Micromechanics-based Finite Element Research Articles

Thermomechanical behavior of carbon nanotube/graphene nanoplatelet-reinforced shape memory polymer nanocomposites: A micromechanics-based finite element approach

Stimuli-responsive shape memory polymer (SMP) nanocomposites, characterized by their shape memory capability and customizable properties, have significantly expanded their range of applications when compared to pristine SMPs. This pioneering paper is centered on describing an efficient numerical approach for evaluating the thermomechanical behavior of ternary acrylate-based SMP nanocomposites containing carbon nanotube (CNT) and graphene nanoplatelet (GNP) hybrids. To this aim, a micromechanical procedure based on thermo-visco-hyperelastic constitutive model, which aids in avoiding employing intricate user-defined material subroutines, is developed through the finite element method (FEM). The parameters required for satisfying the governing equations of the rheological model, including thermal expansion and Prony series coefficients, plus Williams-Landel-Ferry equation and Neo-Hookean strain energy function parameters, are derived from accessible experiments to assign SMP properties. A Python-based script is implemented in a stochastic-iterative process to generate appropriate periodic representative volume elements (RVEs) with various microstructures. Thereupon, thermomechanical shape memory cycles in uniaxial tension are simulated by creating loading, cooling, unloading, and heating steps in the Abaqus solver. Following achieving satisfactory agreement between the presented scheme and experimental measurements, case studies are performed to reflect the influences of dispersion type, volume fraction, and geometry of carbonaceous nanofillers, as well as the contribution of nanofiller/matrix interphase region, upon stress-free/shape-recovery and fixed-strain/stress-recovery thermomechanical cycles.

Bottom-up stochastic multiscale model for the mechanical behavior of multidirectional composite laminates with microvoids

This study for the first time develops a coherent and efficient bottom-up stochastic multiscale modeling approach, which aims at revealing the impact of microvoids on the mechanical properties and damage mechanisms of multidirectional (MD) carbon fiber-reinforced polymer (CFRP) composites. To this end, void defects within the composites are characterized using X-ray micro-computed tomography to construct a high-fidelity representative defective volume (RDV). Subsequently, the influence of voids on the microscale failure modes and macroscopic mechanical properties are analyzed by using micromechanics-based finite element (FE) method. Finally, a stochastic multiscale analysis method is developed to predict the mechanical response of MD CFRP laminates and validated by tensile and three-point bending experiments. The results indicate that the proposed framework can accurately predict the mechanical behavior and damage mechanisms of MD CFRP composites. This framework is believed to be a promising method to provide valuable guidance for reliability design and optimization of CFRP composites.

An efficient micromechanics-based finite element model for failure analysis of laminated composites

Accurately predicting ultimate strength of composite laminate is still a great challenge, especially only based on the constituent properties. In this paper, the micromechanics Bridging Model and systematic failure criteria for the constituent materials with emphasis on matrix failures subjected to three dimensional (3D) loads are compiled into a UMAT subroutine for ABAQUS to analyze failures of a laminated composite structure. The main purpose of this research is to greatly reduce calculation costs for loading conditions of in-plane tension or compression by introducing a simplified 3D finite element model based on the Pipes-Pagano theory. In all calculation cases, only the constituent properties together with the transverse tensile strength of unidirectional composite are needed as input data. Later in this paper, sufficient illustrations of 81 different composite laminates composed of 14 material systems are analyzed to confirm the practicability of this model.

