Repeating Unit Cell Research Articles

From Brittle to Ductile: Symmetry Breaking in Strut-Based Architected Materials

Strut-based cellular structures have gained remarkable attention in recent years due to their improved strength-to-weight ratio, energy absorption abilities, and heat transfer properties. A key feature of cellular structures employed in modern infrastructure and devices is a symmetric configuration with repeating unit cells. This periodic design makes fabrication more feasible for next-generation aerospace and biomedical materials. However, such a design with brittle constituents often undergoes a sudden and catastrophic failure as all unit cells along a fracture surface tend to fail simultaneously at a critical loading condition. In this paper, we propose an elegant solution to achieve progressive failure by adjusting the diameter of each strut to create asymmetric or irregular cellular structures. Finite element simulations are conducted and validated by comparing with experiments on additively manufactured samples. Designs are then categorized into three failure modes and the relationship between the failure modes and the stress–strain curves are analyzed. Lastly, simulation-based Bayesian optimization is applied to design the structures with a more distributed stress field before failure and therefore improve their strength and energy absorption capabilities. Results show that the proposed designs fail at the boundaries and the cracks grow locally without penetrating through the entire structure, leading to more progressive failure. This research proposes novel cellular structures via symmetry breaking to achieve structures with promising manufacturability and damage-tolerant failure, greatly broadening their applications.

Analysis of strut‐based lattice cores in sandwich panels using homogenization and dehomogenization methods

AbstractThe design freedom provided by additive manufacturing offers new opportunities to fabricate novel structures with a high lightweight potential, such as strut‐based lattice structures. These lattice structures consist of periodically repeated unit cells and can be used in several applications due to their outstanding mechanical performance. One of the possible applications are cores of sandwich panels since the strut‐based lattices offer comparable mechanical properties to conventional honeycomb structures. Moreover, multifunctional use of the sandwich core is enabled by allowing the heat and fluid transfer through the sandwich due to the open‐celled lattice structure. However, strut‐based lattices are rarely utilized as cores in sandwich panels in engineering practice. One of the main reasons for that is the unknown mechanical behavior of lattice cores. In particular, when the sandwich is subjected to concentrated loads, localized stresses and deformations occur in the sandwich core, leading to core damage. In this work, we present a novel analytical model to determine stresses and deformations in the struts of lattice cores of sandwich panels using homogenization and dehomogenization methods. The local core compression caused by localized transverse forces can also be determined by the derived model.

Woven ceramic matrix composite surrogate model based on physics-informed recurrent neural network

• Recurrent neural network-based surrogate model for nonlinear, non-monotonic CMC constitutive response presented. • Physics-informed constraints employed through regularization to enforce requisite physics. • Surrogate model accurately represents non-monotonic, included reversed loading, behavior of multiple textile CMC material systems. • Efficiency over multiscale numerical approach improved several orders of magnitude. A recurrent neural network (RNN) based surrogate model is developed to emulate the nonlinear constitutive behavior of woven ceramic matrix composites (CMCs) driven by matrix damage at multiple length scales. Physics-informed constraints are introduced into the surrogate model through regularization to ground the prediction in physics and improve its predictive capabilities. Training data is generated using the multiscale generalized method of cells (MSGMC) approach coupled with a matrix damage model. This coupling permits simulating the nonlinear behavior of woven CMCs based on constituent response at the micro-, meso-, and macroscales. The multiscale repeating unit cell is loaded under non-monotonic conditions including multiple load / unload cycles and tension / compression. The fiber volume fraction as well as the intra- and intertow void volume fractions are also varied in the generation of training data. Therefore, the RNN-based surrogate model is tasked with predicting, as a function of variable input strain sequence and fiber and void volume fractions, the resulting stress versus strain response while satisfying physical constraints such as positive semi-definiteness of the tangent stiffness matrix and linear elastic unloading. The trained surrogate model effectively matches the stress versus strain response and successfully predicts the tangent modulus throughout the loading regime. Neural network based surrogate models can offer efficient alternatives to running computationally intensive multiscale material models to simulate the nonlinear response of large structural models. Therefore the presented work provides evidence towards the feasibility of developing, training, and running such models for CMCs with complex architectures, nonlinear multiaxial material response, and under non-monotonic loading conditions.

