Meso-scale Finite Element Method Research Articles

Highly efficient and accurate algorithm for multiscale equivalent modeling and mechanical performance simulation of printed circuit boards

The increasing prevalence of reliability issues related to printed circuit boards (PCBs) has led to significant interest in applying finite element analysis (FEA) for PCBs. This study presents an equivalent property algorithm based on the mesoscale finite element method (FEM), which took into account the intricate structural features of conductive layers in PCBs. Additionally, a series of automated scripts were developed to streamline the modeling and calculating process, markedly enhancing the accuracy and efficiency of equivalent modeling and simulation of the PCB. Based on the proposed algorithm, a multiscale three-point bending finite element model of a PCB was established. By comparing the results to experimental data from three-point bending tests, it was demonstrated that the stress field simulated using the proposed algorithm accurately represented the anisotropic properties of the intricate copper traces in the conductive layers, leading to more accurate predictions of mechanical responses than those obtained using conventional algorithms. Furthermore, the research on the impact of partition size on both simulation accuracy and computational efficiency clearly demonstrated that partition size significantly affected these aspects. In conclusion, the proposed algorithm provided a more reliable and efficient approach for applying FEA and FEM to PCBs, contributing to advancements in the field of PCB analysis and fostering improvements in electronics design and manufacturing.

Assessing thermophysical properties of parameterized woven composite models using image-based simulations

Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the reality of as-manufactured materials often differs from the ideal, both in terms of tow geometry and manufacturing heterogeneity. As such, resultant composite properties may differ from analytical predictions and exhibit significant local variations within a material.We employ mesoscale finite element method simulations to compare idealized analytical and as-manufactured woven composite materials and study the sensitivity of their effective properties to the mesoscale geometry. Three-dimensional geometries are reconstructed from X-ray computed tomography, image segmentation is performed using deep learning methods, and local fiber orientation is obtained using the structure tensor calculated from image scans. Suitable approximations to composite properties, using analytical unit cell calculations and effective media theory, are assessed. Our findings show that an analytical geometry and sub-unit cell geometry provide reasonable approximations of the full-scale predictions for the effective thermal properties of a multi-layer production composite.

Energy Dissipation on an Elastic Interface as a Metric for Evaluating Three Friction Models

Abstract The effect of three different friction interface models on an elastic half-space is presented. Three constitutive friction models are studied: Coulomb, soil–concrete interface, and Bouc–Wen, using a computational mechanics framework that can represent the contact patch's material response to static and dynamic surface tractions. This response is observed as strains and stresses present from reciprocating sliding using an elastoplastic friction (EPF) algorithm that also captures energy dissipation and hysteresis due to friction sliding. Additionally, the use of the four-parameter Bouc–Wen model represents a new development in contact mechanics that allows micro-slip of the contact interface to be modeled. Hysteresis loops are generated for the three friction models based on a quasi-static assumption. This algorithm is built into a mesoscale finite element method solver that is able to simulate different loading conditions and provide insight into how the friction models respond to load conditions and inform on experimental data. The energy dissipation from reciprocating friction sliding will be generated for each friction model as a metric that captures surface wear and potential material damage.

Effect of 3D aggregate shape on thermo-mechanical properties of asphalt concrete using a mesostructure-based homogenisation method

ABSTRACT Morphological characteristics of aggregates have long been recognised as an essential factor influencing the thermo-mechanical behaviour of asphalt concrete. However, studies on accurate quantification of this influence are still very limited. For this reason, the present study developed a mesoscale finite element method to investigate the effects of three-dimensional (3D) aggregate shape on the complex modulus, thermal expansion coefficient, thermal conductivity, and mesoscale responses of asphalt concrete. An upscaling homogenisation method was adopted to predict the effective thermo-mechanical properties of asphalt concrete. The 3D true sphericity (3DTS) was used as an index to characterise the aggregate shape. The computational results showed that the temperature and loading frequency significantly affect the role of aggregate shapes in determining the effective dynamic modulus of asphalt concrete. The high-angularity aggregates can increase the deformation resistance of asphalt concrete under thermal load, and thus reduces the thermal contraction coefficient of asphalt concrete. However, aggregate shape has no significant effect on the thermal conductivity of the asphalt concrete. In addition, the asphalt concretes with less angular aggregates have stronger low-temperature damage resistance, while the aggregates with high angularity can improve the rutting resistance of asphalt pavements.

