Mechanical metamaterials are artificially manufactured materials with properties, which cannot be obtained from natural materials, consisting of deliberately designed microscopic internal structures. Those conceptual artificial materials are ready to fabricate with the advent of additive manufacturing technology. Recently, a class of metamaterials has been actively studied due to its potentials for performance improvements and extensions of structural capabilities. Mechanical metamaterials can exhibit exotic material characteristics and/or macroscopic behaviors attributed to their micro/mesoscale internal structural designs such as truss or porous in μm/mm order in addition to material properties constructing the structural components. In this paper, the strength characteristics of lattice-based mechanical metamaterials will be studied. The objectives of this paper will be 1) to develop an analysis framework, which enables effective structural evaluations to design mechanical metamaterials with structural integrity, and 2) to demonstrate the feasibility of the methodology to evaluate stiffness and strength characteristics of lattice-based mechanical metamaterials. In order to efficiently model such structures, a computational homogenization method for lattice-based mechanical metamaterials capturing characteristics of a representative unit cell is implemented. A unit cell of the periodically distributed structure is modeled as representative finite elements, and the equivalent stiffness properties of the unit cell are calculated based on the computational homogenization procedure. The obtained equivalent stiffness properties are used to perform a multi-scale structural analysis of lattice-based mechanical metamaterials. Similarly, stress amplification factors recovering a stress distribution in a microlattice structure based on macroscopic sectional loads, which are obtained from the multi-scale structural analysis, are calculated with the present finite element procedure. A microscopic stress distribution recovered based on stress amplification factors is then be used for strength evaluation.
We investigate Lya, [OIII]5007, Ha, and [CII]158um emission from 1124 galaxies at z=4.9-7.0. Our sample is composed of 1092 Lya emitters (LAEs) at z=4.9, 5.7, 6.6, and 7.0 identified by Subaru/Hyper Suprime-Cam (HSC) narrowband surveys covered by Spitzer large area survey with Subaru/HSC (SPLASH) and 34 galaxies at z=5.148-7.508 with deep ALMA [CII]158um data in the literature. Fluxes of strong rest-frame optical lines of [OIII] and Ha (Hb) are constrained by significant excesses found in the SPLASH 3.6 and 4.5um photometry. At z=4.9, we find that the rest-frame Ha equivalent width and the Lya escape fraction f_Lya positively correlate with the rest-frame Lya equivalent width EW^0_Lya. The f_Lya-EW^0_Lya correlation is similarly found at z~0-2, suggesting no evolution of the correlation over z~0-5. The typical ionizing photon production efficiency of LAEs is logxi_ion/[Hz erg^-1]~25.5 significantly (60-100%) higher than those of LBGs at a given UV magnitude. At z=5.7-7.0, there exists an interesting turn-over trend that the [OIII]/Ha flux ratio increases in EW^0_Lya~0-30 A, and then decreases out to EW^0_Lya~130 A. We also identify an anti-correlation between a [CII] luminosity to star-formation rate ratio (L_[CII]/SFR) and EW^0_Lya at the >99% confidence level. We carefully investigate physical origins of the correlations with stellar-synthesis and photoionization models, and find that a simple anti-correlation between EW_Lya^0 and metallicity explains self-consistently all of the correlations of Lya, Ha, [OIII]/Ha, and [CII] identified in our study, indicating detections of metal-poor (~0.03 Zo) galaxies with EW^0_Lya~200 A.
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In this study, we develop a conditional diffusion model that proposes the optimal process parameters, such as processing temperature, and predicts the microstructure for the desired mechanical properties, such as the elastic constants of the matrix resin contained in carbon fiber reinforced thermoplastics (CFRTPs). In CFRTPs, not only the carbon fibers but also the matrix resin contribute to the macroscopic mechanical properties. Matrix resins contain a mixture of dendrites, which are crystalline phases, and amorphous phases even after crystal growth is complete, and it is important to consider the microstructures consisting of the crystalline structure and the remaining amorphous phase to achieve the desired mechanical properties. Typically, the temperature during forming affects the microstructures, which in turn affect the macroscopic mechanical properties. The training data for the conditional diffusion model in this study are the crystallization temperatures, microstructures and the elasticity matrix. The elasticity matrix is normalized and introduced into the model as a condition. The trained diffusion model can propose not only the processing temperature but also the microstructure when Young's modulus and Poisson's ratio are given. The capability of our conditional diffusion model to represent complex dendrites is also noteworthy.
