Influence of manufacturing process-induced geometrical defects on the energy absorption capacity of polymer lattice structures

Modern additive manufacturing processes enable fabricating architected cellular materials of complex shape,which can be used for different purposes.Among them,lattice structures are increasingly used in applications requiring a compromise among lightness and suited mechanical properties,like improved energy absorption capacity and specific stiffness-to-weight and strength-to-weight ratios.A dedicated modeling strategy to assess the energy absorption capacity of lattice structures under uni-axial compression loading is presented in this work.The numerical model is developed in a non-linear framework accounting for the strain rate effect on the mechanical responses of the lattice structure.Four geometries,i.e.,cubic body centered cell,octet cell,rhombic-dodecahedron and truncated cuboctahedron 2+,are investigated.Specifically,the influence of the relative density of the representative volume element of each geometry,the strain-rate dependency of the bulk material and of the presence of the manufacturing process-induced geometrical imperfections on the energy absorption capacity of the lattice structure is investigated.The main outcome of this study points out the importance of correctly integrating geometrical imperfections into the modeling strategy when shock absorption applications are aimed for.

Geometric Accuracy and Energy Absorption Characteristics of 3D Printed Continuous Ramie Fiber Reinforced Thin-Walled Composite Structures

The application of continuous natural fibers as reinforcement in composite thin-walled structures offers a feasible approach to achieve light weight and high strength while remaining environmentally friendly.In addition,additive manufacturing technology provides a favorable process foundation for its realization.In this study,the printability and energy absorption properties of 3D printed continuous fiber reinforced thin-walled structures with different configurations were investigated.The results suggested that a low printing speed and a proper layer thickness would mitigate the printing defects within the structures.The printing geometry accuracy of the structures could be further improved by rounding the sharp corners with appropriate radii.This study successfully fabricated structures with vari-ous configurations characterized by high geometric accuracy through printing parameters optimization and path smoothing.Moreover,the compressive property and energy absorption characteristics of the structures under quasi-static axial compression were evaluated and compared.It was found that all studied thin-walled structures exhibited progressive folding deformation patterns during compression.In particular,energy absorption process was achieved through the combined damage modes of plastic deformation,fiber pullout and delamination.Furthermore,the com-parison results showed that the hexagonal structure exhibited the best energy absorption performance.The study revealed the structure-mechanical property relationship of 3D printed continuous fiber reinforced composite thin-walled structures through the analysis of multiscale failure characteristics and load response,which is valuable for broadening their applications.

Geometric properties of the first singlet S-wave excited state of two-electron atoms near the critical nuclear charge

The geometric structure parameters and radial density distribution of 1s2s1S excited state of the two-electron atomic system near the critical nuclear charge Z_(c)were calculated in detail under tripled Hylleraas basis set.Contrary to the localized behavior observed in the ground and the doubly excited 2p^(23)Pe states,for this state our results identify that while the behavior of the inner electron increasingly resembles that of a hydrogen-like atomic system,the outer electron in the excited state exhibits diffused hydrogen-like character and becomes perpendicular to the inner electron as nuclear charge Z approaches Z_(c).This study provides insights into the electronic structure and stability of the two-electron system in the vicinity of the critical nuclear charge.

An Original Didactic of the Standard Model “The Particle’s Geometric Model” (Nucleons and K-Mesons)

This paper shows a didactic model (PGM), and not only, but representative of the Hadrons described in the Standard Model (SM). In this model, particles are represented by structures corresponding to geometric shapes of coupled quantum oscillators (IQuO). By the properties of IQuO one can define the electric charge and that of color of quarks. Showing the “aurea” (golden) triangular shape of all quarks, we manage to represent the geometric combinations of the nucleons, light mesons, and K-mesons. By the geometric shape of W-bosons, we represent the weak decay of pions and charged Kaons and neutral, highlighting in geometric terms the possibilities of decay in two and three pions of neutral Kaon and the transition to anti-Kaon. In conclusion, from this didactic representation, an in-depth and exhaustive phenomenology of hadrons emerges, which even manages to resolve some problematic aspects of the SM.

An Original Didactic about Standard Model (Geometric Model of Particle: The Quarks)

This work shows a didactic model representative of the quarks described in the Standard Model (SM). In the model, particles are represented by structures corresponding to geometric shapes of coupled quantum oscillators (GMP). From these didactic hypotheses emerges an in-depth phenomenology of particles (quarks) fully compatible with that of SM, showing, besides, that the number of possible quarks is six.