A computational method for determining the linear elastic properties of 2D aperiodic lattice structures

This paper develops a framework for determining the linear elastic properties of non-periodic lattice structures. An element-based material assignment methodology is implemented that facilitates the generation and analyses of arbitrary patterns on a structured mesh. An adapted numerical homogenization strategy features the inclusion of a homogenized region in the neighbourhood of the domain boundary that validates the implementation of periodic boundary conditions for an arbitrary finite patch of a periodic or non-periodic lattice structure. To demonstrate the method, the linear elastic properties of an aperiodic lattice pattern based on the Penrose (P3) pattern is evaluated. Such a structure exhibits order without translational symmetry and consequently lacks a repeating unit cell. The isotropic performance of the aperiodic lattice structure is investigated and compared to that of the well-known square periodic lattice. The framework opens the door to the investigation and analyses of other novel cellular structures which are not based on a repeating unit cell. Additive manufacturing facilitates the physical realization of such lattice structures, presenting them as viable alternatives to conventional periodic structures in the aerospace and bio-engineering industries.

Continuum damage mechanics-based finite-volume homogenization of unidirectional elastoplastic fiber-reinforced composites

The Finite-Volume Direct Averaging Micromechanics (FVDAM) method has been further extended to predict nonlinear behaviors of unidirectional boron/aluminum (B/Al) composites, induced by plastic deformation and ductile damage for the first time. The latter is considered by gradual stiffness degradation via the continuum damage mechanics (CDM) model. The convergence of homogenized and local response generated by the new FVDAM damage framework has been demonstrated by considering the hexagonal and square repeating unit cells (RUC) with different mesh discretizations under transverse tensile, transverse shear and axial shear loading paths. Then, the reliability of the developed approach to predict the nonlinear response of B/Al composites has been verified extensively vis-à-vis the experimental response available in the literature, under monotonic loading path with various off-axis angles. To accurately capture the experimental response, an RUC with actual microstructure characterized by a random fiber distribution is constructed and utilized in the numerical simulations. In addition, the developed model is also applied to predict the cyclic response of B/Al composites with different off-axis angles in further support of the theory’s potential to capture the macroscopic behaviors of B/Al composites under complex loading conditions.

Refined nonlinear micromechanical models using artificial neural networks for multiscale analysis of laminated composites subject to low-velocity impact

The parametric high fidelity generalized method of cells (PHFGMC) is an advanced micromechanical method that can be used for the nonlinear and failure analysis of several composite materials. The computational effort required for studying the nonlinear and damage multiaxial behavior is relatively small, depending on the size of the discretized repeating unit cell (RUC). However, it is computationally challenging, if not impossible, to integrate refined nonlinear micromechanical models within a multiscale analysis of composite structures. This is due to the thousands or more RUC models required at the integration points within a multiscale finite-element (FE) model of laminated structures. To that end, we propose a new artificial neural network (ANN) based micromechanical modeling framework, termed ANN-PHFGMC, for exploring the nonlinear behavior of fiber-reinforced polymeric (FRP) materials. Pre-simulated mechanical stress–strain responses and behaviors are determined using the PHFGMC to generate a multiaxial training database for the ANN micromodel. The simulated training data is founded on the PHFGMC-RUC results based on a hexagonal RUC. The PHFGMC effective stress–strain responses for different applied multiaxial strain paths are divided into two sets of data; one for the training and the other for verifying the trained ANN-PHFGMC model. The resulting trained ANN-PHFGMC is accurate, with less than 5% error in the verified predictions. The ANN-PHFGMC can be used as a stand-alone or embedded as a surrogate proxy model within a multiscale analysis of composite structures. Next, the ANN-PHFGMC model is integrated within a commercial explicit FE code for low-velocity impact (LVI) analysis of laminated composite plates. Multiscale LVI analyses are performed for two composite plates with different layups. Further, results are compared to experimental data to demonstrate the new model's ability to integrate refined nonlinear micromechanical models within a multiscale analysis.