Machine learning and materials informatics approaches for predicting transverse mechanical properties of unidirectional CFRP composites with microvoids

The mechanical properties of composites are traditionally measured using numerical and experimental approaches, which impede the innovation of materials due to the cost, time, or effort involved. This study for the first time develops a machine learning-assisted model, which aims at predicting the transverse mechanical properties of unidirectional (UD) carbon fiber reinforced polymer (CFRP) composites with microvoids. To this end, the stochastic microstructures are generated by random sequential expansion (RSE) and hard-core model. And the transverse elastic modulus, transverse tensile strength and transverse compressive strength are computed by micromechanics-based finite element (FE) method. Then, the reduced order representation of microstructures is determined using 2-point spatial correlations and principal component analysis (PCA). Finally, a genetic algorithm (GA) optimized back propagation (BP) neural network is implemented to capture the potential nonlinear relationship between microstructure and transverse mechanical properties. The presented data-driven techniques can reproduce the FE simulation results with an R-value of 0.89 or greater. The excellent agreement between the predicted results and test datasets verifies the successful application of data science methodologies in elucidating the microstructure-property linkages of UD-CFRP composites with microvoids, and thus provides a promising tool for accelerating the smart design and optimization of composites.

Microstructural analysis and multiscale modeling for stiffening and strengthening of consolidated earthen-site soils

While experimental explorations to consolidate earthen-site soils using composite materials have obtained desirable reinforcing effect, few modeling efforts were conducted to reveal how microstructures of consolidated soils affect their effective stiffness and strength. The current study develops a multiscale modeling technique to quantify the stiffening and strengthening effects of consolidants to earthen-site soils. Specifically, a micromechanics-based finite element method is applied to simulate the homogenized constitutive relations of the untreated and consolidated soils, based on the microstructures from scanning electron microscopy images and image-processing procedures. Multiscale models are used to examine the influence of input properties of consolidants on the sensitivity of mechanical properties of the earthen-site samples. Comparison between modeling and experimental results shows a satisfactory agreement. The macroscopic mechanical properties of soils are remarkably affected by their microstructures. This study demonstrates the feasibility of integrating scanning electron microscopy and image processing technology into the finite-element modeling for stiffening and strengthening analysis of consolidated earthen-site soils.

Micromechanics-based simulation of anisotropic magneto-mechanical properties of magnetorheological elastomers with chained microstructures

Magnetorheological elastomers (MREs) are ferromagnetic particle-reinforced composites that have a wide application prospect in engineering because of their tunable stiffness with applied magnetic fields. While a large number of experimental efforts have been carried out to characterize the magneto-mechanical properties of MREs, few physics-based quantitative modeling and simulation have been explored. Here a micromechanics-based finite element model and computational homogenization is developed to determine the field-dependent shear moduli of MREs. The magneto-elastic coupling is realized with the magnetic field-induced body forces in the local mechanical field. The three-dimensional body forces are solved with consideration of magnetization and demagnetizing fields. Effects of essential microstructure parameters (particle concentration and particle spacing) are investigated on the effective magneto-mechanical properties of chain-structured MREs. The numerical results demonstrate that the microstructures and demagnetizing field have significant effects on the field-induced moduli of MREs. RVEs with appropriate microstructures are selected to compare our model predictions of magneto-mechanical properties with multiple groups of experiment data in the literature, showing the capability and validity of the proposed model.

Effect of microstructure inhomogeneity on mechanical properties of different zones in TA15 electron beam welded joints

Abstract The effects of microstructure inhomogeneity on the mechanical properties of different zones in TA15 electron beam welded joints were investigated using a micromechanics-based finite element method. Considering the indentation size effect, the mechanical properties for constituent phases of the base metal (BM) and heat affected zone (HAZ) were determined by the instrumented nano-indentation test. The macroscopic mechanical properties of BM and HAZ obtained from the tensile test agree well with the numerical results. The incompatible deformation between the constituent phases tends to localize along the softer primary phase α where failure usually initiates in form of localized plastic strain. Compared with the BM, the mechanical properties of constituent phases in the HAZ differ substantially, leading to more serious strain localization behavior.