Topology Optimization of Compliant Mechanisms with Geometrical Nonlinearities Using the Ground Structure Approach

The majority of topology optimization of compliant mechanisms uses linear finite element models to find the structure responses.Because the displacements of compliant mechanisms are intrinsically large,the topological design can not provide quantitatively accurate result.Thus,topological design of these mechanisms considering geometrical nonlinearities is essential.A new methodology for geometrical nonlinear topology optimization of compliant mechanisms under displacement loading is presented.Frame elements are chosen to represent the design domain because they are capable of capturing the bending modes.Geometrically nonlinear structural response is obtained by using the co-rotational total Lagrange finite element formulation,and the equilibrium is solved by using the incremental scheme combined with Newton-Raphson iteration.The multi-objective function is developed by the minimum strain energy and maximum geometric advantage to design the mechanism which meets both stiffness and flexibility requirements, respectively.The adjoint method and the direct differentiation method are applied to obtain the sensitivities of the objective functions. The method of moving asymptotes（MMA） is employed as optimizer.The numerical example is simulated to show that the optimal mechanism based on geometrically nonlinear formulation not only has more flexibility and stiffness than that based on linear formulation,but also has better stress distribution than the one.It is necessary to design compliant mechanisms using geometrically nonlinear topology optimization.Compared with linear formulation,the formulation for geometrically nonlinear topology optimization of compliant mechanisms can give the compliant mechanism that has better mechanical performance.A new method is provided for topological design of large displacement compliant mechanisms.

Geometric Structures of Stable Time-Variant State Feedback Systems

A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedback gains is given. Moreover, a diffeomorphic structure between the set of stabilizing time-variant state feedback gains and the Cartesian product of positive definite matrix and skew symmetric matrix satisfying certain algebraic conditions is constructed. Furthermore, an immersion and some results about the eigenvalue locations of stable state feedback systems are derived.

A Density Functional Theory Study of the Geometric and Electronic Structure of MgF_2 (110) Surface

Abstract＂ Ab initio density functional theory （DFT） was employed to study geometric and electronic structure of MgF2 （110） surface. Three different clean surface models have been considered. The results show that the surface terminated with one-layer F has the smallest relaxation and the lowest surface energy, which indicates this model is the most energetically favorable structure of MgF2（110） surface. Furthermore, the electronic properties are also discussed from the point of density of states and charge density. Analysis of electronic structure shows that the band gap of the surface is significantly narrowed with respect to the bulk. The electrons of the surface exhibit strong locality and larger effective mass.

An Initial Research on the Geometric Theory of Quasicrystal Structures

The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattice , and put them together to form the geometric lattices of quasicrystal structures . The general characteristics of quasicrystal geometric lattices , the relation between structural models and geometric lattices , and the relation formula (k=0 , 2 , 4 , 6 , 8, 10,12) of the symmetric axis between quasicrystal and crystal are discussed based on the quasicrystal space geometric lattices. This is of significant in quasicrystal research .

Information Geometric Structures for the Thermodynamic Manifold

In view of information geometry,the state space S of thermodynamic parameters is investigated.First a Riemannian metric for S is defined and then the α-geometric structures of S is given.Some of results obtained by other authors are extended.

Geometrical Structures of Certain Class of Statistical Manifolds

The geometrical structures of the certain class of statistical manifolds are investigated. The geometwhich includes the original geometrical metrics of S.Amari.

GEOMETRIC STRUCTURE OF ETHYLENOXIDE ADSORBED ON Cu(110) SURFACE

The binding energies of ethylene oxide (Et-O) adsorbed on Cu(110) surface for different adsorption sites and orientations are calculated with an atom superposition and electron delocalization molecular orbital (ASED-MO) using cluster models. It shows that the top site of Cu(110) surface is preferable for Et-O adsorption and the orientation of C-C bond of Et-O is parallel to the [110] direction of the substratc. The distance of an oxygen of Et-O to the Cu atom is approximately 1.5817(?). It is different from the supposition of C. Benndorf et al., in which the oxygen was proposed on the short bridge site with C-C bond orientating to [110] direction of Cu(110)

THE THERMAL STRESS ANALYSIS OF THE INTERFACIAL EDGE IN DISSIMILAR STRUCTURE AND THE EFFECTS OF GEOMETRIC SHAPE

This paper describes the analysis of the thermal stress concentration and the effects of geometrical shape in the interfacial edge by FEM. It is shown that the elevated stress in a dissimilar material caused by temperature is only restricted in a minor region of the interfacial edge, where the stress peak value and and the stress gradient are high. It is also found that narrowing the boundary angle can effectively reduce the peak value of stress components on the interfacial layer, especially the peeling stress σ y , which is a condition of the debonding failure in the interface.θ=60, an obvious variation, proves that selecting a reasonable edge geometrical shape helps to reduce the value of the maximum stress. At last the methods of relaxing stress concentration and effects of the geometric blunt are also discussed.

