Micromechanical Finite Element Analysis Research Articles

A composite material characterisation tool: UnitCells

Unit cells in conjunction with micromechanical finite-element analysis have been widely used as a means for material characterisation of modern composites. However, they have been mostly applied in an ad hoc manner based on individual cases. Their implementation is often a demanding task for most unit-cell users, even with the formulation given in typical publications. The typical challenges are outlined in this paper. A significant and systematic development has been carried out in recent years to automate their implementation. Eventually, a software program, UnitCells, was released as a secondary development on the Abaqus/CAE platform. It is a code written in Python which incorporates various unit cells in a rigorous and systematic way according to their formulations; at the same time, it automates the implementation of their modelling processes. The developed code has been thoroughly verified, and some of the validation cases are given in this paper as examples of its application.

Design and finite element analysis of a short piezoelectric fiber-reinforced composite actuator

Piezoelectric distributed actuators are exhaustively utilized in control of the structural deformation/vibration. These actuators are also used in the form of smart composite of which active fiber composite (AFC) and macro-fiber composite (MFC) are the most popular smart composites. In the present work, few shortcomings of MFC/AFC actuator in its structural applications are identified and those are alleviated through the proposition of a short piezoelectric fiber-reinforced composite (SPFRC) actuator. The SPFRC is composed of equally spaced coaxial short piezoelectric fibers embedded within the polymer matrix. Every fiber is poled along its length that yields maximum piezoelectric stress/strain within the composite along the same direction in effect of co-directional applied electric field. This piezoelectric effect quantified by the coefficient (e11) is the main parameter in its use as an actuator with a special arrangement of electrodes in microscale. The SPFRC is designed with an objective of improved magnitude of major effective coefficient (e11), and it is performed through a continuum micro-mechanics finite element analysis of its effective electro-elastic properties. The actuation-capability of SPFRC actuator according to its present design is verified by analyzing the geometrically nonlinear electro-elastic deformations of a simply supported smart beam. The micro-mechanics analysis reveals a significant magnitude of e11 of SPFRC although it is lesser than the case of continuous fibers within the similar composite. However, the analysis of smart beam reveals better actuation-capability of the smart composite actuator when short fibers are used instead of continuous fibers retaining the same applied voltage and electrodes.

Investigation on the Effect of Resin Content on Buckling of Laminated Composite Plates

Aerospace applications of composites involve components that are relatively thin plate or shell like structures, thus requiring the consideration of buckling as one of the many possible failure modes. To study the effect of the resin volume fraction on stability of composites, a finite element method based on micromechanics and classical lamination theory has been established to compute buckling loads of simply supported symmetric laminated composite plates subjected to the load of in-plane axial compress and shear load, respectively. The analysis procedure includes a Micromechanical finite element analysis that predicts the elastic modulus of lamina and a finite element linear buckling analysis that predicts buckling load of the composite plates. Three kinds of resin volume fraction that are equal to 44 percent, 47 percent, and 50 percent respectively are considered. The results show that the resin volume fraction has obvious influence on the stability of composite plate. The plate exhibits a relatively large increase in buckling load, about 12 percent, when the resin volume fraction increases by 3 percent. It is finds that the bending stiffness that has an obvious influence on the stability is an incremental function of elastic modulus and cubic thickness. The elastic modulus will be decreased slightly with the increase of resin volume fraction. However, the thickness of the plates is proportional to resin volume fraction.