A new modeling method to predict the mechanical properties of braided composites

The present research signifies a new modeling method for calculating the stiffness of braided composites. In previous works, the modeling approach has been related to repetitive unit cells for analysis of braided composites based on a single area or a few added areas. Also, no confirmed modeling method has recently been available for braided composites because of different fibers’ configuration considerations. Therefore, there is no preferred one, and fiber bundle arrangements are complex in practicality; it is unclear whether their shape is straight or curved. Also, the previously proposed mesoscale repetitive unit cell models have many elements and nodes in the finite element analysis phase, so applying periodic boundary and mesh conditions can mislead the results when they are used. So current research proposes a multi-cell multi-domain strategy and verifies it for modeling and computation of mechanical properties while showing the significance of braiding path and manufacturing process. The currently proposed method is tested with selected sections’ configuration and shown for actual braided composites’ scenario. So, according to the literature, the section is modeled as a complex shape with a squeezing effect. Then, that model is analyzed, and calculated properties are verified by the existing methods and found results with a maximum and minimum difference of 2.7% and 0.25%, respectively. Afterward, it is divided into cells, which are then analyzed and checked to determine which number of simplistic division stages can represent a section. It is found that a minimum of 15 divisions can be defined with a maximum 2% difference, and over that has approximately the same results as of the current considered section model. Additionally, the study examines how the elastic constants of 2D braided composites are influenced by the braiding angle and fiber volume fractions.

Functional gradation of the morphological properties of TPMS channel for enhanced flow performance

A triply periodic minimal surface (TPMS) is a functional cellular structure that is designed by defining the signed distance field (SDF) for periodically repeated unit cells. This study proposes a novel design methodology to functionally grade the morphology of a TPMS channel for enhancement of the fluid flow performance. Mathematical filtering was performed to change the SDF distribution through various combinations of multiple sigmoid functions, thus locally changing the TPMS geometry. The proposed local filtering was then implemented in the design of a TPMS flow channel to reduce the flow resistance in the inlet and outlet regions. Pressure drop tests were conducted using additively manufactured TPMS channels, and the results showed that the pressure drop decreased by 20% for the filtered design with a volume change of only 2.6%. Numerical simulations were performed to analyze the cause of reduced flow resistance in the locally filtered regions, and the results were verified through flow visualization experiments. Considering that a TPMS structure has a complex geometry and thus its manual modification is very difficult, the proposed filtering method offers an efficient approach for functionally changing the morphology of the TPMS structure.

Experimental Verification of Pulse Shaping in Elastic Metamaterials Under Impact Excitation

Abstract We present experimental verification of pulse shaping in elastic metamaterials together with a procedure to design, fabricate, and verify metamaterial pulse shapers under impact excitation. The split Hopkinson pressure bar (SHPB) test, a fundamental dynamic test introduced more than 70 years ago, often incorporates pulse shaping as a means to alter a stress wave, providing the primary motivation for the presented study. Elastic metamaterials hold promise for enhancing conventional pulse shaping abilities and improving capabilities of the SHPB test. We first design the pulse shaper by numerically optimizing its response using finite element analysis. The pulse shaper consists of repeated unit cells based on a combination of a phononic crystal and a local resonator. Then, we fabricate and test pulse shaper candidates to validate the procedural efficacy. An iterative element corrects inaccuracies in input force and material properties and allows convergence on an appropriate pulse shaper. We carry out this procedure by designing pulse shapers fabricated from 3D-printed polylactic acid (PLA) to achieve an extended dwell acceleration pulse shape. In experimental impact tests, the procedure results in rise, dwell, and fall behaviors comparable to that predicted, effectively confirming the efficacy of the presented procedure and verifying the performance of metamaterial-based pulse shapers.