Effects of microvoids on strength of unidirectional fiber-reinforced composite materials

Microvoids are common defects generated during manufacturing or prolonged services of composites. Depending on the local physical environment, microvoids may form as two types, namely, matrix voids and interfiber voids. These voids are known to have detrimental effects on the load bearing capacity of composites. However, it is relatively unknown the quantitative influence of these voids on the mechanical strength of composites. Without a direct mapping between defects and ply-level constitutive behavior, high-fidelity progressive failure predictions of composite structures is challenging. To bridge the gap, a micromechanics-based finite element framework is developed to investigate composites failure in the presence of three interfiber voids and the matrix void under transverse compression, tension, shearing, and longitudinal shearing. Mechanical strengths under these four loading modes are correlated with microstructural parameters including the void volume fraction, fiber-to-void number ratio, and void orientation. In general, at the same void volume fraction, the pentagonal interfiber void lowers strength the most, followed by the square interfiber void, the triangular interfiber void, and the circular matrix void. The weakening effect is strongly associated with stress concentration in the vicinity of voids, making the fiber-to-void number ratio an important parameter as it determines the local geometry. While void orientation shows limited influence, void size is found to play an important role. Results are expected to guide design and manufacturing of composite materials to achieve less critical flaws and higher strengths. Quantitative understanding of the criticality of voids of various configurations will also assist in-situ evaluation of composite materials.

Type IV failure in weldment of creep resistant ferritic alloys: II. Creep fracture and lifetime prediction

The creep rupture behavior (Type IV failure) for weldments of creep strength enhanced ferritic steel is numerically analyzed, using an integrated microstructure- and micromechanics-based finite element model. To account for the large microstructure gradients across weldments, a two-dimensional digital microstructure is constructed based on the actual observed microstructure of ferritic steel weldment by using the Voronoi-tessellation method. According to the fracture mechanism studies and literature experimental observations, the Type IV failure is identified as an intergranular creep fracture in the fine-grained or intercritical heated affected zone (FGHAZ or ICHAZ). In the present study, the following micromechanics model is employed to determine the micromechanical and microstructural origins for the failure process above, accounting for the underlying physical fracture mechanisms at different length scales, including nucleation of grain boundary cavities, their growth by competition of grain boundary diffusion and grain interior creep, viscous grain boundary sliding, and the emergence of microcracks by coalescence and their evolution to the ultimate failure. The methodology demonstrates the capabilities in modeling the Type IV failure and providing quantitative creep rupture lifetime prediction which shows an excellent agreement with long-term creep experimental data for creep strength enhanced ferritic steels and their weldments. In particular, the drop-off in time to rupture at high temperatures and low stress levels in the creep rupture curves is quantitatively predicted, and the transition of failure mechanisms from creep-controlled to diffusion-controlled creep fracture mechanism is illustrated.

Shakedown of porous material with Drucker-Prager dilatant matrix under general cyclic loadings

This paper is concerned with the shakedown limit states of porous ductile materials with Drucker-Prager matrix under cyclically repeated loads. Using the hollow sphere model and Melan’s shakedown theorem based on time-independent residual stress fields, a macroscopic fatigue criterion is derived for the general conditions of cyclic loads. First, the case of the hollow sphere subjected to pure hydrostatic loading is studied and the limit states of collapse by fatigue or by development of mechanism are derived. Then, the general case involving shear effects with any arbitrary cyclic load fluctuations ranging from the pulsating load to the alternating one is considered. The key idea is in two steps: (i) the choice of appropriate trial stress and trial residual stress fields and (ii) then maximizing the size of the load domain in the spirit of the standard lower shakedown theorem. The new macroscopic shakedown criterion depends on the porosity, the friction angle, Poisson’s ratio, the two stress invariants of the effective stress tensor and the sign of the third one. Together with the limit analysis-based yield criterion corresponding to the sudden collapse by development of a mechanism at the first cycle, it defines the safety domain of porous materials subjected to cyclic load processes. Interestingly, it is found that the safe domain is little sensitive to variations of the friction angle, however, it is considerably reduced compared to the one under monotonic loads obtained by limit analysis. Finally, a comparative study between the analytical results and numerical predictions performed by micromechanics-based finite element simulations is conducted for different porosities and friction angles.