Micromechanical finite element analysis of effective properties of a unidirectional short piezoelectric fiber reinforced composite

A micromechanical finite element analysis of effective properties of a unidirectional short piezoelectric fiber reinforced composite is presented. The identical short piezoelectric fibers in the composite lamina are coaxial, equally spaced and aligned in the plane of lamina. A continuum micromechanics approach is utilized for predicting the effective electro-elastic material coefficients through the evaluation of Hill’s volume average electro-elastic coupled field concentration matrices. An electro-elastic finite element model of unit cell and the corresponding appropriate electro-elastic boundary conditions are presented for numerical evaluation of concentration matrices. The finite element based micromechanics model and the imposed boundary conditions are verified through the evaluation of effective coefficients of an existing unidirectional continuous piezoelectric fiber reinforced composite. The numerical illustrations reveal an improved effective piezoelectric coefficient over that of the fiber counterpart. It is found that the increase in the length ratio between a fiber and the corresponding unit cell not only causes improved piezoelectric coefficients but also makes the cross sectional area ratio (A r ) between the same components as an important parameter for material coefficients. The optimal length and the optimal cross sectional A r for improved effective piezoelectric coefficients at a specified fiber volume fraction are presented. The effect of fiber aspect ratio on the effective piezoelectric coefficients is also presented that reveals an upper limit of increasing fiber aspect ratio in order to achieve maximum possible improvement in the magnitude of an effective coefficient.

A micromechanical procedure for viscoelastic characterization of the axons and ECM of the brainstem

In this study, the optimal viscoelastic material parameters of axon and extracellular matrix (ECM) in porcine brain white matter were identified using a genetic algorithm (GA) optimization procedure. The procedure was combined with micromechanical finite element analysis (FEA) of brain tissue and experimental stress relaxation tests on brainstem specimens to find the optimal material coefficients of axon and ECM. The stress relaxation tests were performed in tension on 10 brainstem specimens at 3% strain level. The axonal volume fraction in brainstem was measured from the Scanning Electron Microscopy images of the brain tissue. A square periodic volume element was selected to represent the microscale homogenized brainstem tissue. Periodic boundary conditions were applied on the square volume element to mimics the repetitive nature of the volume element. Linear viscoelastic material properties were assumed for the brain tissue constituents under small deformation. The constitutive behavior was expressed in terms of Prony series. The GA procedure searched for the optimal material parameters by fitting the time-dependent tissue stresses of brain tissue FEA to the stresses of relaxation tests under the same loading conditions. The optimization procedure converged after 60 iterations. The initial elastic modulus of axon was found to be 12.86kPa, three times larger than that of ECM. The long-term elastic modulus of axon was 3.7kPa, while for ECM this value was 1.03kPa. The concordance correlation coefficient between FEA estimated elastic modulus of brainstem tissue using the optimal material properties and the experimental elastic modulus of brainstem specimens was 0.952, showing a strong agreement. The optimal material properties of brain tissue constituents can find applications in micromechanical analysis of brain tissue to gain insight into diffuse axonal injures (DAIs).

Silicon Nitride—Grain Boundary Oxynitride Glass Interfaces: Deductions From Glass Bulk Properties

Oxynitride glasses exist as grain boundary phases in Si3N4 ceramics. This paper provides an overview of oxynitride glasses outlining effects of composition on properties. A review of the effects of grain boundary glass chemistry on fracture resistance of silicon nitride is given. A knowledge of overall additive compositions and their quantities in Si3N4 combined with measured properties of bulk glasses allows residual stresses in the interfacial glasses to be calculated. Increase in Y:Al ratio leads to higher thermal expansion mismatch and higher residual stresses in intergranular glasses. Values are in good agreement with those obtained using micromechanical finite element analysis.

Influence of nano-clay compounding on thermo-oxidative stability and mechanical properties of a thermoset polymer system

