Anisotropic yield models for lattice unit cell structures exploiting orthotropic symmetry

Herein new lattice unit cells with buckling load 261–308% higher than the classical octet unit cell were reported. Lattice structures have been widely used in sandwich structures as lightweight core. While stretching dominated and bending dominated cells such as octahedron, tetrahedron and octet have been designed for lightweight structures, it is plausible that other cells exist which might perform better than the existing counterparts. Machine learning technique was used to discover new optimal unit cells. An 8-node cube containing a maximum of 27 elements, which extended into an eightfold unit cell, was taken as representative volume element (RVE). Numerous possible unit cells within the RVE were generated using permutations and combinations through MATLAB coding. Uniaxial compression tests using ANSYS were performed to form a dataset, which was used to train machine learning algorithms and form predictive model. The model was then used to further optimize the unit cells. A total of 20 optimal symmetric unit cells were predicted which showed 51–57% higher capacity than octet cell. Particularly, if the solid rods were replaced by porous biomimetic rods, an additional 130–160% increase in buckling resistance was achieved. Sandwich structures made of these 3D printed optimal symmetric unit cells showed 13–35% higher flexural strength than octet cell cored counterpart. This study opens up new opportunities to design high-performance sandwich structures.

We consider 2+1D lattice models of interacting bosons or spins, with both magnetic flux and fractional spin in the unit cell. We propose and prove a modified Lieb-Shultz Mattis (LSM) theorem in this setting, which applies even when the spin in the enlarged magnetic unit cell is integral. There are two nontrivial outcomes for gapped ground states that preserve all symmetries. In the first case, one necessarily obtains a symmetry protected topological (SPT) phase with protected edge states. This allows us to readily construct models of SPT states by decorating dimer models of Mott insulators to yield SPT phases, which should be useful in their physical realization. In the second case, exotic bulk excitations, i.e. topological order, is necessarily present. While both scenarios require fractional spin in the lattice unit cell, the second requires that the symmetries protecting the fractional spin is related to that involved in the magnetic translations. Our discussion encompasses the general notion of fractional spin (projective symmetry representations) and magnetic flux (magnetic translations tied to a symmetry generator). The resulting SPTs display a dyonic character in that they associate charge with symmetry flux, allowing the flux in the unit cell to screen the projective representation on the sites. We provide an explicit formula that encapsulates this physics, which identifies a specific set of allowed SPT phases.

An investigation into parametric modeling of lattice structures is conducted in pursuit of an effective and efficient process for manufacturing lattice structures via masked stereolithography apparatus (MSLA). Principals of Design for Additive Manufacturing (DfAM) are applied, keeping in mind the manufacturing process to be used. Key design features are parameterized to decrease the effort required to design and implement changes to the structures. Unit cells are modeled as interconnected struts according to parameters such as unit cell side length and strut diameter or thickness. As well as parameterizing the unit cell geometry, the number of cells in each of the three cartesian directions are parameterized such that a three dimensional array of unit cells is constructed based on the single unit cell. Three unit cells are to be considered: the simple cubic (SC) unit cell, the body-centered cubic + simple cubic (BCC|SC) unit cell, and the face-centered cubic + simple cubic (FCC|SC) unit cell. A simple procedure for interfacing the lattice to bulk material is proposed. The proposed design process is validated through qualitative analysis of lattice samples designed with varying unit cell and overall lattice properties with results supporting future studies. Additionally, an example of replacing a solid model’s interior with the lattice structure is detailed to demonstrate the simplicity and power of the approach. It is found that even very thin features with maximum dimensions less than 10 pixels or layers depending on feature orientation (0.34mm and 0.5mm, respectively) are able to be manufactured using affordable consumer grade equipment, which allows for a multitude of potential applications from general purpose lightening to primitive object strength augmentation.

Issues raised in the authors’ previous works are further explored, introducing a multilevel, multiphase approach with a surrogate model. Previous approaches did not show a clear indication of the communication between global and local levels because both levels reached the optimal solution without iteration between levels. To guarantee the need for an iterative process, the blade model was changed, and surrogate models were embedded in the procedure to ensure the communication between global and local levels. Concomitantly, values of the design variables were forced to stay in the feasible design space. Candidate surrogate models include Kriging, and linear and quadratic Response Surface Regression (RSM). These models are compared and the most suitable surrogate model was adopted to finalize the iterative process of the methodology. The new example is the Elastic Articulation (EA) rotor system which is the rotor system of the Generic Georgia Tech Helicopter. The EA rotor is a soft-in-plane bearingless rotor with 10% effective flapping hinge offset and forward sweep. To ensure the dynamic stability of such a system, the methodology utilizes high-fidelity blade structural analysis tools DYMORE and VABS, which reduces the computation time by allowing hierarchical decomposition of the problem. This separates the local (cross-sectional) sub-problem, with constraints on local quantities as maximum stresses, from the global optimization, with constraints on global parameters such as on the Autorotation Index (AI). The procedure is implemented using MATLAB as the overall optimizer.