Crack detection and localization in RC beams through smart MWCNT/epoxy strip-like strain sensors

In recent years, self-sensing structural materials have drawn enormous attention of scientific community due to their potential to enable continuous monitoring of the integrity of structures. The new paradigm of smart condition-based maintenance advocates the use of next-generation structures completely or partly constituted by self-sensing materials, that is, the structure or part of it also behaves as a sensor. In this context, the remarkable mechanical and electrical properties of multi walled carbon nanotubes (MWCNTs) have fostered an increasing number of applications as fillers for composites with multifunctional properties. Among a wide spectrum of potential applications, the development of skin-type piezoresistive distributed strain sensors shows great promise. Such sensors can be deployed onto large-scale structures, enabling a continuous monitoring of the strain state in the global area of the structure. In this paper, a theoretical study on the potential application of smart MWCNT/epoxy strip-like strain sensors for damage detection/localization/quantification in reinforced concrete (RC) beams is presented. A micromechanics-based finite element model is proposed for the electromechanical analysis of MWCNT/epoxy strips. Furthermore, a damage detection algorithm through model updating approach is introduced. To do so, an Euler–Bernoulli model for beams equipped with a smart MWCNT/epoxy strip is developed. Finally, two numerical case studies are presented including: a 2D concrete beam with multiple prescribed crack-like damages, and a 3D RC beam under four-point flexural conditions with non-prescribed cracking. Results show that the proposed smart strips are capable of exploiting the damage-induced variations in the electrical output to locate and quantify damages for real-time distributed structural health monitoring of RC beam structures.

Computational prediction of mechanical properties of a C-Mn weld metal based on the microstructures and micromechanical properties

The effects of the mechanical properties and microstructure of grain boundary ferrite (GF) and acicular ferrite (AF) on the tensile properties of C-Mn steel weld metal were investigated using a micromechanics-based finite element method. Considering indentation size effect, the uniaxial elastic-plastic properties for the constituent phases were determined by the instrumented nano-indentation test. Actual microstructures of the weld deposited metal obtained by optical microscopy were used as the representative volume elements (RVEs) in the modelling. Periodic boundary condition was used in the simulation to quantitatively evaluate the strain distribution due to the microstructure-level heterogeneity in terms of the mechanical properties and the distribution of the individual grain boundary ferrite and acicular ferrite. The macroscopic mechanical properties of the weld metal obtained from the tensile test were predicted well by the numerical results. It is found that the incompatible deformation between the harder acicular ferrite and the softer grain boundary ferrite tends to localize along grain boundary ferrite where failure usually initiate in the form of localized plastic strain as observed in the experiment.

Nonlinear finite element analysis of fibre-reinforced polymer/concrete joints

The objective of this research work is to simulate the interfacial shear response of fibre-reinforced polymer/concrete joints using a micromechanics-based concrete approach. The M4 version of the microplane concrete theory is coded in FORTRAN and implemented as a parallel user-defined subroutine into the commercial finite element software package ADINA. This article first focuses on three-dimensional nonlinear micromechanics-based finite element analyses. Then, validations are carried out using experimental results of 40 fibre-reinforced polymer/concrete joints. The objective is to assess the accuracy of the microplane approach to represent the interfacial shear behaviour of the fibre-reinforced polymer/concrete joints as an alternative to implementing interface elements. At the end of this article, numerical comparisons are presented between the predictions using a phenomenological concrete constitutive law adopted in the software package (with a smeared crack model) and the micromechanics-based analysis (microplane theory) to simulate the concrete behaviour.