Geometric Structure and Tectonic Activities of Wanquan Fault,Hebei Province

Based on detailed investigations and prospecting,this paper describes the geometrical characteristics and tectonic activities of Wanquan fault in northwest of Beijing. This fault strikes mainly northeast or northeast to north,dipping southeast,and extends over a length of 15km. It is a major geological and geomorphological margin,controlling the neotectonic movement in this region. On the southeast side of Wanquan fault are the Late Quaternary unconsolidated deposits,forming a basin or deposition; but on the other side is Mesozoic volcano debris,forming lower-mountains and hills. Wanquan fault is a mid- to-high-angle normal fault dipping southeast. This fault was more active in the Quaternary. Since the middle-late part of the alate Pleistocene,the average rate with vertical slip of a single fault is over 0. 03 ～ 0. 3mm /a,but the fault has multiple slipping surfaces,and a total rate with vertical slip will be estimated.

The Hamiltonian Structures and Algebro-geometric Solution of the Generalized Kaup-Newell Soliton Equations

Staring from a new spectral problem,a hierarchy of the generalized Kaup-Newell soliton equations is derived.By employing the trace identity their Hamiltonian structures are also generated.Then,the generalized Kaup-Newell soliton equations are decomposed into two systems of ordinary differential equations.The Abel-Jacobi coordinates are introduced to straighten the flows,from which the algebro-geometric solutions of the generalized KaupNewell soliton equations are obtained in terms of the Riemann theta functions.

Structure-preserving geometric particle-in-cell methods for Vlasov-Maxwell systems

Recent development of structure-preserving geometric particle-in-cell （PIC） algorithms for Vlasov-Maxwell systems is summarized. With the arrival of 100 petaflop and exaflop computing power, it is now possible to carry out direct simulations of multi-scale plasma dynamics based on first-principles. However, standard algorithms currently adopted by the plasma physics community do not possess the long-term accuracy and fidelity required for these large-scale simulations. This is because conventional simulation algorithms are based on numerically solving the underpinning differential （or integro-differential） equations, and the algorithms used in general do not preserve the geometric and physical structures of the systems, such as the local energy-momentum conservation law, the symplectic structure, and the gauge symmetry. As a consequence, numerical errors accumulate coherently with time and long-term simulation results are not reliable. To overcome this difficulty and to harness the power of exascale computers, a new generation of structure-preserving geometric PIC algorithms have been developed. This new generation of algorithms utilizes modem mathematical techniques, such as discrete manifolds, interpolating differential forms, and non-canonical symplectic integrators, to ensure gauge symmetry, space-time symmetry and the conservation of charge, energy-momentum, and the symplectic structure. These highly desired properties are difficult to achieve using the conventional PIC algorithms. In addition to summarizing the recent development and demonstrating practical implementations, several new results are also presented, including a structure-preserving geometric relativistic PIC algorithm, the proof of the correspondence between discrete gauge symmetry and discrete charge conservation law, and a reformulation of the explicit non-canonical symplectic algorithm for the discrete Poisson bracket using the variational approach. Numerical examples are given to verify the advantages of the structure- preserving geometric PIC algorithms in comparison with the conventional PIC methods.

