Finite Element Unit Cell Model Research Articles

A direct prediction method for 3D woven composites bending properties based on unit-cell finite element model

The deformation distribution along the thickness direction of 3D woven composites under bending loading is inhomogeneous, and hence there is difficulty in numerically predicting the bending behavior of woven composites. This paper aims to propose a direct mesoscopic method for predicting the bending behavior of woven composites using the unit-cell finite element model. Firstly, four-point bending tests were conducted in the warp and weft directions, respectively. Then, the periodic boundary conditions are established for the unit-cell model with non-uniformly distributed deformations under pure bending loading. Finally, the bending properties and damage accumulation process of the woven composites are analyzed based on the elasto-plastic damage model with different mechanical properties in tension and compression. The simulated moment-curvature curves and failure modes are in good agreement with the experimental results. It is shown that the developed unit-cell finite element model can accurately predict the bending behavior of woven composites.

Investigation of single and multicell honeycomb reinforced shape memory polymer composites: Shape optimization and experimental characterization

Honeycomb materials as reinforcements for shape memory polymers have been considered for their commercial availability, ease of geometric tailoring, and high in-plane stiffnesses. The design optimization of these honeycomb cells remains an open field of research, with many approaches taken in formulating the structural optimization problems. This investigation focuses on implementing a shape variable parametrization of the honeycomb to study the possible value of both cell asymmetry and spatially varying cell geometries in multicell networks. A unit cell finite element model framework was developed to predict the in-plane elastic properties of these composites, and two design objectives were selected to be optimized. Pareto fronts were estimated for multiple loading cases and cell wall material models, and experimental results were collected for model validation. The optimization results find that these composites can achieve a large range of performances, with maximum moduli as high as 17.2 GPa. Large asymmetry is found in the optimized cell geometries, and relationships are identified between loading cases and for different wall materials. Furthermore, the experimental results validate the finite element model predictions, with relative errors as low as 20% for the predicted maximum modulus and 2% for the modulus ratio.

Sizing optimization and experimental characterization of a variable stiffness shape memory polymer filled honeycomb composite

Variable stiffness structures and materials have been considered for many applications, including active vibration control and shape morphing. With regards to shape morphing, variable stiffness materials and composites have been considered for reconfigurable skin materials in aerospace vehicles. Of the many concepts that have been developed for such applications, shape memory polymers (SMPs) are one such promising materials for shape morphing. SMPs exhibit both high modulus ratios and recoverable strains but suffer from a low overall modulus and often require reinforcements, such as honeycomb. This work investigates the design space of such honeycomb reinforced SMPs as variable stiffness materials. Unit cell finite element models are developed for the material, and parametric studies are completed for varying honeycomb cell geometries. A multiobjective, constrained Pareto front optimization is completed for two honeycomb material models and in two loading directions using selected sizing design variables. Pareto fronts are established, and cell geometries are selected and fabricated to experimentally verify the optimized model predictions. The results both predict and demonstrate the advantages of using honeycomb reinforcements for SMPs. Effective in-plane moduli as high as 45 GPa are predicted while achieving a change in modulus of 450X. Compared to existing reinforcement strategies for shape memory polymers, these composites exhibit favorable combinations of both high stiffness and high changes in stiffness with a high degree of tailorability through the honeycomb cell geometry and predicted performances that meet and exceed the state of the art.

Meso/macroscale study on the shear failure of CFRP laminates considering fibre rotation

The shear failure mechanisms of ±45° braided and unidirectional carbon fibre reinforced polymer (CFRP) laminates are investigated. Off-axis tensile tests were carried out to determine the performance and failure modes of laminates with different numbers of layers. A mesoscale unit cell finite element model was established, and the simulation was validated. The results show that braided laminates and unidirectional laminates have different failure cracks. With the increase in the number of layers, the failure mode of laminates changes. For laminates with 8 or more layers, the necking effect appears at the fracture, and there is a fibre rotation strengthening stage in the stress–strain curve. The stress–strain response functions of laminates in the fibre rotation strengthening stage fitted according to test data can effectively reflect the properties of ±45° braided and unidirectional CFRP laminates.