The multi-scale meso-mechanics model of viscoelastic dentin

Human dentin is a hierarchical material with multi-level micro-/nano-structures, consisting of tubule, perti-tubular dentin (PTD) and intertubular dentin (ITD) as the major constituents at microscale; and the PTD and ITD are further composed of collagen and hydroxyapatite (HAp) crystals with different volume fractions at nanoscale. In most cases, the HAp is considered as elastic while the collagen as viscoelastic material. It is of great significance to study the hierarchical structure and viscoelasticity of human dentin to understand the mechanical properties of dentin for further development of restorative materials. Based on this, this paper focuses on multiscale modeling of the elastic properties and dynamic viscoelastic response of dentin and establishes a bottom-up micromechanics model from nano-to macro-scale. In order to study the nanostructural effect on the viscoelastic behavior of hierarchical structures, the homogenization theories of random platelets composites (HTRPC) and the locally-exact homogenization theory (LEHT) are introduced for the homogenization of heterogeneous materials of microstructures at different levels. The HTRPC, based on Eshelby Inclusion theory, is used to predict the effective modulus of PTD and ITD. The LEHT is a method for homogenizing multiphase dentin characterized by repeated unit cells (RUCs). The resulting predictions are in very good agreement with several experimental data from the literature. In addition, the results of nanostructrual effect on dentin show that the viscoelasticity of dentin is majorly contributed by collagen and the HAp greatly provide the strength and hardness of dentin. Furthermore, the ageing effect on dentin's viscoelasticity is considered from the proposed multiscale micromechanics model. It is demonstrated that the ageing effect is much more influential in affecting the loss moduli of dentin than the storage.

Broadband Sound Transmission Loss in a Corrugated Sound Panel Using Periodic Structure Theory

Abstract The vibration and sound radiation characteristics of a double leaf panel wall with corrugated core are analyzed. The core comprises of repeating unit cells along the length of the panel. Each cell is a combination of a straight beam with uniform cross section and curved beams with varying cross section. The vibroacoustic property of the corrugated panel is analyzed assuming plain strain condition. The analysis presented in the work shows that the proposed sandwich panel design provides broadband sound transmission loss (STL) characteristics. The dispersion analysis, forced response characteristics, and sound radiation characteristics of the structure are presented. It is found that bending frequency band gap obtained from the dispersion analysis is a prominent criterion to achieve a higher STL. The structural and acoustic behaviors of the sandwich panel are analyzed through the spectral finite element model. The STL for the core element for various taper ratios is presented. It is found that a higher taper ratio shifts the STL characteristics to the low frequency range.

A Thermo-Mechanical Properties Evaluation of Multi-Directional Carbon/Carbon Composite Materials in Aerospace Applications

Carbon/carbon (C/C) composite materials are widely used in aerospace structures operating in high temperature environments based on their high performance thermal and mechanical properties. The C/C composite material has a yarn architecture in which fiber bundles in different directions cross each other, and it is also divided into architecture types, such as 3-D orthogonal, 4-D in-plane, and 4-D diagonal, according to the arrangement of the fiber bundles. The thermo-mechanical performance of the carbon/carbon composite material may vary depending on the yarn architecture, and the material properties are also tailored according to constituent materials, such as fiber and matrix, and manufacturing parameters, such as yarn size, yarn spacing, and fiber volume fraction. In this paper, three types of geometric models are defined for repeating unit cells (RUCs), according to the yarn architecture of the C/C composite material, and the effective stiffness was predicted by applying the iso-strain assumption and stress averaging technique. In addition, the thermo-mechanical characteristics according to the yarn architecture and fiber volume fraction of RUC were compared and evaluated.