Abstract This paper investigates the effect of Cloisite 20A (C20A) nano-clay compounding on the thermo-oxidative degradation and the residual stresses due to thermal oxidation for a thermoset polymer. A variant of bismaleimide (BMI) is considered for this work, which could potentially be used in high temperature airframe applications. To examine the influence of nano-clay compounding on the thermo-oxidative behavior of BMI, isothermal aging experiments were conducted at 250 °C on nano-clay modified BMI with 3 wt% C20A and baseline BMI in different oxygen environments (0%, 20% and 60% O2) for more than 1000 h. Comparing the weight loss data for neat BMI and C20A modified BMI; it was observed that nano-clay enhances the thermal stability of thermoset polymer BMI by reducing oxygen diffusion and mitigating oxidative degradation during isothermal aging. Reaction–diffusion modeling parameters involved in the modeling of thermal-oxidation of BMI were obtained from weight loss data. To study the effect of nano-clay compounding on the mechanical properties, nano-indentation experiments were conducted on neat as well as nano-clay modified BMI. To determine the long term shrinkage strains caused by thermal oxidation at elevated temperatures, shrinkage experiments were conducted at 250 °C. For these experiments, digital image correlation (DIC) technique was used to capture the strain field. Using data from these experiments as input, a three-dimensional (3-D) micro-mechanics based finite element analysis (FEA) was carried out to investigate the residual stresses due to thermal oxidation using an in-house FEA code (NOVA-3D). Based on the FEA analysis, the presence of elevated radial stresses at the fiber–matrix interface near the free edge during the early stages of oxidation makes the fiber end a likely site for debond initiation, both for neat resin and for C20A modified resin. Similarly, elevated hoop stresses, responsible for possible matrix cracking were also observed, and are corroborated by experimental observations. The micromechanical FEA model predicted a significant (∼25%) reduction in the residual radial and hoop stresses for the 3 wt% C20A modified BMI, because of the ameliorating effect of dispersed nano-clay on resin shrinkage.

Three-dimensional micromechanical finite element analysis on gauge length dependency of the dynamic modulus of asphalt mixtures

The dynamic modulus of asphalt mixture is one of the major parameters for pavement design. It is generally measured by gauge-point-mounted (GPM) measurement system based on indirect tensile test (IDT), which is very costly and time-consuming. Furthermore, the gauge length in the GPM system has a significant effect on the dynamic modulus but has not been taken into account. This paper focuses on the numerical simulation of the dynamic modulus of asphalt mixture and its dependency on gauge length. The microstructure of asphalt mixture was captured using the non-destructive X-ray computed tomography technique. The series of images were transformed into a three-dimensional (3D) data array that can be mapped into finite element method elements to build a 3D model. Meanwhile, the general Maxwell model was applied for viscoelastic mastic and calibrated from Prony series analysis of the mastic test data. The IDT numerical simulations by incorporating specimen microstructure and ingredient properties were conducted within linear viscoelastic range. The simulation results of the dynamic modulus have good correlations with the testing results. Moreover, the simulation shows the relationship between the dynamic modulus and gauge length. These results indicate that different gauge lengths affect the dynamic modulus significantly. Additionally, this study simulated the gauge length dependency of the dynamic modulus when considering viscoelasticity and heterogeneity.

Micromechanical finite-element modeling and experimental characterization of the compressive mechanical properties of polycaprolactone–hydroxyapatite composite scaffolds prepared by selective laser sintering for bone tissue engineering

Bioresorbable scaffolds with mechanical properties suitable for bone tissue engineering were fabricated from polycaprolactone (PCL) and hydroxyapatite (HA) by selective laser sintering (SLS) and modeled by finite-element analysis (FEA). Both solid gage parts and scaffolds having 1-D, 2-D and 3-D orthogonal, periodic porous architectures were made with 0, 10, 20 and 30vol.% HA. PCL:HA scaffolds manufactured by SLS had nearly full density (99%) in the designed solid regions and had excellent geometric and dimensional control. Through optimization of the SLS process, the compressive moduli for our solid gage parts and scaffolds are the highest reported in the literature for additive manufacturing. The compressive moduli of solid gage parts were 299.3, 311.2, 415.5 and 498.3MPa for PCL:HA loading at 100:0, 90:10, 80:20 and 70:30, respectively. The compressive effective stiffness tended to increase as the loading of HA was increased and the designed porosity was lowered. In the case of the most 3-D porous scaffold, the compressive modulus more than doubled from 14.9 to 36.2MPa when changing the material from 100:0 to 70:30 PCL:HA. A micromechanical FEA model was developed to investigate the reinforcement effect of HA loading on the compressive modulus of the bulk material. Using a first-principles based approach, the random distribution of HA particles in a solidified PCL matrix was modeled for any HA loading to predict the bulk mechanical properties of the composites. The bulk mechanical properties were also used for FEA of the scaffold geometries. The results of the FEA were found to be in good agreement with experimental mechanical testing. The development of patient- and site-specific composite tissue-engineering constructs with tailored properties can be seen as a direct extension of this work on computational design, a priori modeling of mechanical properties and direct digital manufacturing.

