C/C plies with different coefficients of thermal expansion. Firstly, multiscale finite element (FE) modeling is performed to capture the interlaminar RTS induced by the alternate stacking and evaluate the risk of delamination due to the free edge effect. Secondly, mechanisms responsible for the controlled cracking are elaborated with the aid of the FE modeling and experimental characterizations, and the controlled deflections and bifurcations of the crack strongly shield the influence of multiscale flaws. Finally, by adopting this strategy, the flexural strength of the C/Cs increases by 66% while the statistical Weibull modulus also increases from 4.9 to 8.3, verifying the simultaneously improved strength and reliability of the C/Cs.