In‐plane mechanical properties of thick‐walled polymer‐filled honeycomb composites: Analysis and experiments

AbstractPolymer‐filled honeycomb composites are composite materials that exhibit effective in‐plane moduli greater than either the honeycomb or polymer alone. Previous numerical modeling work by the authors has identified two key mechanisms by which this stiffness amplification is achieved. For thin honeycomb cells, the difference in Poisson's ratio between the infill and honeycomb drives the in‐plane composite behavior. For large cell depths, the volume change of the hexagonal cells, acting on the infill polymer, is the dominant factor in stiffness amplification. This work aims to extend these findings to thick walled honeycombs, and to experimentally validate the model predictions while making comparisons to existing analytic models. A unit cell finite element model is created for the composite, with isotropic material properties for the honeycomb and infill obtained from characterization tests on 3D printed honeycomb wall material and polyurethane elastomer infill materials. An experimental investigation is completed, where both empty and polymer filled honeycomb samples are 3D printed and tested for a range of cell geometries, varying the cell angle, cell depth, and infill polymer, and are testing in two in‐plane loading directions. The results support both the model predictions of the effective Young's moduli and the mechanisms of stiffness amplification previously found, with a maximum percent error of 16.9% found and an amplification factor of the infill modulus of up 16 demonstrated. The improved understanding demonstrated in this work supports the use of these composites in applications where reinforcement of the honeycomb by a polymer, or vice versa, is desired.

Compression behaviour of an extremely lightweight structure with a gyroid core used for bridge bearings

This article reports an extremely lightweight structure used as a sandwich core for bridge bearings due to their superior mechanical properties, such as uniform stress distribution with no concentration stresses at the intersection of the structure, lightweight, rigidity, and energy absorption. The structure is based on triply periodic minimal surfaces (TPMS) conceived by observing the scales of butterflies’ wings. The compression behaviour of this innovative structure used in these typical bearings is not well-known and has never been fully investigated. Therefore, it is important to comprehend their compression behaviour and also to identify a failure mode of these bridge bearings under compression. A gyroid unit cell finite element model used in the sandwich core for bridge bearing application is examined with a computational method. The numerical investigation shows the compression mechanisms and provides the failure mode, which is important in establishing relationships between its mechanical performance and geometry. The results have shown that the model exibits a stretch-dominated and uniform stress distribution behaviour under compression. These results can be implemented to better generate informed lightweight structure designs for bridge bearings which are subjected to different compression conditions.

Postbuckling behavior and imperfection sensitivity of elastic–plastic periodic plate-lattice materials

Advances in additive manufacturing have enabled a new generation of materials with advantageous properties inherent to their architecture. Recently, architected materials with periodic arrangements of plates, called plate-lattice materials, have been developed to reach theoretical least upper bounds for stiffness and strength of isotropic materials. This work investigates the buckling behavior of several plate-lattice architectures with relative densities between 0.5% to 25% when subjected to uniaxial compression. Finite element unit cell models with shell elements and periodic boundary conditions are used to simulate the buckling and post-buckling behavior of plate-lattices made from an elastic-perfectly plastic parent material. Five plate-lattice architectures with cubic symmetry are investigated — three anisotropic architectures (simple cubic, body-centered cubic, face-centered cubic) and two isotropic architectures (simple cubic and body-centered cubic combination, simple cubic and face-centered cubic combination). Geometric imperfections of varying amplitude are applied to determine the imperfection sensitivity of these plate-lattice materials, and to calculate their buckling knockdown factors. Consistent with the behavior of the elastic–plastic plate building blocks that comprise the lattice, this investigation reveals that plate-lattice materials are generally imperfection insensitive when their constituent plates become thinner and first bifurcation occurs in the elastic range away from the yield stress. When this occurs, the initial post-buckling behavior is stable and the ultimate strength can be many times higher than the initial buckling stress.