Micromechanical finite element analyses of fire-retarded woven fabric composites at elevated temperatures using unit cells at multiple length scales

This paper presents a micromechanical Finite Element (FE) model developed to predict the effective mechanical properties of glass fibre-reinforced (woven fabric) polymer composites with/without fire retardant particulate additives at elevated temperatures. The elevated mechanical properties of glass fibre-reinforced epoxy composites with/without fire retardants were predicted using three unit cells of varying length scales in micromechanical FE analysis. Theoretically predictions of flexural behaviour of these fibre-reinforced polymer composites at elevated temperatures were satisfactorily validated against experimentally measured data. The numerical model developed herein was then used for the prediction of other mechanical properties of fibre-reinforced polymer composites that would have been difficult to collect at elevated temperatures. Micromechanical FE models such as the one contained in this paper are useful to architectural engineers as they can be used to guide the design and qualification of new engineering composites that satisfy stringent Building codes in fire prone engineering applications.

Characterization and finite element modeling of montmorillonite/polypropylene nanocomposites

Finite element modeling can be a useful tool for predicting the behavior of composite materials and arriving at desirable filler contents for maximizing mechanical performance. In the present study, to corroborate finite element analysis results, quantitative information on the effect of reinforcing polypropylene (PP) with various proportions of nanoclay (in the range of 3–9% by weight) is obtained through experiments; in particular, attention is paid to the Young’s modulus, tensile strength and failure strain. Micromechanical finite element analysis combined with Monte Carlo simulation have been carried out to establish the validity of the modeling procedure and accuracy of prediction by comparing against experimentally determined stiffness moduli of nanocomposites. In the same context, predictions of Young’s modulus yielded by theoretical micromechanics-based models are compared with experimental results. Macromechanical modeling was done to capture the non-linear stress–strain behavior including failure observed in experiments as this is deemed to be a more viable tool for analyzing products made of nanocomposites including applications of dynamics.

Parametric Generation of Random Distribution of Fibers in Long-Fiber Reinforced Composites and Micromechanical FE Analysis

A method for the parametric generation of the transversal cross-section microstructure model of unidirectional long-fiber reinforced composite (LFRC) is presented in this paper. Meanwhile, both the random distribution of the fibers and high fiber volume fraction are considered in the algorithm. The fiber distribution in the cross-section is generated through random movements of the fibers from their initial regular square arrangement. Furthermore, cohesive zone element is introduced into modeling the interphase between the fiber and the matrix. All these processes are carried out by the secondary development of the finite element codes (ABAQUS) via Python language programming. Based on the model generated, micromechanical finite element analysis (FEA) is performed to predict the damage initiation and subsequent evolution of the composites. The results show that this technique is capable of capturing the random distribution nature of these composites even for high fiber volume fraction. Moreover, the results prove that a good agreement with the experimental results is found.

Micromechanical analysis of periodic composites by prescribing the average stress