Effective Inertia Coefficients Prediction and Cell Size Effects in Thickness Direction of Periodic Composite Plates

This paper develops a new homogenization method for free vibration problems of periodic composite plates. In this new method, three-dimensional (3D) periodic plates are equivalent to Reissner–Mindlin plates with both effective stiffnesses and effective inertia coefficients. The effective stiffnesses for the dynamic problems are the same as those for the static problems, and they can be achieved by the equivalence principle of macro- and microscopic internal virtual work. To fully take the inertia effects into account, the effective inertia coefficients including the effective translational, translational–rotational and rotational inertias are determined by the two-scale equivalence principle of kinetic energies under three rigid modes. In addition, cell size effects in the thickness direction of composite plates are investigated by using the proposed method and the asymptotic homogenization method (AHM). Numerical experiments validate the effectiveness of the proposed equivalent method for different scale factors, and show that the rotational inertia cannot be ignored for out-of-plane deformations, especially for higher-order modes. Besides, numerical comparisons show that the cell size effects are not negligible when using the AHM to analyze the out-of-plane deformations, and three or more repeated unit cells in the thickness direction are required to ensure accuracy.

Finite element analysis of biaxial tensile mechanical properties and burst properties of woven fabric for layflat hose

AbstractThis paper explores the effects of woven fabric structures on the biaxial tensile mechanical properties and burst properties of woven fabric for layflat hose. A repeat unit cell finite element modeling for woven fabrics for layfalt hose is adopted. To investigate the effects of fabric structure, two parameters are studied: warp yarn spacing and weft yarn linear density. The mechanical response outcomes such as stress distribution, intensity, breaking elongation, and burst properties such as burst pressure, burst direction, are defined and the effects of structure parameters studied on these outcomes are studied. The effects of the warp yarn spacing and the weft yarn linear density on the biaxial tensile mechanical properties and the burst properties of woven fabric for layflat hose are determined. Moreover, the results suggest finite element method exhibits high accuracy in predicting the burst pressure of layflat hose.

Failure zone homogenization at mode II and mixed mode loading including gradient-extended damage and interface debonding at finite strains

Homogenization based on Hills approach is widely used in many scale breaching applications such as the analysis of repeating unit cells (RUCs). However, it was shown that Hills approach is not applicable at the presence of localization phenomena, since in the standard averaging sense the representativeness of the considered micro-scale volume is lost. The failure zone averaging method was shown to overcome these drawbacks and yield converging results even in the softening region. In this paper the failure zone homogenization approach is applied to shear and mixed mode loading of long fiber reinforced plastics. For an accurate description of material failure within the epoxy matrix, a scalar damage model at large strains with gradient enhancement – for mesh size independent results – is used. After a mesh and size convergence study, a statistical analysis of different RUC sizes with random micro structures is performed. Further, the influence of crack closure effects as well as different loading conditions such as simple shear and mixed mode loading are analyzed. It is shown that the implementation of crack closure and application of simple shear lead to different stress–stretch responses. Additionally, crack closure can lead to a different orientation of the failure zone. Finally, an analysis of RUCs with cohesive zone elements for fiber–matrix debonding are shown. Here, lower stresses but higher strains until final failure are observed as well as generally higher dissipation compared to RUCs with perfect interfaces.

Design Approaches on Inner Bodies of Gears with Methods Topology Optimization and Lattice Structures

Gears have wide range application areas in various industries which no matter they are small-scaled or large-scaled. As a part of their design, gears inner bodies are full filled with their solid material and significantly increase the weight of systems which they used in. If the weight of gears’ body mass can be decrease during their design process, the mechanical properties that expected from the systems can be achieved with the minimum cost of material via additive manufacturing comparing to the traditional manufacturing processes. First ideas which comes to mind presents two choices for the way should follow. This study focused on design optimization of material layout rather than material selection. Generative design technic also known as topology optimization can create new designs via mathematical methods that optimize material layouts within a specific design space. Absolute geometry is depending on various parameters such as given set of loads, boundary conditions and constraints. Alternatively, lattice structures are designs which inspired from bio-entities based on repeating unit cells. As a result of static analysis of a helical gear’ s uniform lattice structure, output parameters have been used for varying unit cells’ beam thickness and optimize lattice design. End of this study which used nTopology as engineering software for whole implicit design and analysis process, the analysis of generative designed geometry and pattern of lattice structure gave different results. These outputs compared on point of weight savings.