Numerical simulation on structural behavior of UHPFRC beams with steel and GFRP bars

This study simulates the flexural behavior of ultra-high-performance fiber-reinforced concrete (UHPFRC) beams reinforced with steel and glass fiber-reinforced polymer (GFRP) rebars. For this, micromechanics-based modeling was first carried out on the basis of single fiber pullout models considering inclination angle. Two different tension-softening curves (TSCs) with the assumptions of 2-dimensional (2-D) and 3-dimensional (3-D) random fiber orientations were obtained from the micromechanics-based modeling, and linear elastic compressive and tensile models before the occurrence of cracks were obtained from the mechanical tests and rule of mixture. Finite element analysis incorporating smeared crack model was used due to the multiple cracking behaviors of structural UHPFRC beams, and the characteristic length of two times the element width (or two times the average crack spacing at the peak load) was suggested as a result of parametric study. Analytical results showed that the assumption of 2-D random fiber orientation is appropriate to a non-reinforced UHPFRC beam, whereas the assumption of 3-D random fiber orientation is suitable for UHPFRC beams reinforced with steel and GFRP rebars due to disorder of fiber alignment from the internal reinforcements. The micromechanics-based finite element analysis also well predicted the serviceability deflections of UHPFRC beams with GFRP rebars and hybrid reinforcements.

Insights from the Lattice-Strain Evolution on Deformation Mechanisms in Metallic-Glass-Matrix Composites

In situ high-energy synchrotron X-ray diffraction experiments and micromechanics-based finite element simulations have been conducted to examine the lattice-strain evolution in metallic-glass-matrix composites (MGMCs) with dendritic crystalline phases dispersed in the metallic-glass matrix. Significant plastic deformation can be observed prior to failure from the macroscopic stress–strain curves in these MGMCs. The entire lattice-strain evolution curves can be divided into elastic–elastic (denoting deformation behavior of matrix and inclusion, respectively), elastic–plastic, and plastic–plastic stages. Characteristics of these three stages are governed by the constitutive laws of the two phases (modeled by free-volume theory and crystal plasticity) and geometric information (crystalline phase morphology and distribution). The load-partitioning mechanisms have been revealed among various crystalline orientations and between the two phases, as determined by slip strain fields in crystalline phase and by strain localizations in matrix. Implications on ductility enhancement of MGMCs are also discussed.

Strain tensor determination of compressed individual silica sand particles using high-energy synchrotron diffraction

The three-dimensional X-ray diffraction (3DXRD) nondestructive technique was used to measure lattice strains within individual sand particles subjected to compressive loading. Three experiments were conducted on similar single columns of silica sand particles with particle sizes between 0.595 and 0.841 mm. In each experiment, three sand particles were placed inside an acrylic mold with an inner diameter of 1 mm. Multiple in situ 3DXRD scans were acquired for each sand column as compressive load was increased. The volume-averaged lattice strain tensor was calculated for each sand particle. In addition, particle orientation and volumetric strain were calculated for individual sand particles. The axial normal strain $$\upvarepsilon _\mathrm{zz}$$ exhibited a linear response in the range of 0 to $$10^{-3}$$ when the applied compressive axial load (F) increased from 0 to $$\sim $$ 30 N when one particle in the sand column fractured. Stress tensor of individual particles was calculated from the acquired lattice strain measurements and elastic constants of silica sand that were reported in the literature. To the best of our knowledge, there have been no reported experimental measurements of the lattice strain tensor measurements within individual silica sand particles. The quantitative measurements reported in this paper at the particle level are very valuable for developing, validating or calibrating micromechanics-based finite element and discrete element models to predict the constitutive behavior of granular materials. 3DXRD represents an exciting new non-destructive technique to directly measure constitutive behavior at the scale of individual particles.