A new method for the micromechanical finite element analysis of unidirectional composites is presented. The method is especially effective in time-dependent analyses, as those involving viscoplasticity and viscoelasticity. The microstructure of the composites under consideration is characterized by periodicity and central symmetry, which allow analysing half of a unit cell for solving the micromechanical problem. Half of the unit cell contains only half of the continuous fibre and this makes the numerical analyses inexpensive in terms of computer memory usage and processing time. New boundary conditions are presented in order to prescribe the average stress on half of the unit cell of hexagonal and rectangular distributions of heterogeneities in the case of static analysis. Then, the new boundary conditions are used to prescribe the precise rate of the average stress in time-dependent analyses. With respect to other existing procedures, the proposed method is easy to adopt in commercial software and it does not require the modification of parts of the source code that are not usually accessible to the user. The proposed method is applied to the interesting case of composites with aligned long fibres imperfectly bonded to a viscoelastic matrix. The numerical simulations carried out in this work provide the loci of the average stress and strain corresponding to the initiation of the fibre-matrix debonding, which determines a considerable decay of the composite stiffness and strength. The influence of the geometrical properties of the microstructure is evaluated by analysing both hexagonal and rectangular distributions of fibres. The numerical results show how the inelastic behaviour of the matrix affects the loci corresponding to the initiation of the debonding.

Cosserat model for periodic masonry deduced by nonlinear homogenization

The paper deals with the problem of the determination of the in-plane behavior of periodic masonry material. The macromechanical equivalent Cosserat medium, which naturally accounts for the absolute size of the constituents, is derived by a rational homogenization procedure based on the Transformation Field Analysis. The micromechanical analysis is developed considering a Cauchy model for masonry components. In particular, a linear elastic constitutive relationship is considered for the blocks, while a nonlinear constitutive law is adopted for the mortar joints, accounting for the damage and friction phenomena occurring during the loading history. Some numerical applications are performed on a Representative Volume Element characterized by a selected commonly used texture, without performing at this stage structural analyses. A comparison between the results obtained adopting the proposed procedure and a nonlinear micromechanical Finite Element Analysis is presented. Moreover, the substantial differences in the nonlinear behavior of the homogenized Cosserat material model with respect to the classical Cauchy one, are illustrated.

Polyurethane Foams Behaviour. Experiments versus Modeling

. Polyurethane foam materials are widely used as cores in sandwich composites, for packing and cushioning. The main characteristics of foams are light weight, high porosity, high crushability and good energy absorption capacity. The paper presents the experimental results obtained for the mechanical properties of polyurethane foams in different loading conditions and the influence of impregnation on the mechanical properties. A 200 kg/m3 density polyurethane foam was investigated in the experimental program in three different Strength of Materials laboratories from Lublin, Bucharest and Timisoara. The paper assesses the possibility to describe the polyurethane foam behaviour trough compression tests, micromechanical models and Finite Element Analysis (FEA). The micromechanical models and Finite Element Analysis could be used successfully for representing the engineering stress – strain behaviour if the compression tests provide reliable material parameters.

Analysis of Time-Dependent Deformation of CFRP Considering the Anisotropy of Moisture Diffusion

The moisture absorption behavior of carbon fiber-reinforced plastic (CFRP) and its effect on dimensional stability were examined. Moisture diffusivity in CFRP was determined by measuring a specimen's weight during the moisture absorption test. Three types of CFRP specimens were prepared: a unidirectionally reinforced laminate, a quasi-isotropic laminate and woven fabric. Each CFRP was processed into two geometries — a thin plate for determination of diffusivity and a rod with a square cross-section for the discussion of two-dimensional diffusion behavior. By solving Fick's law expanded to 3 dimensions, the diffusivities in the three orthogonal directions were obtained and analyzed in terms of the anisotropy of CFRP moisture diffusion. Coefficients of moisture expansion (CMEs) were also obtained from specimen deformation caused by moisture absorption. During moisture absorption, the specimen surfaces showed larger deformation near the edges due to the distribution of moisture contents. This deformation was reasonably predicted by the finite element analysis using experimentally determined diffusivities and CMEs. For unidirectional CFRP, the effect of the fiber alignment on CME was analyzed by micromechanical finite element analysis (FEA) and discussed.