Pyroelectric metamaterial millimeter-wave detector

We present experimental demonstration of a multi-functional metamaterial absorber, which operates as an efficient detector of millimeter wave radiation at room temperature. Intimate integration of a pyroelectric crystal directly within the metamaterial unit cell enables an efficient large area sensing element made up of repeating unit cells that are nearly ten times smaller than the operational wavelength. An un-amplified intrinsic responsivity of 3.90 V/W is demonstrated at 91.5 GHz, which is close to the peak of the spectral absorption at 97.8 GHz. Numerical full-wave electromagnetic simulations match well to experiments and clarify the underlying absorption mechanism, while thermal simulations permit optimization of the responsivity. The demonstrated results show that the monolithic pyroelectric metamaterial geometry well functions as a detector and represents an ideal device platform for realization of novel and compact room temperature millimeter wave sensing and imaging components.

Computational Study of Non-Porous Auxetic Plates with Diamond Shape Inclusions

Creating non-porous structures that offer auxetic behavior can have a variety of industrial applications, especially when the porosity impairs the functionality of the auxetic structures. This study presents the design and finite element analysis of architected bi-material auxetic plates consisting of repeating unit cells that comprise rigid rotary units and soft inclusions. The change in the design parameters of unit cells produces a variety of mechanical properties, such as different levels of Poisson’s ratio and stiffness for the architected plates that can result in specific static or dynamic responses. The natural frequencies and deflection under uniform lateral loading of the architected plates with clamped boundary conditions were investigated. Furthermore, the effectiveness of the homogenization technique based on the mechanical properties obtained from finite element analysis in predicting the dynamic and static response of the architected plate was also studied.

Mechanical Characterization of Compliant Cellular Robots. Part II: Active Strain

Abstract Modular active cell robots (MACROs) is a design approach in which a large number of linear actuators and passive compliant joints are assembled to create an active structure with a repeating unit cell. Such a mesh-like robotic structure can be actuated to achieve large deformation and shape-change. In this two-part paper, we use finite element analysis (FEA) to model the deformation behavior of different MACRO mesh topologies and evaluate their passive and active mechanical characteristics. In Part I, we presented the passive stiffness characteristics of different MACRO meshes. In this Part II of the paper, we investigate the active strain characteristics of planar MACRO meshes. Using FEA, we quantify and compare the strains generated for the specific choice of MACRO mesh topology and further for the specific choice of actuators actuated in that particular mesh. We simulate a series of actuation modes that are based on the angular orientation of the actuators within the mesh and show that such actuation modes result in deformation that is independent of the size of the mesh. We also show that there exists a subset of such actuation modes that spans the range of deformation behavior. Finally, we compare the actuation effort required to actuate different MACRO meshes and show that the actuation effort is related to the nodal connectivity of the mesh.

Atomic structure and Mott nature of the insulating charge density wave phase of 1T-TaS2

Using x-ray pair distribution function (PDF) analysis and computer modeling, we explore structure models for the complex charge density wave (CDW) phases of layered 1T-TaS2 that both well capture their atomic-level features and are amenable to electronic structure calculations. The models give the most probable position of constituent atoms in terms of 3D repetitive unit cells comprising a minimum number of Ta–S layers. Structure modeling results confirm the emergence of star-of-David (SD) like clusters of Ta atoms in the high-temperature incommensurate (IC) CDW phase and show that, contrary to the suggestions of recent studies, the low-temperature commensurate (C) CDW phase expands upon cooling thus reducing lattice strain. The C-CDW phase is also found to preserve the stacking sequence of Ta–S layers found in the room temperature, nearly commensurate (NC) CDW phase to a large extent. DFT based on the PDF refined model shows that bulk C-CDW 1T-TaS2 also preserves the insulating state of individual layers of SD clusters, favoring the Mott physics description of the metal-to-insulator (NC-CDW to C-CDW) phase transition in 1T-TaS2. Our work highlights the importance of using precise crystal structure models in determining the nature of electronic phases in complex materials.