Analysing shear strength of reinforced concrete beams using a meso-scale finite-element method

An analytical exploration of the effects of shear span-to-depth ratio on the shear strength of reinforced concrete beams was carried out using a meso-scale finite-element method. Prior to the numerical analysis, a method of defining concrete as meso-scale composites of multi-phases was described. The concrete was assumed to be a composite with three phases (aggregates, cement matrix and interfacial transition zone), and the material properties of each phase were applied for the numerical analysis. The shear failure behaviour of reinforced concrete beams was examined by the numerical model that was constructed, and the effect of span-to-depth ratio on shear strength was confirmed through these analyses. An investigation of cases where span-to-depth was less than 1.0 was also carried out. Moreover, the performance of the numerical model was evaluated by comparing the numerical results with the experimental results obtained from the model code and other researchers. It was confirmed that the application of a meso-scale finite-element method was appropriate for the study on the effect of span-to-depth ratio on shear strength and the occurrence and progress of bending and shear cracks.

Influence of pre-static loads on dynamic compression and corresponding size effect of concrete: Mesoscale analysis

Many concrete engineering structures have already withstood the historical loads (such as initial compressive/tensile load) prior to being subjected to dynamic loads. The historical load and structure size are two influential factors on dynamic mechanical performance of concrete. Exploring the dynamic size effect of concrete with different loading histories is a valuable task. In this work, the influence of pre-static compressive/tensile loads on dynamic compressive failure and the corresponding dynamic size effect was investigated by the developed mesoscale finite element method. The research results show that the dynamic compressive strength of concrete decreases with the increasing pre-static compressive load under low strain-rates while it increases with the increasing pre-static tensile load. Dynamic strength under high strain-rates is not affected by the pre-static loads. Moreover, as the concrete has withstood more pre-static loads, the dynamic size effect on compressive strength becomes more obvious under low strain-rates. Finally, the numerical results were analyzed and confirmed by the application of Weibull size effect law.

MSFEM을 적용한 콘크리트 공시체의 압축강도에 대한 크기효과

이 연구에서는 중규모크기 유한요소법을 이용하여 콘크리트 원주공시체와 입방체의 압축강도의 크기효과에 관한 연구를 수행하였다. 해석에 앞서 콘크리트를 중규모크기의 다상의 복합체로 정의하는 방법에 관하여 기술하였다. 즉, 콘크리트를 골재, 시멘트 매트릭스, 그리고 ITZ 3가지 상태를 가지는 복합체로 가정하였고, 이후 각각의 상에 대한 재료특성을 부여하였다. 구축된 해석모형을 이용하여 콘크리트의 압축파괴거동에 대한 해석을 수행하였고, 이를 통하여 크기효과와 균열의 발생 및 진전도 확인하였다. 또한 비표준형 원주공시체에 대하여 ASTM C42에서 제시하는 에 따른 강도보정계수도 비교하였다. 기 수행된 연구결과와 이 연구에서 얻은 결과는 충분히 신뢰할 만한 수준의 결과를 나타내었다. 최종적으로 중규모크기 유한요소법을 이용해서도 원주공시체와 입방체의 압축강도 및 크기효과를 충분히 예측 가능함을 확인하였다.