Optimal design of porous and periodic microstructures through topology identification of the associated periodic unit cell (PUC) constitutes the topic of this work. Here, the attention is confined to two-phase heterogeneous materials in which the topology identification of manufacturable 3D-PUC is conducted by means of a topology optimization technique. The associated objective function is coupled with 3D numerical homogenization approach that connects the elastic properties of the 3D-PUC to the target product. The topology optimization methodology that is adopted in this study is the combination of solid isotropic material with penalization (SIMP) method and optimality criteria algorithm (OCA), referred to as SIMP-OCA methodology. The fairly simple SIMP-OCA is then generalized to handle the topology design of 3D manufacturable microstructures of cubic and orthotropic symmetry. The performance of the presented methodology is experimentally validated by fabricating real prototypes of extremal elastic constants using additive manufacturing. Experimental evaluation is performed on two designed microstructures: an orthotropic sample with Young’s moduli ratios [Formula: see text], [Formula: see text] and a cubic sample with negative Poisson’s ratio of [Formula: see text]. In all practical examples studied, laboratory measurements are in reasonable agreement with the prescribed values; thus, corroborating the applicability of the proposed methodology.

This study presents a method for constructing a surrogate localization model for a periodic microstructure, or equivalently, a unit cell, to efficiently perform micro-macro coupled analyses of hyperelastic composite materials. The offline process in this approach is to make a response data matrix that stores the microscopic stress distributions in response to various patterns of macroscopic deformation gradients, which is followed by the proper orthogonal decomposition (POD) of the matrix to construct a reduced order model (ROM) of the microscopic analysis (localization) with properly extracted POD bases. Then, response surfaces of the POD coefficients are constructed so that the ROM can be continuous with respect to the input datum, namely, the macroscopic deformation gradient. The novel contributions of this study are the application of the L2 regularization to the interpolation approximations of the POD coefficients by use of radial basis functions (RBFs) to make the response surfaces continuous and the combined use of the cross-validation and the Bayesian optimization to search for the optimal set of parameters in both the RBFs and L2regularization formula. The resulting model can be an alternative to microscopic finite element (FE) analyses in the conventional {text {FE}}^2 method and realizes {text {FE}}^r with 1<r<<2 accordingly. Representative numerical examples of micro-macro coupled analysis with the {text {FE}}^r are presented to demonstrate the capability and promise of the surrogate localization model constructed with the proposed approach in comparison with the results with high-fidelity direct {text {FE}}^2.

Incorporating the effects of fabric in the dilatant double shearing model for planar deformation of granular materials

This paper presents the first-ply failure analysis of laminated composite spherical shells by using the finite element method (FEM) in conjunction with Monte Carlo Simulation (MCS) approach. The material and geometric uncertainties caused by anisotropy and randomness inherent in the system configuration are predetermined in such structures and demand the stochastic analysis for realistic design. Finite element formulation is used to derive eight-noded iso-parametric quadratic elements. The input parameters include the ply orientation angle, assembly of ply, the number of layers, ply thickness and degree of orthotropy. The five failure criteria are considered, viz. maximum strain, maximum stress, Tsai-Hill, Tsai-Wu-Hahn and Tsai-Hill Hoffman theories. The variations in first-ply failure load are analysed. A deterministic study is carried out for the analyses of first-ply failure loads with respect to the mentioned failure criteria. The stochastic analysis is carried out firstly by the MCS approach. It is followed by implementation of the surrogate model. Radial basis function (RBF) is incorporated as the surrogate model. The current study predicts that the RBF surrogate model can be utilized to achieve similar computational efficiency with a significant reduction in computational time.

The objective of this paper is to minimize the weight of the forearm of the bucket-wheel stacker reclaimer on the premise of guaranteeing strength, stiffness, and non-resonance. Because the stacking and reclaiming are inseparable from the motion of the forearm, the consumed energy is positively proportional to the self-weight and the forearm supports a lot of loads during the working process; it is necessary to minimize the weight under the requirements of strength, stiffness, and non-resonance. However, it is a high-dimensional problem, and it is of low efficiency when the finite element model is used for optimization. Morris method is used to perform the sensitivity analysis on all the variables. Those with great influence, named main factors, are screened out in order to decrease the number of variables taken into account. Surrogate models are introduced to improve the efficiency of optimization. Herein, Kriging models of the weight, the maximum stress, the maximum displacement, the first-order nature frequency under no-load situation, and the second nature frequency under full-load situation are constructed. In order to improve the model with poor precision, the sequential multi-point infill criterion is introduced. Finally, the weight reduction optimization is performed based on the constructed Kriging models. Compared with the initial design, the weight is reduced greatly. Besides, the Kriging models are of excellent accuracy, which proves that Kriging models or surrogate models are effective substitutes for expensive finite element models to deal with optimization problems.