Influence of notch shape on the quasi-static tensile behavior of 2.5D woven composite structure

The application of 2.5D woven composites (2.5DWC) in engineering structures has received increasing attention, but the mechanical behavior of the 2.5DWC notched structure (2.5DWC-NS) is not very clear, especially the effect of notch shapes. For this purpose, a full-thickness unit cell model, including its finite element model, of 2.5DWC is built in this work based on the actual mesoscale characterization of the material. Subsequently, the unit cell finite element model is spliced and modified, and several macro-meso combined models of 2.5DWC-NS with different notch shapes are constructed. Furthermore, a progressive damage model is derived and the corresponding user-defined subroutine (UserMat) in ANSYS is secondary developed, thus performing numerical simulations for the macro-meso combined models. Moreover, tensile experiments of different 2.5DWC-NS are implemented. Comparing with the experimental results, the maximum error of tensile stiffness and strength of 2.5DWC-NS is found to be only 6.34%, demonstrating the validity of the simulation models. On this basis, the mechanical behavior of 2.5DWC-NS with different notch shapes is compared, and the results show that the notch shape affects the initial stress concentration effect and damage propagation behavior of 2.5DWC-NS, while it has little influence on the structural stiffness and strength. This work provides the design direction of 2.5DWC-NS, which is highly critical for engineering guidance.

Computational modeling to predict the micromechanical environment in tissue engineering scaffolds

Cell fate in tissue engineering (TE) strategies is paramount to regenerate healthy, functional organs. The mechanical loads experienced by cells play an important role in cell fate. However, in TE scaffolds with a cell-laden hydrogel matrix, it is prohibitively complex to prescribe and measure this cellular micromechanical environment (CME). Accordingly, this study aimed to develop a finite element (FE) model of a TE scaffold unit cell that can be subsequently implemented to predict the CME and cell fates under prescribed loading. The compressible hyperelastic mechanics of a fibrin hydrogel were characterized by fitting unconfined compression and confined compression experimental data. This material model was implemented in a unit cell FE model of a TE scaffold. The FE mesh and boundary conditions were evaluated with respect to the mechanical response of a region of interest (ROI). A compressible second-order reduced polynomial hyperelastic model gave the best fit to the experimental data (C10 = 1.72 × 10−4, C20 = 3.83 × 10−4, D1 = 3.41, D2 = 8.06 × 10−2). A mesh with seed sizes of 40 µm and 60 µm in the ROI and non-ROI regions, respectively, yielded a converged model in 54 min. The in-plane boundary conditions demonstrated minimal influence on ROI mechanics for a 2-by-2 unit cell. However, the out-of-plane boundary conditions did exhibit an appreciable influence on ROI mechanics for a two bilayer unit cell. Overall, the developed unit cell model facilitates the modeling of the mechanical state of a cell-laden hydrogel within a TE scaffold under prescribed loading. This model will be utilized to characterize the CME in future studies, and 3D micromechanical criteria may be applied to predict cell fate in these scaffolds.

Relationship between the morphological, mechanical and permeability properties of porous bone scaffolds and the underlying microstructure.

Bone scaffolds are widely used as one of the main bone substitute materials. However, many bone scaffold microstructure topologies exist and it is still unclear which topology to use when designing scaffold for a specific application. The aim of the present study was to reveal the mechanism of the microstructure-driven performance of bone scaffold and thus to provide guideline on scaffold design. Finite element (FE) models of five TPMS (Diamond, Gyroid, Schwarz P, Fischer-Koch S and F-RD) and three traditional (Cube, FD-Cube and Octa) scaffolds were generated. The effective compressive and shear moduli of scaffolds were calculated from the mechanical analysis using the FE unit cell models with the periodic boundary condition. The scaffold permeability was calculated from the computational fluid dynamics (CFD) analysis using the 4×4×4 FE models. It is revealed that the surface-to-volume ratio of the Fischer-Koch S-based scaffold is the highest among the scaffolds investigated. The mechanical analysis revealed that the bending deformation dominated structures (e.g., the Diamond, the Gyroid, the Schwarz P) have higher effective shear moduli. The stretching deformation dominated structures (e.g., the Schwarz P, the Cube) have higher effective compressive moduli. For all the scaffolds, when the same amount of change in scaffold porosity is made, the corresponding change in the scaffold relative shear modulus is larger than that in the relative compressive modulus. The CFD analysis revealed that the structures with the simple and straight pores (e.g., Cube) have higher permeability than the structures with the complex pores (e.g., Fischer-Koch S). The main contribution of the present study is that the relationship between scaffold properties and the underlying microstructure is systematically investigated and thus some guidelines on the design of bone scaffolds are provided, for example, in the scenario where a high surface-to-volume ratio is required, it is suggested to use the Fischer-Koch S based scaffold.