Application of meso-scale finite-element method to strength and size effect of concrete

An analytical study on the compression, tension and shear strengths of concrete and corresponding size effect is conducted using the meso-scale finite-element method (FEM). Prior to the analysis, a method of defining concrete as a meso-scale composite and multi-phase is described. The concrete is assumed to be a composite with three phases: aggregates, cement matrix and interfacial transition zone. The material properties of each phase are applied. Behaviours relating to uniaxial and flexural compressive failure, splitting and direct tensile failure of concrete, and shear failure of reinforced concrete are analysed using the model constructed; the size effect is confirmed through these analyses. The performance of the analytical models is also evaluated by comparing experimental with analytical results. Finally, it is confirmed that the application of the meso-scale size analysis model is enough when studying the occurrence and progress of tensile cracks. This basic study represents a fresh application of meso-scale FEM analysis to concrete; in future research, the authors will apply meso-scale FEM analysis in a wider variety of fields.

Numerical simulation of the debonding process in pull-out tests of near-surface mounted FRP rod in concrete

Purpose Near-surface mounted (NSM) fiber-reinforced polymer (FRP) rod is extensively applied in reinforced concrete (RC) structures. The mechanical performances of NSM FRP-strengthened RC structures depend on the bond behavior between NSM reinforcement and concrete. This behavior is typically studied by performing pull-out tests; however, the failure behavior, which is crucial to the local debonding process, is not yet sufficiently understood. Design/methodology/approach In this study, a three-dimensional meso-scale finite element method considering the cohesion and adhesion failures is presented to model the debonding failure process in pull-out tests of NSM FRP rod in concrete. The smeared crack model is used to capture the cohesion failures in the adhesive or concrete. The interfacial constitutive model is applied to simulate the adhesion failures on the FRP-adhesive and concrete-adhesive contact interfaces. Findings The present method is first validated by two simple examples and then applied to a practical NSM FRP system. This work studied in detail the debonding process, the bond failure types, the location of peak bond stress, the transmitting deformation in adhesive and the morphology of contact zone. The developed method provides a practical and convenient tool applicable for further investigations on the debonding mechanism for the NSM FRP rod in concrete. Originality/value A three-dimensional meso-scale finite element method considering the cohesion and adhesion failures is presented to model the debonding failure in NSM FRP-strengthened RC structures. The smeared crack model and the interfacial constitutive model are introduced to develop a convenient approach to analyze the failures in adhesive, concrete and related interfaces. The developed numerical method is applicable for studying the debonding process, the bond failure types, the location of peak bond stress, the transmitting deformation in adhesive and the morphology of contact zone in detail.

Numerical Modelling of the Mechanical Behaviour of Biaxial Weft-Knitted Fabrics on Different Length Scales.

Weft-knitted fabrics offer an excellent formability into complex shapes for composite application. In biaxial weft-knitted fabric, additional yarns are inserted in the warp (wale-wise) and weft (course-wise) directions as a reinforcement. Due to these straight yarns, the mechanical properties of such fabrics are better than those of unreinforced weft-knitted fabrics. The forming process of flat fabrics into 3D preforms is challenging and requires numerical simulation. In this paper, the mechanical behavior of biaxial weft-knitted fabrics is simulated by means of macro- and meso-scale finite element method (FEM) models. The macro-scale modelling approach is based on a shell element formulation and offers reasonable computational costs but has some limitations by the description of fabric mechanical characteristics and forming behavior. The meso-scale modelling approach based on beam elements can describe the fabric’s mechanical and forming characteristics better at a higher computational cost. The FEM models were validated by comparing the results of various simulations with the equivalent experiments. With the help of the parametric models, the forming of biaxial weft-knitted fabrics into complex shapes can be simulated. These models help to predict material and process parameters for optimized forming conditions without the necessity of costly experimental trials.

The tension failure mechanisms of composite stepped bonding repairs and joints for the aircraft primary load-bearing structures