Resolving the geometric structure of trastuzumab by mobility capillary electrophoresis and native mass spectrometry

Available online Immunoglobulins G(IgGs)are Y-shaped globular proteins,however,their high flexibility and heterogeneity pose great challenges to their structure and conformation determinations.Geometric structure of IgG closely correlates to its biofunctions,such as the antibody escape of human immunodeficiency virus(HIV)could attribute to the distance mismatch between the ends of two Fab arms(antigen-binding sites)and envelope glycoprotein spikes on virion surface.Herein,we report the first use of mobility capillary electrophoresis(MCE)and native mass spectrometry(nMS)to resolve the internal geometric structure and conformation of an IgG(trastuzumab)in solution phase.After proteolysis,the ellipsoid dimensions of IgG and its subunits were measured by MCE-nMS experiments.IgG was then reconstructed,in which the sizes and relative positions of these three subunits in three-dimensional space were characterized.It was found that the two Fab arms have an angle of~102.1°and a distance of~11.0 nm between the two antigen-binding sites under native condition,and the Fc arm was tilted~16.0°towards one of the Fab arms.Fc was not on the plane of Fab-Fab,but has an angle of no larger than 103.1°.Under acidic environment(pH 3.0),each subunit of the IgG would unfold into larger dimensions,and the angles between these subunits also change.With great potential for tumor imaging and therapy,the structure of F(ab')_(2)fragments was also measured and validated by molecular dynamic simulation.It was found that the electrostatic force among these three subunits and steric hindrance stemming from Fc help maintaining the angle between two Fab arms.

Comparative Study of 3D-Printed Porous Titanium Alloy with Rod Designs of Three Different Geometric Structures for Orthopaedic Implantation

Porous titanium alloy is currently widely used in clinical treatment of orthopaedic diseases for its lower elastic modulus and ability to integrate with bone tissue.At the micro-level,cells can respond to different geometries,and at the macro-level,the geometric design of implants will also affect the biological function of cells.In this study,three kinds of porous scaffolds with square,triangular and circle rod shapes were designed and 3D printed.This study observed the proliferation and differentiation of MC3T3-E1 cells during surface culture of the three types of scaffolds.It also evaluated the characteristics of the three scaffolds by means of compression tests and scanning electron microscopy to provide a reference for the design of porous titanium alloy implants for clinical applications.The trends of cell proliferation and gene expression between the three types of scaffolds were observed after treatment with two inhibitors.The results show that the square rod porous scaffolds have the best proliferative and osteogenic activities,and these findings may be due to differences in piezo-type mechanosensitive ion channel component 1(Piezo1)and Yes-associated protein(YAP)expression caused by the macro-geometric topography.

Inheritance of the exciton geometric structure from Bloch electrons in two-dimensional layered semiconductors

We theoretically studied the exciton geometric structure in layered semiconducting transition metal dichalcogenides.Based on a three-orbital tight-binding model for Bloch electrons which incorporates their geometric structures,an effective exciton Hamiltonian is constructed and solved perturbatively to reveal the relation between the exciton and its electron/hole constituent.We show that the electron−hole Coulomb interaction gives rise to a non-trivial inheritance of the exciton geometric structure from Bloch electrons,which manifests as a valley-dependent center-of-mass anomalous Hall velocity of the exciton when two external fields are applied on the electron and hole constituents,respectively.The obtained center-of-mass anomalous velocity is found to exhibit a non-trivial dependence on the fields,as well as the wave function and valley index of the exciton.These findings can serve as a general guide for the field-control of the valley-dependent exciton transport,enabling the design of novel quantum optoelectronic and valleytronic devices.

Electronic structure and geometric construction modulation of carbon-based single/dual atom catalysts for electrocatalysis

Both carbon-based single atom catalysts(SACs)and dual atom catalysts(DACs)have garnered significant attention in the field of electrochemical reactions because of the impressive attributes,including exceptional catalytic activity,selectivity,and cost-effectiveness.The ability to modulate the electronic structure and geometric construction of active sites within SACs/DACs is paramount for unleashing their complete potential,which in turn can ultimately dictate catalytic behavior with unprecedented precision.In this review,the recent major developments of the regulation strategies for modulating electronic structure and geometric construction of carbon-based SACs/DACs are summarized.For the SACs,the recently reported modulation methods are categorized into four strategies,including adjusting the density of single atoms,defect engineering,confinement effect and strain engineering.And for the DACs,the five methods contain bonded dual-atom adjustment,non-bonded and bridged dual-atom adjustment,metal and nonmetal dual-atom adjustment,bilayer dual-atom adjustment and homogeneous dual-atom adjustment.The recently developed synthetic strategies are comprehensively summarized,especially their electronic structure and geometric configuration are discussed in detail,the different catalytic applications of electrochemical reactions,and their unique catalytic mechanism are highlighted.Finally,the challenges and prospects of SACs/DACs for tailoring their electronic structures and geometric arrangements are further discussed.