Micromechanical finite element analysis of metal matrix composites using nonlocal ductile failure models

Finite element studies of ductile damage in the matrix of particle and fiber reinforced metal matrix composites are presented. Three material models capable of supporting such simulations at the constituent level are discussed within a unified framework. They comprise an element removal technique triggered by a ductile damage indicator as well as versions of the ductile rupture models of Gurson and Rousselier. Nonlocal averaging is employed for reducing the mesh dependence typically displayed by continuum damage methods upon the onset of local softening. Implementation issues specific to the use of nonlocal damage models in a continuum micromechanics framework are discussed. The efficacy of the approach in limiting the mesh sensitivity of the predicted behavior of composites subject to matrix damage is demonstrated for a simple three-dimensional matrix-particle configuration. Applications of the method to multi-particle and multi-fiber unit cells subjected to uniaxial tensile loads are presented and effects of microgeometrical parameters on the mechanical response are discussed.

Prediction of Elastic Properties in Discontinuous Composite Materials

The shortcoming of conventional SLT (Shear Lag Theory) is due to the neglect of stress transfer across the fiber ends, which results in the inaccurate stress variation for the fiber when the fiber aspect ratio is small in elastic loading. Thus a new model called NSLT (New Shear Lag Theory) is developed considering the stress concentration effects that exists in the matrix regions near fiber ends. In this paper the prediction of elastic composite modulus is presented to evaluate the stress transfer mechanism using NSLT. A micromechanical FEA (Finite Element Analysis) model with axisymmetry is implemented to verify the results of fiber stresses and interfacial shear stresses. It is found that the proposed model gives a reasonable prediction compared with the results based on other models.

Micromechanical FE analysis of UD fibre-reinforced composites with fibres distributed at random over the transverse cross-section

A methodology is established in this paper for the micromechanical finite element analysis of unidirectionally fibre-reinforced composites having fibres distributed at random over the transverse cross-section, a characteristic that most UD composites in engineering applications bear. Regular packing is often assumed in micromechanical analyses. While this simplifies the analysis greatly, it will never provide understanding of aspects of material's behaviour directly related to the distributions of fibres, such as clustering of fibres over the transverse cross-section. Within the limited results available in the literature, it appears to be difficult to assess the errors due to unrealistic boundary conditions prescribed to the representative volume element (RVE) under consideration, as a uniform displacement or traction along the border of a regularly shaped RVE would not be realistically achievable in general. According to the St Venant's principle, one would expect the effects of such incorrectly prescribed boundary conditions affect only a limited zone next to the boundary. A quantitative analysis on the effects of such incorrectly prescribed boundary conditions is provided in this paper using a numerical means. It has been found that the error due to incorrect boundary conditions diminishes over a couple of times of the distance of fibre spacing (centre-to-centre). It is generally true that uniformly prescribed displacement gives a short decay length than that associated with uniformly prescribed traction. Applying this to the analysis of UD composites with fibres distributed at random over the transverse cross-section, an RVE can be introduced and analysed, within which a sub-domain is defined appropriately distant to the boundary. The deformation and stresses obtained in this sub-domain can be considered to be free from the effects of incorrectly prescribed boundary conditions for the RVE analysed and the results extracted only from this sub-domain can, therefore, be considered correct representation of the behaviour of materials of this type. Examples of application of such a procedure are shown in the paper, through which some interesting perspectives of UD composites with fibres distributed at random over the transverse cross-section have been revealed. A significant improvement in predicted transverse Young's modulus has been obtained as compared with those by assuming regular packing in relation to experimental data. Rather different hardening characteristics between the UD composites with regular and random fibre packing have been found in the plastic regime.

Investigation of Interfacial Stresses in CF-Epoxy Composites by In-Situ Experiments and Micromechanical FE Analysis

A combined experimental and numerical study has been carried out in order to study the mechanism of initial failure in transversely loaded CF/epoxy composites. The failure initiation under transverse tensile loading was investigated in a scanning electron microscope (SEM). It was observed that interfacial failure was the dominating failure mechanism for both materials. The applied load that caused initial failure in the experiment was applied as a global load in a microscopic finite element (FE) calculation. The numerical calculation could explain the experimentally observed results. Furthermore an upper limit of the interfacial normal (INS) and shear (ISS) strength was determined.