A micromechanical unit cell model with an octagonal fiber for continuous fiber reinforced composites

This paper presents a novel micromechanical unit cell model for continuous fiber reinforced composites, which features a fiber with an octagonal cross-section embedded in surrounding matrix, and was named as octagonal fiber model. The cross-section of octagonal fiber model was subdivided into five by five sub-regions, and the conditions of equilibrium and deformation compatibility were applied to derive expression of effective ply properties, and stress amplification factors, which correlate microstresses in sub-regions with ply stresses. For E-glass/epoxy and carbon/epoxy material systems with different fiber volume fractions, effective ply properties and stress amplification factors in sub-regions were evaluated using derived formulae. Results from octagonal fiber model were then compared with those from multiple analytical methods and finite element unit cell model. It was shown that effective ply properties predicted by octagonal fiber model were generally in good agreement with those from finite element model, and octagonal fiber model outperformed other analytical counterparts in estimating stress amplification factors, demonstrating the potential of octagonal fiber model.

Compressive Creep Measurements of Fired Magnesia Bricks at Elevated Temperatures Including Creep Law Parameter Identification and Evaluation by Finite Element Analysis

Creep behavior is very important for the selection of refractory materials. This paper presents a methodology to measure the compressive creep behavior of fired magnesia materials at elevated temperatures. The measurements were carried out at 1150–1500 °C and under compression loads from 1–8 MPa. Creep strain was calculated from the measured total strain data. The obtained creep deformations of the experimental investigations were subjected to detailed analysis to identify the Norton-Bailey creep law parameters. The modulus of elasticity was determined in advance to simplify the inverse estimation process for finding the Norton-Bailey creep parameters. In the next step; an extended material model including creep was used in a finite element analysis (FEA) and the creep testing procedure was reproduced numerically. Within the investigated temperature and load range; the creep deformations calculated by FEA demonstrated a good agreement with the results of the experimental investigations. Finally; a finite element unit cell model of a quarter brick representing a section of the lining of a ferrochrome (FeCr) electric arc furnace (direct current) was used to assess the thermo-mechanical stresses and strains including creep during a heat-up procedure. The implementation of the creep behavior into the design process led to an improved prediction of strains and stresses.

Non-symmetric cyclic bending of helical wires in flexible pipes

Unbonded flexible pipes have superior fatigue performance as the internal armor layers are allowed to move relative to each other, leading to reduced structural loading. The main interactions between the internal layers are the contact forces and the frictional forces. Frictional interaction leads to a complex non-linear response of unbonded flexible pipes making prediction of cyclic bending fatigue a demanding task. Nevertheless, detailed understanding of local armor wire stresses and the related fatigue phenomena is of paramount importance as unbonded flexible risers are often operated close to their mechanical limits. This paper presents a method for calculating the tensile armor wire loading and the hysteresis effect on flexible pipes when subjected to tension, and non-symmetric cyclic bending. The effect of non-symmetric cyclic bending with different tensile armor lay angles, and frictional conditions are studied. The analysis uses an efficient repeated unit cell finite element model, allowing the analysis to be performed on a desktop computer. The study shows that the tensile armor wires gradually translate towards the compression side of the pipe bending plane, when the unbonded flexible pipe is subjected to combined tension and non-symmetric cyclic bending. In the analysis, cyclic bending is applied until steady-state in the bending response is achieved over a full bending cycle. The global bending response of the flexible pipe and the tensile armor wire loading conditions for fully stabilized non-symmetric cyclic bending become symmetric around the frictionless state for the mean cyclic bending curvature. An approximate analytic model for the tensile armor in the stabilized cycle, based on symmetric bending about the geodesic curve corresponding to the mean pipe curvature, is proposed.