Stepped and scarf topology are still the preferred choices for repairs and joints of composite primary load-bearing structures. The stepped bonding scheme is easy to be implemented in real engineering process. The precise stress distribution, load capacity, damage mode and failure mechanism are not adequately clear. This paper adopts static stress analysis of FEM (Finite Element Method), experimental studies and CDM (Continuum Damage Mechanics) to reveal the tension failure mechanism for composite stepped bonding structures. In the static stress analysis, the mesoscale FEM model considered the adhesive thickness was created. It investigated the detail stress distribution and concentration of the step topology adhesive. Then seven specimens with tensile load were studied experimentally through relation of load-deformation and the appearance of damage. For more details, the adhesive damage was simulated by using CZM (Cohesive Zone Model) which includes the mix-mode fracture of normal force and sliding shear force. The process of damage propagation evolution can be clearly observed in the simulation results. The damage initiates at the vertical location of steps adhesive and propagates to the horizontal overlaps adhesive. Simulation for predicting the ultimate load capacity coincides with experiments. This paper’s work will be useful for designing and analyzing the full composite materials airframe and wing repaired by stepped bonding technique.

Meso-Scale Finite Element Simulations of 3D Braided Textile Composites: Effects of Force Loading Modes

Meso-scale finite element method (FEM) is considered as the most effective and economical numerical method to investigate the mechanical behavior of braided textile composites. Applying the periodic boundary conditions on the unit-cell model is a critical step for yielding accurate mechanical response. However, the force loading mode has not been employed in the available meso-scale finite element analysis (FEA) works. In the present work, a meso-scale FEA is conducted to predict the mechanical properties and simulate the progressive damage of 3D braided composites under external loadings. For the same unit-cell model with displacement and force loading modes, the stress distribution, predicted stiffness and strength properties and damage evolution process subjected to typical loading conditions are then analyzed and compared. The obtained numerical results show that the predicted elastic properties are exactly the same, and the strength and damage evolution process are very close under these two loading modes, which validates the feasibility and effectiveness of the force loading mode. This comparison study provides a suitable reference for selecting the loading modes in the unit-cell based mechanical behavior analysis of other textile composites.

중규모크기 유한요소법을 이용한 콘크리트의 압축강도에 대한 크기효과

중규모크기 유한요소법을 이용한 콘크리트의 압축강도에 대한 크기효과

Influence of laser scan speed on micro-segregation in selective laser melting of an iron-carbon alloy: A multi-scale simulation study

Selective laser melting (SLM) is an additive manufacturing method complementary to traditional manufacturing technologies, and it has drawn increasing amount of attention in recent years. However, effective control of microstructure evolution in SLM is usually difficult due to the rapid heating and cooling cycles involved in the process. In this research, multiscale simulation is performed to investigate the influence of laser scan speed on micro-segregation in SLM of binary Fe-C alloy, with the consideration of realistic thermal history and powder-to-dense phase transformation. Meso-scale finite element method (FEM) is used to calculate the temperature field, and micro-scale phase field (PF) method is used to calculate the dendrite evolution and solute redistribution. Three levels of laser scan speeds, i.e., 1000, 1600, and 2400 mm/s are used to perform the simulation. The results indicate that the overall melt pool morphology and temperature distribution are significantly affected by the laser scan speed. Higher scan speed leads to significantly higher cooling rate in the interested solidification region, and therefore alters the dendrite growth velocity and tip radius. Moreover, higher laser scan speed results in lower interdendritic segregation ratio, due to ultra-fast cooling and solute trapping.

Size Effect on Compressive Strength of Concrete Using Meso-scale Finite Element Method

Size Effect on Compressive Strength of Concrete Using Meso-scale Finite Element Method

A three-dimensional meso-scale modelling of concrete fracture, based on cohesive elements and X-ray μCT images

The paper shows three-dimensional numerical results regarding concrete fracture at aggregate level in a notched concrete beam under bending using cohesive interface elements. Concrete heterogeneity was taken into account by considering a 3-phase material description: aggregate, cement matrix and interfacial transitional zones (ITZs). The real shape and location of aggregate particles in concrete were assumed in numerical analyses based on X-ray μCT scans. The 3D meso-scale finite element method (FEM) with cohesive elements embedded in the cement matrix and ITZs was used in simulations. The effect of different properties of ITZs and cement matrix was investigated in parametric studies. A satisfactory agreement in terms of the vertical force versus crack mouth opening displacement evolution and crack geometry was achieved between analyses and laboratory tests.