미시역학적 유한요소 모델을 이용한 다공성 복합재료의 기공 탄성 인자 산출

본 논문에서는 다공성 복합재료의 열탄성 거동 예측을 위하여 미시역학적 유한요소 해석을 통해 기공 탄성 인자를 측정하였다. 먼저 기공 압력에 의한 복합재료의 응력 및 변형 상태를 기술하기 위해서 구성 방정식에 기공 탄성 인자를 도입하였다. 기공 탄성 인자의 산출에 필요한 기공 압력에 의한 팽창 변형도와 기공 형성에 따른 균질화 탄성 계수의 저하를 측정하였다. 기공의 형상, 크기, 배열 형태에 따른 이차원 대표 체적 요소의 모델링과 유한요소 해석을 수행하였다. 기공도, 재료 이 방성이 기공 탄성 인자에 미치는 영향과 기공 압력에 따른 변형 에너지 밀도 분포를 살펴보았다. 또한, 측정된 기공 탄성 인자의 유용성을 검토하기 위하여 탄소/페놀릭 복합재료의 열탄성 거동을 예측하였다. In order to predict the thermoelastic behavior of porous composites, poroelastic parameters are measured by using micromechanics-based finite element models. The expanding deformation caused by pore pressure, and the degradation of homogenized elastic moduli with pores are calculated for the assessment of the poroelastic parameters. Various representative volume elements considering the shape, size, and array pattern of pores are modeled and analyzed by a finite element method. The effects of porosity and material anisotropy, and the distribution of stain energy density are investigated carefully. In addition, the measured poroelastic parameters are verified by predicting the thermo-pore-elastic behavior of carbon/phenolic composites.

Nonlinear micromechanics-based bond–slip model for FRP/concrete interfaces

Various experimental studies in the literature have reported that the local bond–slip profiles for fibre reinforced polymer (FRP)/concrete joints subjected to direct shear loading and the associated local bond strength values vary along the bonded length. This peculiarity of the local bond–slip curves has apparently not yet been considered in any of the available interface models.In this work, a procedure is developed for deriving a nonlinear bond–slip model for FRP/concrete interfaces that accounts for the variation of local bond strength along the bonded length. The bond–slip law was developed based on 3D nonlinear micromechanics-based finite element results using the microplane theory for concrete. In the finite element analysis, the microplane constitutive law is implemented as a user-defined subroutine in the ADINA finite element package to run the simulations. Subsequently, the finite element results have been used to develop the nonlinear bond–slip constitutive law for the FRP/concrete joints. This constitutive relation is developed considering the interaction between the interfacial normal stress components along the bonded length and local bond strength. Then a new mathematical approach is proposed to describe the entire local bond–slip relationship. The proposed interface law accounts for the nonlinear contributions of the FRP laminates, adhesive and concrete layers.Finally, to assess the efficacy of the proposed bond–slip model, validations are carried out using a large experimental database (results of 118 specimens). The predicted ultimate load carrying capacities show a satisfactory agreement with the test data. Furthermore, comparisons are made among the characteristics and predictions of the proposed model and those of two bond–slip models from the literature.

A Micromechanics-Based Finite Element for Dynamic Modeling of Heterogeneous Materials

International Journal of Aerospace and Lightweight Structures (IJALS) | The journal aims to promote international exchange of new knowledge and recent development in aspects of aerospace, vehicle, ship and ocean engineering. Topics of interest include strength and vibration of structures, mechanical behavior of materials, dynamics and vibration control, fluid-structure interaction, etc.. The journal solicits contributions from scientists, engineers and others who are directly or indirectly involved in the promotion of aerospace and lightweight structures in the form of full length paper or technical note. It explores analytical, computational and experimental progresses in all the above mentioned areas.

Applicability of Micromechanics Model Based on Actual Microstructure for Failure Prediction of DP Steels

In this paper, various micromechanics models based on actual microstructures of DP steels are examined in order to determine the reasonable range of martensite volume fraction where the methodology described in this study can be applied. For this purpose, various micromechanics-based finite element models are first created based on the actual microstructures of DP steels with different martensite volume fractions. These models are, then, used to investigate the influence of ductility of the constituent ferrite and martensite phases and also the influence of voids in the ferrite phase on the overall ductility of DP steels. The computational results indicate that there is a range of martensite volume fraction where the phase inhomogeneity between the ferrite and martensite phases has dominant effect on the overall ductility of DP steels, defeating the influence of the ductility of each phase and the voids in the ferrite phase, and that this phase inhomogeneity dominant region includes the range of marteniste volume fraction between 15% and 40%. Therefore, the methodology, adopted in this study, may be applied to DP steels within the phase inhomogeneity dominant region in tailoring the DP steel design for its intended purpose and desired properties.