The anisotropic elastic behavior of the widely-used triply-periodic minimal surface based scaffolds

The Triple Periodic Minimal Surface (TPMS) has emerged as a new approach for producing open cell porous scaffolds for biomedical applications. However, different from the traditional scaffolds, the TPMS scaffolds always exhibit anisotropic elastic behaviors and consequently the simple mechanical testing is not capable to provide a full characterization of their mechanical behaviors. Additionally, it is still unclear if the TPMS scaffolds possess the similar anisotropic behaviors as the natural bones. The aim of the present study was to analyze the anisotropic elastic behaviors of TPMS based scaffolds using the numerical homogenization method and the analytical analysis approach. Five widely-used TPMS scaffold topologies (Diamond, Gyroid, Fischer-Koch S, Schwarz P and F-RD) were investigated. The independent elastic constants were determined from the analytical analysis and then, the values for these independent constants were determined using the finite element (FE) unit cell models of the scaffolds combined with the periodic boundary condition. The analytical analysis revealed that the Diamond, Gyroid and Fischer-Koch S topologies are threefold rotational symmetric and consequently have seven independent elastic constants. The Schwarz P and F-RD topologies are cubic symmetric and have three independent elastic constants. The FE analysis showed that the Diamond, Gyroid and Fischer-Koch S based scaffolds have only three non-zero independent elastic constants, implying the cubic symmetric property of these scaffolds. All the independent elastic constants decreased quadratically with the increase of scaffold porosity. The absolute difference between the Zener anisotropic factor and one increased the most for the Gyroid based scaffold, while the value for the Fischer-Koch S based scaffold increased the least. The present study revealed that all the five TPMS scaffolds possess cubic symmetry, limiting their anisotropic behaviors. The information on the Zener anisotropic factor and the relationship between the scaffold elastic constants and the porosity can facilitate the selection and design of scaffolds in biomedicine and relevant fields.

Nanocellulose reinforced polymer composites: Computational analysis of structure-mechanical properties relationships

Structure-mechanical properties relationships of nanocellulose reinforced polymer composites are studied in computational experiments. A code for the generation of 3D unit cell finite element models of nanocellulose reinforced polymers with “snake”-shaped nanocellulose fibrils is developed. The code allows the generation of pre-defined nanocomposites structures, with varied angles between nanocellulose snakes segments and hydrogen bonds between nanocellulose fibrils. In a series of computational studies, it is demonstrated that the nanocellulose reinforcement leads to higher stiffness of the matrix polymer, but makes it more brittle.

Progressive damage modelling and experimental investigation of three-dimensional orthogonal woven composites with tilted binder

This paper investigates the tensile properties of 3D orthogonal woven carbon fiber composites with tilted binder by experiment and simulation. The tensile failure strain and fracture mode of this composite show distinguished discrepancy with idealized 3D orthogonal woven composites experimentally. In order to explain this specific failure mechanism, a unit cell finite element model incorporated with damage models of constituents is established to reproduce the damage initiation and propagation of 3D orthogonal woven composites with tilted binder during tensile test. A three-dimensional failure criterion based on Hashin's criterion and Pinho's criterion is utilized to describe the progressive damage of yarns, while the non-linear behavior of the matrix is predicted by Drucker-Prager yield criterion. Besides, a traction-separation law is applied to predict the damage of yarn-matrix interface. The proposed unit cell model is correlated and validated by global stress–strain curves, DIC full-field strain distributions and modulus history curve. The damage evolution process of 3D orthogonal woven carbon fiber composites with tilted binder, including fiber tow failure, matrix cracking, and interfacial debonding, is recorded and investigated by the modulus history curve from simulation.