Two-dimensional simulations of concrete fracture at aggregate level with cohesive elements based on X-ray μCT images

The paper presents results of two-dimensional meso-scale simulations of fracture in notched concrete beams subjected to three-point bending test. Concrete was assumed as a 4-phase material composed of aggregate grains placed in the cement matrix, interfacial transitional zones (ITZs) and macro-voids. The particle distribution was taken from real concrete beams on the basis of X-ray μCT images. Comprehensive numerical analyses were carried out using the 2D meso-scale finite element method (FEM) with cohesive elements located in the cement matrix and along the ITZs. In addition, parametric studies were carried out for different material constants. The effect of the shape, content and density of aggregate packing was also investigated. A satisfactory agreement with respect to the load-displacement and crack geometry was achieved between FE analyses and experiments.

Softening the ultra-stiff: Controlled variation of Young’s modulus in single-crystal diamond by ion implantation

A combined experimental and numerical study on the variation of the elastic properties of defective single-crystal diamond is presented for the first time, by comparing nano-indentation measurements on MeV-ion-implanted samples with multi-scale modeling consisting of both ab initio atomistic calculations and meso-scale Finite Element Method (FEM) simulations. It is found that by locally introducing defects in the 2 × 1018–5 × 1021 cm−3 density range, a significant reduction of Young’s modulus, as well as of density, can be induced in the diamond crystal structure without incurring in the graphitization of the material. Ab initio atomistic simulations confirm the experimental findings with a good degree of confidence. FEM simulations are further employed to verify the consistency of measured deformations with a stiffness reduction, and to derive strain and stress levels in the implanted region. Combining these experimental and numerical results, we also provide insight into the mechanism responsible for the depth dependence of the graphitization threshold in diamond. This work prospects the possibility of achieving accurate tunability of the mechanical properties of single-crystal diamond through defect engineering, with significant technological applications, e.g. the fabrication and control of the resonant frequency of diamond-based micromechanical resonators.

Bridging crack propagation at the atomistic and mesoscopic scale for BCC-Fe with hybrid multiscale methods

The hybrid multiscale method bridging the atomistic and mesoscopic scale is proposed in the current study, which combines the concurrent generalized particle (GP) dynamics method and the bottom-up hierarchical cohesive zone model (CZM) with embedded traction–separation law. The primary purpose is to transfer the GP-obtained physical parameters to the upper mesoscale finite element method (FEM) to investigate the meso- and microscopic crack propagation. The local fracture energy, stress and opening relationships under tension loading during steady-state crack propagation are extracted from the three-scale GP model. In this procedure, the scale duality technique is conducted using the GP analog, which can allow material to exist as particles via a lumping process and allows them to decompose into atoms at crack tips and interfaces. Crack extension resistance is detected by coordination vector (CV) snapshots, and energy release rates in the subdomain are used to evaluate the material behavior against the crack propagation when the current crack tip grows. Using the unique cohesive element length, four-scale tension specimen FE models are designed to reveal the accuracy of the intrinsic correlation between the atomistic and mesoscopic scale under a stress intensity factor to study the brittle body-centered cubic (BCC)-Fe fracture behavior. The result appears reasonable and encouraging.

Transverse tensile damage behaviors of three-dimensional five-directional braided composites by meso-scale finite element approach

In this paper, the meso-scale finite element method is used to evaluate the transverse tensile damage behaviors of three-dimensional five-directional braided composites based on the representative volume cell. Finite element models with two kinds of interior braiding angles, 30° and 45°, are established on the basis of the realistic geometry shape of each yarn. A continuum damage mechanics model, which is implemented as a user-defined material subroutines in the ABAQUS commercial finite element code, is used to capture the complete damage initiation/evolution in yarns and matrix. The local responses and the failure mechanisms are analyzed. Numerical results show that the transverse tensile strength and the failure mechanisms are significantly influenced by the braiding angle. The predicted stress–strain responses and final damage morphology agree well with the experimental data, verifying the applicability of the meso-scale finite element method.