Inhomogeneity in ferroelectrics can exist as undesirable defects in the single crystalline structure or as designable factors in the composite structure. Surface or interface is inhomogeneous in nature, and superlattices or mixed-phases are inhomogeneous under plan. Effects of the inhomogeneous interfacial layer on ferroelectric nonlinearity have been investigated using a time-dependent Ginzburg-Landau model based on phenomenological equation for a two-dimensional lattice of ferroelectric unit cells. The simulation is based on Ba0.8Sr0.2TiO3 (BST) with and without the inhomogeneous interfacial layer, e.g., nonswitchable fixed dielectric, switchable linear dielectric, or switchable nonlinear dielectric, and with and without Ginzburg-type gradient effect originated from the interactions between the BST and interfacial layers. Homogenization of the inhomogeneous systems is realized by the gradient effect allowing the gradual variation in polarization between the neighboring unit cells, and it heavily depends on the dielectric type of the interfacial layer—whether or not the gradient effect is applied to the interfacial layer. Effects of frequency, electric field type, depolarization, lattice strain, temperature, and thickness on the inhomogeneous nonlinearity are discussed.

The design optimisation of lattice metamaterial unit cells for enhanced properties has been a central theme in current studies. This study contributes to this cause through the development of modified re-entrant structure geometries. Through geometric tailoring and hybridisation of the conventional re-entrant lattice structure, three novel geometries have been developed, and their respective mechanical properties and deformation behaviour under in-plane compressive loading have been investigated using numerical modelling through the finite element analysis technique. Model 3, which comprised a centrally placed auxetic star shape fused onto the re-entrant structure, demonstrated higher stiffness and greater energy absorption properties. Model 1, which comprised a cellular arranged star with double arrow-head auxetic structures around the walls of the re-entrant geometry, demonstrated a lower stiffness with unique elasticity. Model 2, which consisted of an integrated rib comprising different auxetic geometries, demonstrated functionally graded deformation behaviour suitable for tailored mechanical properties. Models 1 and 3 displayed unique properties as a result of the resulting load paths and deformation models associated with each geometric configuration. The findings offer valuable insights for guiding future research aimed at optimising re-entrant lattice structures for tailored mechanical properties. The demonstrated improvements provide a strong foundation for exploring additional design variations.

formula omitted] tilt grain boundaries as barriers for slip transfer in bcc Fe

In this study, first-principles density functional theory (DFT) calculations of the structural and optoelectronic properties of Sn-based inorganic metal halide perovskite CsSnBr3 are carried out and discussed in details. The Wu-Cohen (WC)-Generalized Gradient Approximation (GGA) based on the full-potential linearized augmented plane-wave (FPLAPW) method is used to optimize the geometry structure of unit cell and then find the accurate optoelectronic properties of CsSnBr3. Analysis of structural optimization results revealed that the lattice parameters (𝑎0 = 5.776 Å) and unit cell volume of CsSnBr3 are exactly consistent with the experiments reports. Based on the results of band structures and density of states, CsSnBr3 is found to be nonmagnetic semiconductor with suitable direct band gap of (Eg = 0.610 eV) along the R symmetry point. In addition, the calculations of optical properties of CsSnBr3, such as the real 𝜀1 (𝜔) and imaginary 𝜀2 (𝜔) parts of the dielectric function, 𝜀(𝜔), absorption coefficient 𝛼(𝜔), reflectivity 𝑅(𝜔) and refractive index 𝑛(𝜔), have been performed in the photonic energy range of (0.0 – 15.0 eV). Finally, the results attained in the present study, which include the stable crystal structure and the high accurate optoelectronic properties such as appropriate direct band gap and high absorption of visible radiation, confirm the possible utilization of CsSnBr3 materials in novel optoelectronics applications as photovoltaic solar cells, photosensors, photodetectors, photodiodes and other related optoelectronics devices

Summary Multifactor analysis and accurate prediction of dynamic stress in shale reservoirs are of great practical significance for designing hydraulic fracturing. In this paper, a surrogate model for the rapid prediction of shale stress is proposed by considering the geomechanical heterogeneity and multiscale seepage mechanism of shale gas. The Plackett-Burman method is used to compare the influence of different parameters on shale stress, and significant parameters are selected as decision variables for establishing a surrogate model. The surrogate model for predicting stress is obtained by central composite design fitting, and the interaction of significant factors on shale stress is studied. The results show that after considering the heterogeneity, the minimum horizontal stress fluctuation range is 20.25 to 44.03 MPa and the maximum horizontal stress fluctuation range is 26.46 to 49.77 MPa in the area controlling hydraulic fracture. The initial reservoir pressure, as well as the length and width of hydraulic fractures, are the key factors influencing reservoir stress. The analysis of variance demonstrates that the proposed method is effective for predicting shale stress. The research results are helpful for gaining a deeper understanding of the evolution mechanism of dynamic stress fields in shale reservoirs and provide guidance for treatment design and dynamic optimization of gas wells.

Unveiling the pressure-driven modulations in AGeF3 (A = Na, Tl) cubic perovskite halides for enhanced optoelectronic performance