Tension-bending analysis of flexible pipe by a repeated unit cell finite element model

Unbonded flexible pipes consist of multiple subcomponents which interact through frictional contact. A full 3-D finite element analysis of unbonded flexible pipes is computationally expensive, and a more efficient approach for practical engineering purposes is required. This work presents a repeated unit cell (RUC) finite element model for analyzing flexible pipes subjected to combined constant tension and curvature. Periodic boundary conditions reduce the model size by taking advantage of the structural and loading periodicities, and by assuming uniform wire behavior in the armor layer. The RUC model is suitable for resolving the local tensile armor stress distribution and the global pipe response. A flexible pipe is studied with the RUC model for various tension-bending load configurations and the results have been compared with existing analytical models for validation. The study showed strong correlation between the RUC model and the analytical models, with some difference in the wire bending stresses. This difference can to some degree be explained by the difference in the wire kinematics assumptions. It is found that the proposed RUC model is a robust and computationally efficient approach for analyzing flexible pipes.

THERMAL-RELATED PARAMETER IDENTIFICATION OF BRAIDED COMPOSITES AT HIGH TEMPERATURE

To obtain accurate elastic parameters and coefficient of thermal expansion (CTE) of braided composites at high temperature, An approach for identifying thermal-related parameters based on homogenization theory is proposed. Firstly, on the basis of the finite element model of unit cell, the thermo-elastic parameters of the braided composites are predicted, basing on the theory of homogenization and thermos elasticity, and by applying the periodic displacement and temperature boundary conditions. Secondly, considering the errors in the equivalent process causing by the uneven distributed stress, the thermal modal frequencies of the refined model are taken as the supplementary information to further identify the thermo-elastic parameters, as a calibration of the predicted parameters. Based on the finite element unit cell model of two-dimensional braided structure, this paper carries out equivalent prediction and identification, to verify the validity and accuracy of the proposed method. after comparing the error of the thermal mode of equival model and identification model, it is shown that the proposed method based on equivalent prediction and parameter identification can accurately identify the macro-thermo-elasticity related parameters of braided composites at high temperature.

The symmetric buckling mode in laminated elastoplastic micro-structures under plane strain

The present work considers lamellar (micro) structures of thin, elastic lamellae embedded in a yielding matrix as a stability problem in the context of the theory of stability and uniqueness of path-dependent systems. The volume ratio of the stiff lamellae to the relatively soft matrix is assumed low enough to initiate a symmetric buckling mode, which is investigated by analytical and numerical means. Using a highly abstracted, incompatible model, a first approach is made, and the principal features of the problem are highlighted. Assuming plane strain deformation, an analytic expression for the bifurcation load of a refined, compatible model is derived for the special case of ideal plasticity and verified by numerical results. The effect of lamella spacing and matrix hardening on the bifurcation load is studied by a finite element unit cell model. Some of the findings for the ideal plastic matrix are shown to also apply for a mildly hardening matrix material. Furthermore, the postbuckling behaviour and the limit load are investigated by simulating a bulk lamella array.

Nanomorphology of graphene and CNT reinforced polymer and its effect on damage: Micromechanical numerical study

Abstract The effect of morphology, shapes and distribution of nanoscale carbon reinforcement in polymers on their strength and damage resistance is studied using computational micromechanical modeling. A new software and approach were developed for the automatic generation of finite element unit cell models of nanocomposites with inclusions of arbitrary and complex shapes. The effect of curved, zigzagged, snake-like shapes of real carbon nanotubes, as well as re-stacking of graphene on the damage evolution was studied in the computational experiments based on the developed code. The potential of hybrid (carbon nanotubes and graphene) nanoscale reinforcement was studied with view on its effect of damage resistance. It was demonstrated that idealized, cylinder like models of carbon nanotubes in polymers lead to an underestimation of the stress concentration and damage likelihood in the nanocomposites. The main damage mechanisms in CNT reinforced polymers are debonding and pull-out/fiber bridging, while in graphene reinforced polymers the main role is played by crack deviation and stack splitting, with following micro-crack merging. The potential of hybrid (carbon nanotubes and graphene) nanoscale reinforcement was studied with view on its effect of damage resistance.